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Essays on decision making and the sunk cost phenomenon Parayre, Roch 1991

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ESSAYS ON DECISION MAKING AND THE SUNK COST PHENOMENON by ROCH PARAYRE B.Adm., The University of Ottawa, 1978 B.Man.Sc., The University of Ottawa, 1979 M.Sc, Stanford University, 1980 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Business Policy). We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July 1991 © Roch Parayre, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Business Policy Faculty of Commerce and Business Administration The University of British Columbia Vancouver, Canada July 12th, 1991 ABSTRACT This dissertation consists of three separate essays, each dealing with a different aspect of the sunk cost phenomenon. The first essay proposes a multiattribute utility model of the sunk cost phenomenon. We argue that this phenomenon, the tendency toward over-investment in losing courses of action, is the result of tensions between economic and psychological factors such as cognitive dissonance. We formalize this tension by decomposing the investor's total utility into its economic and psychological components, and develop a two-attribute utility model which describes sunk cost behavior. We establish the interaction between the economic and psychological factors, which determines the form of the resulting model, both for decisions under certainty and under uncertainty. The model helps reconcile past explanations of sunk cost behavior, and also generates new predictions. We explore the behavioral ramifications of the model, and introduce formal concepts that are useful in characterizing the presence and intensity of a sunk cost effect. The model is then extended beyond the sunk cost problem, to more general allocation situations involving multiple projects or mental accounts. The second essay examines some of the strategic implications of the sunk cost phenomenon in sequential allocation decisions. Drawing from psychology and behavioral decision theory, we first present a typology of possible causes for this ii tendency. We then present a generic two-period allocation model of the phenomenon within a utility-maximization framework, and derive some comparative statics results — thus showing that the sunk cost phenomenon can be accommodated within formal micro-economic models. The model is used to formalize many of the possible causes of the phenomenon. We then move on to the analysis of some implications of this behavior in strategic situations. A strategic game analysis is used to derive the optimal allocations as a function of sunk cost behavior. We establish when this behavior can be used as a successful precommitment strategy by the sunk cost player, and when it is exploitable by an opponent. Numerous strategic applications of our game-theoretic approach are discussed. The third essay addresses key questions surrounding the financial implications of sunk cost behavior by using data on actual decisions made by firms, and the stock market reaction to these decisions. Specifically, using field evidence we test for the presence of a systematic sunk cost phenomenon in allocation decisions made by publicly traded firms, as recognized by the stock market and reflected in the prices of these firms' shares. We use a financial event study methodology to determine whether share prices reflect the stock market's belief that managers display a sunk cost effect, and use these results to infer the magnitude of the financial implications or "cost" of managers' sunk cost behavior to these firms. iii T A B L E OF CONTENTS Page Abstract (ii) Table of Contents (iv) List of Figures (viii) Acknowledgement (x) CHAPTER 1 : INTRODUCTION 1 1. Introduction 2 2. Psychological Considerations 5 3. Synopsis of the Dissertation 14 References 18 Figure 20 CHAPTER 2 : BEHAVIORAL DECISION MAKING AND THE SUNK COST PHENOMENON: A Multiattribute Approach 22 1. Introduction 23 2. A Multiattribute Utility Model of Sunk Cost Behavior . . . . 29 3. Implications of the Model 49 4. Future Directions - Beyond the Sunk Cost Problem 71 5. Conclusion 75 References 76 iv T A B L E OF CONTENTS (continued) Appendix A: The Problems of Combining Separate Mental Accounts Directly 78 Appendix 8: Prospect Theory as a Special Case of our Additive ($,y) Decomposition 81 Appendix C: Proof of Theorem 3 84 Figures 87 CHAPTER 3 : MODELING THE SUNK COST PHENOMENON, ITS CAUSES AND SOME STRATEGIC IMPLICATIONS 101 1. Introduction 102 2. A Typology of Causes 108 3. A Generic Model of the Sunk Cost Phenomenon Under Utility Maximization 109 4. Analysis of Some Two-Player Strategic Implications 136 5. Concluding Thoughts 166 References 168 Appendix A: Mathematical Proofs 171 Appendix B: Extensive Form Representations of Specific Strategic Games 181 Figures 188 v T A B L E OF CONTENTS (continued) CHAPTER 4 : ESCALATING COMMITMENT AND THE MARKET IMPACT OF DISCONTINUATION DECISIONS: An Empirical Study 200 1. Introduction 201 2. Theoretical Concerns and Hypotheses 206 3. Event Selection 212 4. Analysis of Terminations 219 5. Terminations: A Comparison with the Results of Statman and Sepe 225 6. Analysis of Sell-Offe 230 7. Discussion 237 References 246 Appendix A: The Final Sample of 131 Termination Events . . 248 Appendix B: The Final Sample of 388 Sell-Off Events 252 Appendix C: The Initial Sample of 2,034 Firms 264 Appendix D: Methodology for Estimating Abnormal Stock Returns from the Market Model 297 Appendix E: Detailed Announcement Period Returns for Terminations and Sell-Offs 301 Table 312 vi T A B L E OF CONTENTS (continued) C H A P T E R 5 : C O N C L U D I N G T H O U G H T S A N D D I R E C T I O N S F O R F U R T H E R R E S E A R C H vii LIST OF FIGURES Page CHAPTER 1 Figure 1: Prospect Theory's Value Function 21 CHAPTER 2 Figure 1: Prospect Theory's Value Function 88 Figure 2: Riskless Value and Commitment to a Course of Action 88 Figure 3: The Two-Period Allocation Decision 89 Figure 4: Decomposing Total Value 90 Figure 5: Testing the Corresponding Tradeoffs Condition 91 Figure 6: Testing the Corresponding Tradeoffs Condition -Breakeven-or-Better Tradeoffs 91 Figure 7: Likely Tradeoffs in the Case of Sunk Costs 91 Figure 8: Representing the Sunk Cost Decision through Multiple Attributes 92 Figure 9: Testing the Independence Conditions for u 93 Figure 10: Showing the Need for Deterministic Tradeoffs 94 Figure 11: Gambles in the Absence of Any Sunk Cost Effect 95 Figure 12: Indifference Curves as Wealth Increases 96 Figure 13: Indifference Curves as rtj Increases 96 Figure 14: The Riskless Sunk Cost Premium 97 Figure 15: Gambling on Project 1 vs. Project 2 97 Figure 16: Determining the Risky Sunk Cost Premium 98 Figure 17: Decomposing Two Mental Accounts 99 Figure 18: Two Separate Mental Accounts 100 viii LIST OF FIGURES (continued) CHAPTER 3 Figure BI: Addiction 182 Figure B2: Sunk Costs in an Ongoing Business Relationship 183 Figure B3: Low-Balling 184 Figure B4: The Foot-in-the-Door Phenomenon 185 Figure B5: Loss Leader Pricing 186 Figure B6: Bait and Switch Strategy 187 Figure 1: Further Investment in a Committed Project: A Typology of Causes 189 Figure 2: The Two-Period Allocation Decision 190 Figure 3: The Importance of Uncertainty at to 190 Figure 4: The Case of Myopic Decision Making 191 Figure 5: The Presence of Uncertainty at tj 191 Figure 6: The Two-Player Allocation Decision 192 Figure 7: Game Tree for the Signalling Example 193 Figure 8: Player B's Output Decision via Reaction Functions 194 Figure 9: The Three Parameter Scenarios for the Signalling Game 195 Figure 10: Detailed Game Tree for Sunk Costs as Precommitment 196 Figure 11: Generic Structure in which B Can Influence A's Sunk Costs 197 Figure 12: Generic Game Tree for our Various Commitment Examples 198 Figure 13: Low-Balling Example 199 ix ACKNOWLEDGEMENT I wish to acknowledge the guidance provided by my dissertation committee throughout the dissertation process. Professor Kenneth MacCrimmon planted the initial sunk cost seed in my mind, and was a critical evaluator in the early stages of the dissertation. Along with Professor Daniel Kahneman, he was instrumental in introducing and directing me to the field of behavioral decision making. Chapter 2 was written under the close supervision of Professor Donald Wehrung. Professor James Brander guided my work on Chapter 3, and in doing so really introduced me to formal economic thinking. Chapter 4 benefitted greatly from the comments of Professors MacCrimmon, Brander and Wehrung. All three chapters also benefitted from the helpful comments of others, too numerous to list. I thank them all. Finally, I wish to acknowledge the support of my research supervisor, Professor Donald Wehrung. His patience and direction, particularly at the later stages of the dissertation, were greatly appreciated. x a la mdmoire de ma mere xi Chapter 1 INTRODUCTION l "[People] are irrational, that's all there is to that. Their heads are full of cotton wool and rags." Frederick J. Lerner, My Fair Lady "...between the thin theory of the rational and the full theory of the true and the good there is room and need for a broad theory of the rational." Jon Elster, Sour Grapes: Studies in the Subversion of Rationality, 1983 1. INTRODUCTION One of the more perplexing problems facing managers is that of deciding on the allocation of resources to a project that requires a sequence of repeated investments before any or all of the benefits arise. Once some resources have been allocated to the project, further information may become available, and the manager may find out that he is better off by NOT investing further in the project. But there is a dilemma: by letting go of the project, it will be difficult for the manager to escape the feeling that the resources previously committed have been Vasted' - even though, before the additional information became available, it may have been perfectly rational for him 2 to invest in the project's early stages.1 This problem, and the associated tendency to "throw good money after bad", is commonly known as a sunk cost problem, where the manager is torn between 'cutting his losses' part-way through the project or persisting with it in the hope that, against the odds or the better judgment of a financial analysis, additional investment will bring the project to a successful fruition. It is a common dilemma, faced not only in the context of economic project decisions but in any situation that involves the temporal allocation of some resource: be it money, time, or any other physical or psychological investment. The sunk cost problem is particularly notorious in that the greater the amount committed to the unsuccessful project, the greater the wish to salvage the investment. The resulting process can become one of escalation of commitment to that project, in which it becomes increasingly difficult to let go.2 Most of us have, at some point, experienced the sunk cost situation in one form or another. We consider this problem to be important because of the major economic \A slightly different definition of the sunk cost effect (proposed by Colin Camerer) is that sinking costs reveals information about a project. When the information is bad, we then observe greater subsequent investment in that project than when the information is good. The question of whether information is viewed as good or bad will be a function of one's priors as well as one's aspirations. This definition relates very closely to our definition, based on whether the initial sunk cost led to a 'successful' outcome. "Repeated attempts at salvaging a previous investment - and the admission of having made the same "mistake" several times over - only adds to the difficulty of letting go. It results in a downward spiral of increasing commitment to that project. 3 implications of escalating commitment to losing courses of action. Case studies of major investment decisions, both private and public, point to the economic importance of the sunk cost effect: • The Vietnam war, in the eyes of many, escalated out of a need to justify past losses - so that American lives would not be lost *in vain*. • In developing its L 1011 Tri-Star jet aircraft, Lockheed may have been guilty of falling into a sunk cost trap. Despite pessimistic sales projections recommending that the project be abandoned, the aircraft was completed, and the company accumulated enormous losses. • Similar thinking may have contributed to the commercial disaster of the Concorde aircraft. Even after major airlines cancelled their purchase options, development still went ahead. Project costs escalated to more than ten times the original figure. Losses on the project have been estimated to be in excess of 2 billion British pounds (Hall, 1982). • The EXPO 86 world's fair, staged in Vancouver, British Columbia, in 1986, is yet another case of sunk costs at work (Ross & Staw, 1986). Deficit projections for the fair escalated from $6 million (projected in 1978) to $311 million (projected in 1985). Despite many pleas to abandon the project once it was realized that the initial projections would clearly not be met, the political forces involved decided to go ahead with the project anyway. Too many 4 private, public and political interests were riding on the fair being held. Loss of face would have been too great. • Other documented cases of escalation in large-scale investment projects in the United States include the Washington Public Supply System, the Deep Tunnel Project in Chicago, and the Tennessee-Tombigbee Waterway Project. These are but a few investment situations in which decision makers may have felt that they simply had too much invested to quit. The number and variety of large or smaller scale decisions that are subject to the sunk cost effect is limited only by the imagination. In many projects, cost overruns are incurred primarily because of the attention paid to sunk costs. Based on the amounts just given, one could reasonably estimate the sunk cost effect to result in average real net losses in the hundreds of millions of dollars annually. 2. PSYCHOLOGICAL CONSIDERATIONS 2.1 Evidence Casual introspection suggests the sunk cost phenomenon to be potentially widespread. Empirical studies have substantiated this, formally demonstrating the existence, and even the pervasiveness, of the phenomenon both in the laboratory (Arkes & Blumer, 1985) and in the field (Staw & Ross, 1987a). 5 Experimentally, the sunk cost phenomenon has been studied under the titles of psychological traps and of escalating commitment to a losing course of action. During the last decade, social psychologists have employed laboratory simulations, involving primarily hypothetical decisions, to probe the situational conditions that stimulate the occurrence of the sunk cost phenomenon. Three independent groups of researchers have conducted major empirical studies of escalating commitment: Teger's (1980) study of the Dollar Auction (Shubik, 1971) paradigm, Brockner & Rubin's study of entrapment, and Staves study of escalation situations. Summaries of major laboratory findings can be found in Teger (1980), Staw (1981), Brockner & Rubin (1985), and Schwenk (1986). Staw & Ross (1987b) also present a thorough discussion of the current state of escalation research. These studies, for example, found commitment to correlate positively with the level of personal responsibility for a failure, with a noncalculating decision strategy and with the competitiveness of a situation. Commitment to a project, often measured by total investment in that project, has also been correlated (empirically or theoretically) to a variety of other psychological and social determinants, as well as to particular project, organizational and business environment characteristics. But while the presence of the sunk cost phenomenon and its intensity have been linked to a number of personal and situational factors, the basic psychological determinants of the sunk cost phenomenon remain somewhat evasive. As a result, no clear psychological theory of the sunk cost phenomenon has yet emerged. 2.2 Psychological Causes of the Sunk Cost Phenomenon 6 Psychological hypotheses about the sunk cost phenomenon have been formulated along two distinct directions. In his work on escalation of commitment, Staw (1980) suggested self-justification as the underlying cause of the phenomenon. The self-justification hypothesis is premised on the idea that individuals, who wish to appear as being rational or effective decision makers, are often compelled to justify past decisions that may have yielded less than satisfactory outcomes.3 This self-justification can be 'internal' (to protect one's own self-esteem) or 'external' (to save face4). Justifying past decisions is done by investing further in the committed project, sacrificing economic rationality and a financially 'superior' alternative. Other authors (Thaler, 1980; Arkes & Blumer, 1985; Whyte, 1986) have taken a different direction. They propose a model of the sunk cost phenomenon based on the value function of prospect theory, Kahneman & Tversky's (1979) model of risky choice. The value function is defined on positive and negative deviations from a reference point, i.e. on gains and losses, rather than on total wealth. A key assumption of prospect theory is that people are risk-seeking (their value function is convex) in the domain of losses. A typical value function is shown in Figure 1. In a sunk cost situation, the investor who has not "made peace with his losses" will frame the decision as a choice between a sure loss of the sunk amount (if no further investment 'Bad outcomes are often equated with bad decisions. Outcome is indeed the only clear, objective criterion available to most outsiders, as well as ourselves, in judging decision quality. When reputation is at stake, the prospect of being recognized as unsuccessful, or of having to admit failure, becomes quite aversive. Self-justification becomes important. 4"Face saving" denotes the desire to be perceived as an effective decision maker, which may also include the wish to be consistent, or any other trait deemed important to the decision-maker's self-presentation. 7 takes place), or a risky outcome resulting from further investment in the committed project. The risk-seeking hypothesis may well imply the choice of the risky alternative: further investment in the committed project, and hence an apparent sunk cost effect Laughhunn & Payne (1984) found only partial experimental support for the risk seeking prediction of prospect theory. They suggest that affect (or mood) following sunk outcomes may also influence future risky choices, in the opposite direction to the prospect theory prediction. — Insert Figure 1 here — The postulates of prospect theory have been empirically demonstrated, and will not be critically examined here. The reasoning underlying the prospect theory explanation of the sunk cost is quite credible: the sunk cost effect is the result of moving down one's 'utility' function. However, it fails to capture the sunk cost intuition when alternative projects are available. An investor may well continue to invest in the previously sunk project even though a riskier option is available with some other project. In this case, risk seeking does not make the same predictions as self-justification6, and misses the intuitive reasoning supporting the choice of the sunk project. More generally, the concept of risk attitude does not capture the psychological determinants of the sunk cost phenomenon. While the sunk cost "Self-justification is premised on the two projects being framed as separate mental accounts. The prospect theory explanation, developed in the context of a single project, applies to a single mental account. If the outcomes from the various projects are aggregated, as in economic theory, into a single 'total' account, prospect theory would predict choosing the new, riskier alternative. Further discussion on framing and mental accounting can be found in Tversky & Kahneman (1981), Kahneman & Tversky (1984), and Thaler (1985). 8 phenomenon may in some instances result from a model based on risk seeking, the more fundamental issue of framing, and more specifically of multiple frames, also needs to be tackled in order for the sunk cost phenomenon to be explained by prospect theory. These issues are addressed in chapter 2, which presents a behavioral decision model of the sunk cost phenomenon. As a slight variant of the basic model, Thaler (1980) actually interprets and applies the value function deterministically. A value function that is convex over losses, interpreted deterministically, i.e. measuring strength-of-preference, means that the first few dollars lost "hurt" the most. Given the choice between continuing or abandoning a committed course of action which has accummulated losses, such a function will favor increasing commitment. This is also discussed in more detail in chapter 2. 2.3 Further Speculations About Causes A useful conceptual model for understanding the sunk cost phenomenon can also be found in the theory of cognitive dissonance (Festinger, 1957), a simple yet powerful theory of Internal' self-justification. The theory is premised on the idea that people strive for cognitive consistency. When in possession of two contradictory or dissonant cognitions, people will try to reduce the dissonance by distorting one of them. In particular, people resolve post-decision uncertainty by increasing the relative attractiveness of the option they have chosen. They adjust their attitudes and 9 beliefs to be consistent with their behavior.6 An investor who sinks some money into a project, which turns out to be unsuccessful, ends up with two cognitions: his prior 'best' decision alternative (what he thought was best), and his posterior 'best' decision alternative (what he now thinks would have been best). If these two cognitions differ, there is dissonance. Further investment in the unsuccessful project offers the opportunity to reduce or even dispel the dissonance, with the hope of making the project profitable. But this opportunity comes at the expense of traditional economic rationality.7 A number of alternative mechanisms are available to reduce post-decision dissonance. In simple terms, we can reduce dissonance by increasing the cognition of the benefits associated with an action, by decreasing the cognition of the costs (including opportunity costs) of that action, or by adding some other, new cognition, not previously considered. Either beliefs or attitudes can be modified, which in the present case translates into: - increasing the perceived probability of success of further investment;8 - modifying the subjective outcomes resulting from further investment; or 6Akerlof & Dickens (1982) have examined some of the economic implications of cognitive dissonance for a labour market in a hazardous industry. 7Dissonance will likely be even greater in the case of a completely deterministic environment. There, dissonance occurs from the realization of having made a true 'mistake' (which includes having had mis-specified preferences). 'The ways in which this can happen (e.g. wishful thinking), and how they can be modeled, are explored further in our discussion of uncertainty in chapter 3. 10 - changing the subjective utility evaluation (preferences) over these outcomes.9 As well, a new cognition relating to reputation effects can be added. Alternatively, a non-economic cognition relating to face saving10, or even the wish for 'consistency in decisions' - as a personal goal rather than for reputation - can also be introduced. Once these modifications have taken place, choices are assumed to be made rationally via utility (or expected utility) maximization, using the new beliefs, outcomes and preferences. Rationality is not sacrificed - only subjective parameters are modified. A number of experiments (summarized in Aronson, 1980) support the cognitive dissonance theory contention that hindsight rationalization acts to modify one's subjective evaluation of payoffs, or of beliefs about payoffs. The "sour grapes" rationalization is a well-known example of hindsight preference adjustment. Similarly, empirical evidence has shown that post-decision dissonance reduction occurs through selective filtering of information, as a means of substantiating one's prior beliefs (Knox & Inkster, 1968; Arkes & Blumer, 1985). The particular dissonance reduction mechanism employed, just as the exact causes of the sunk cost phenomenon in a given problem setting, will be a function of the characteristics of the specific decision situation - including the nature of the decision maker involved.11 ^y symmetry, one can reduce dissonance either by increasing the attractiveness of one cognition or by decreasing the attractiveness of alternative cognitions. Only relative attractiveness matters. 10This suggests that face saving may be a means to, and a subset of, reducing cognitive dissonance - although it may well take place independently of any dissonant cognitions, or without reducing dissonant cognitions. "It is unlikely that clear, economic profit payoffs would undergo major modifications following sunk costs. Cognitions about 'subjective' outcomes may be more easily adjusted than objective ones. This is especially true of deterministically known outcomes, where there 11 Reducing cognitive dissonance through preference adjustment relies on the assumption that preferences are, at least indirectly, partly under one's control. This represents an ideological departure from the economic assumption of built-in, stable preferences determining behavior. Several theories in social psychology (see Myers, 1983, Ch.2), such as self-justification and self-perception theories, indeed postulate that behavior influences attitudes (and preferences) much more than is recognized in the economic model. A concept related to cognitive dissonance in our investment context is that of REGRET, the feeling of remorse that results from the belief of having made a mistake. We can think of regret as a Likely consequence of unresolved post-decision dissonance. Although not necessarily occurring together, regret and cognitive dissonance are quite similar in that they both result from an ex post comparison of decisions with outcomes - regret being an emotional manifestation of salient cognitive dissonance (Festinger, 1964, p.99). Though it has not been identified as a driving force behind the sunk cost effect, regret may still contribute to the problem - and enhance our understanding of the phenomenon. Many sunk cost decisions may indeed rest on concerns of minimizing regret rather than on self-justification or face saving. Regret can act as a second attribute in the decision problem, combining with objective economic concerns to are no subjective probabilities to be adjusted. The sunk cost effect may not take hold when clear, objective outcomes (such as dollar profits) can be foreseen with complete certainty. Any sunk cost effect in a deterministic setting needs some subjective payoff component. Similarly, it may be easier to rationalize changes in future, rather than in past, subjective outcomes (as future outcomes have yet to be experienced). 12 produce the resulting sunk cost decision. The way in which regret combines or trades off against economic concerns will determine the presence and intensity of the sunk cost effect. Bell (1982) and Loomes and Sugden (1982) have developed formal models of decision regret to explain some of the paradoxes of expected utility theory. The mechanisms that help reduce cognitive dissonance will, by extension, also mitigate regret. However, if regret is interpreted merely as an additional attribute entering the decision maker's utility function, decisions aimed at reducing regret can occur without any of the cognitive distortions that reduce dissonance. The sunk cost effect may simply be the result of maximizing this two-attribute utility function. A similar distinction can be drawn between cognitive dissonance theory and face saving, the 'internal' and 'external' sides of self-justification. Saving face, unlike cognitive dissonance reduction, does not require the investor to adjust his cognitions. Cognitive dissonance reduction operates on beliefs and preferences, while face saving results from a conscious choice of perseverance, regardless of the beliefs and preferences involved. One could argue that face saving does with actions what dissonance reduction does through cognitions. Both, however, can well result in a sunk cost effect. Despite their differences, each of the existing causal explanations of the sunk cost phenomenon has its roots in the fundamental issue of evaluating decisions in 13 hindsight - what Staw & Ross (1978) refer to as "retrospective rationality"12. Cognitive dissonance, regret, as well as the need for saving face13, result from the investor not having come to terms with the uncertainty inherent in his initial decision.14 Prospect theory, by framing a sunk outcome as a loss' in an individual mental account, again reflects the investor looking back rather than looking ahead. 3. SYNOPSIS OF THE DISSERTATION The three chapters that follow consist of three separate essays, each dealing with a different aspect of the sunk cost phenomenon. Each of the three essays was written to stand on its own. While the key concepts (of rationality, economic and psychological causes, and implications of the sunk cost phenomenon) are common across all three essays, the questions, tools and methods used, and types of conclusions to be drawn will vary significantly from one essay to the next. The three distinct facets that we study are: Chapter 2: How economic and psychological motives interact to generate the sunk cost phenomenon; Chapter 3: How the sunk cost phenomenon can be accommodated within "It is always difficult to judge decision quality independently of the quality of the outcomes obtained. As a result, "prospective" rationality gets contaminated by the hindsight knowledge of a better alternative. "In the case of face saving, the problem lies with those evaluating the outcome of the investor's decisions. "People who accept the uncertain nature of their decisions will be much less likely to display a sunk cost effect! The lack of cognitive dissonance or of a need to justify past decisions can only lead to greater economic rationality. 14 formal micro-economic models, and some implications of the sunk cost phenomenon in competitive and strategic settings; Chapter 4: Some field evidence about the presence, magnitude and financial implications of the sunk cost phenomenon. More specifically, chapter 2 proposes a multiattribute utility model of the sunk cost phenomenon. We argue that this phenomenon, the tendency toward over-investment in losing courses of action, is the result of tensions between economic and psychological factors such as cognitive dissonance. We formalize this tension by decomposing the investor's total utility into its economic and psychological components, and develop a two-attribute utility model which describes sunk cost behavior. We establish the exact relationship between the economic and psychological factors, which in turn determines the form of the resulting model, both for decisions under certainty and under uncertainty. The model helps reconcile past explanations of sunk cost behavior, and also generates new predictions. We explore the behavioral ramifications of the model, and introduce formal concepts that are useful in characterizing the presence and intensity of a sunk cost effect. The model is then extended beyond the sunk cost problem, to more general allocation situations involving multiple projects or mental accounts. Chapter 3 examines some of the strategic implications of the sunk cost phenomenon in sequential allocation decisions. Drawing from psychology and behavioral decision theory, we first present a typology of possible causes for this tendency. We then present a generic two-period allocation model of the phenomenon 15 within a utiBty-maximization framework, and derive some comparative statics results. The model is used to formalize many of the possible causes. We then move on to the analysis of some implications of this behavior in strategic situations. A strategic game analysis is used to derive the optimal allocations as a function of sunk cost behavior. We establish when this behavior can be used as a successful precommitment strategy by the sunk cost player, and when it is exploitable by an opponent. Numerous strategic applications are discussed. Most studies on escalating commitment have examined the antecedent conditions and causes of sunk cost behavior - little has been done on its implications. Moreover, few studies of escalating commitment have systematically employed field data to go beyond the level of casual or anecdotal evidence. Chapter 4 addresses key questions surrounding the financial implications of sunk cost behavior by using data on actual decisions made by firms, and the stock market reaction to these decisions. In this essay, we test for the presence of a systematic sunk cost phenomenon in allocation decisions made in publicly traded firms, as recognized by the stock market and reflected in the prices of these firms' shares. We use a financial event study methodology to determine whether share prices reflect the stock market's belief that managers display a sunk cost effect, and use these results to infer the "cost" of managers' sunk cost behavior to these firms. As a set, these three essays address a wide spectrum of issues about the sunk cost phenomenon. The conducting chapter summarizes the different perspectives taken in the three essays, discusses some of the linkages that can be established 16 between them, and addresses directions for future research. 17 REFERENCES Akerlof, George A., & William T. Dickens. (1982). "The Economic Consequences of Cognitive Dissonance." American Economic Review 72, 307-319. Arkes, Hal R., & Catherine Blumer. (1985). "The Psychology of Sunk Cost." Organizational Behavior and Human Decision Processes 35,124-140. Aronson, Elliot (1980). The Social Animal (3rd edition). San Francisco: W.H. Freeman. Bell, David E. (1982). "Regret in Decision Making Under Uncertainty." Operations Research 30, 961-981. Brockner, Joel, & Jeffrey Z. Rubin. (1985). Entrapment in Escalating Conflicts. New York: Springer-Verlag. Elster, Jon. (1983). Sour Grapes: Studies in the Subversion of Rationality. New York: Cambridge University Press. Festinger, Leon. (1957). A Theory of Cognitive Dissonance. Evanston, IL: Row Peterson. 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"Behavior in Escalation Situations: Antecedents, Prototypes, and Solutions." In L.L. Cummings & Barry M. Staw (Eds.), Research in Organizational Behavior, Volume 9. Greenwich, CT: JAI Press. Teger, Allan I. (1980). Too Much Invested to Quit. New York: Permagon Press. Thaler, Richard. (1980). "Toward a Positive Theory of Consumer Choice." Journal of Economic Behavior and Organization 1, 39-60. Thaler, Richard. (1985). "Mental Accounting and Consumer Choice." Marketing Science 4,199-214. Tversky, Amos, & Daniel Kahneman. (1981). "The Framing of Decisions and the Psychology of Choice." Science 211,453-458. Whyte, Glen. (1986). "Escalating Commitment to a Course of Action: A Reinterpretation." Academy of Management Review 11,311-321. 19 FIGURE FOR CHAPTER 1 20 V FIGURE 1: Prospect Theory's Value Function 21 Chapter 2 BEHAVIORAL DECISION MAKING AND THE SUNK COST PHENOMENON A Multiattribute Approach 22 1. INTRODUCTION The problem of sunk costs has long been an important concern to Behavioral Decision Theory. Recent work has shown this concern to be quite legitimate: the influence of sunk costs on subsequent decisions has been empirically established (Laughhunn & Payne (1984), Arkes & Blumer (1985), Battalio et al. (1989)), and the considerable ramifications of sunk cost behavior have been pointed out (Staw & Ross (1987); see also chapter 1 of this dissertation). Yet we lack a full theoretical understanding of the sunk cost problem, that can lead to accurate predictions of its occurrence. The problem therefore presents an opportunity: like many other decision "paradoxes" that violate economic rationality, the sunk cost phenomenon allows us to better understand and describe behavior through the development of alternative models of decision making. We define the sunk cost phenomenon as the tendency to persist with a committed course of action beyond what economic rationality, based on marginal costs and benefits, would dictate.1 In this paper, we construct a behavioral decision model that formalizes and incorporates the basic psychological determinants of the sunk cost effect.2 We consider these psychological antecedents - reducing cognitive dissonance, face saving or self-justification - as the true primitives of sunk cost behavior, and set out to model how they affect economic rationality and give way to a sunk cost effect. *Also see Camerer's definition of the sunk cost effect based on information, presented in chapter 1. -The psychological causes of the sunk cost phenomenon were discussed in chapter 1 of this dissertation. 23 1.1 Existing Models of Sunk Cost Behavior : The Single Project Case There have been few attempts aimed at formalizing the sunk cost phenomenon within analytical choice models. Efforts so far have focused on Kahneman & Tversky's (1979) prospect theory8, and more specifically its value function interpreted both under certainty and under uncertainty, as a basis for modeling sunk cost behavior. It applies to decisions involving a single project - or a single mental account*. The prospect theory value function is shown in Figure 1. It is defined on positive and negative deviations from a reference point, i.e. on gains and losses, rather than on total wealth. It is convex in the domain of losses and concave in the domain of gains. — Insert Figure 1 here — The deterministic interpretation of prospect theory's value function was first used to explain commitment to a course of action by Thaler (1980). In the riskless case, a convex value function in the domain of losses implies that the first few dollars lost on a project are the ones that "hurt" the most. This interpretation supports a tendency for persisting with an already committed course of action. This can be seen by considering the following example, consisting of two different Prospect theory's value function has also been employed as a descriptive model of choice in a variety of risky and riskless settings outside the realm of sunk costs (see, among others, Thaler (1980,1985), Bowman (1982), and Tversky & Kahneman (1991)). Thaler (1985) discusses the concept of mental accounting and its potential importance in economic decisions. 24 situations. In the first case, you need to spend an amount $x to obtain some positive outcome. In the second case, you have already sunk an amount $y into this venture and must spend an extra $x to obtain the same positive outcome - otherwise you get nothing, and lose the initial $y. With a convex value function v defined over costs (and assuming the segregation of gains and costs), the change in value brought upon by spending $x in the first case, |v(-x)|, is greater than |v(-y-x) - v(-y)|, the change in value brought upon by spending $x in the second case. This supports the greater tendency for spending $x in the second case, as compared to the first. See Figure 2. — Insert Figure 2 here — In the uncertainty case, the sunk cost effect has been modeled through prospect theory as the result of a change in local risk attitude following sunk costs (Whyte, 1986). Interpreting the value function as a von Neumann-Morgenstern (1947) (vN-M) utility function, incurring sunk costs moves the individual down to a lower point on his utility function. The investor who has not "made peace with his losses"5 will then perceive or frame the decision as a choice between a sure loss of the sunk amount -s (if no further investment takes place), or a risky outcome arising from further investment in the committed project. Because the value function is convex in the domain of losses, the investor displays risk seeking behavior (see Figure 1), committing further funds to the project in the hope of turning it around. "The issue of adaptation is central to the sunk cost problem. Adapting to one's losses moves the inflection point of the prospect theory value function down to -s, thereby eliminating any sunk cost effect. 25 We point out that it may well be economically rational to modify one's behavior in the presence of sunk costs. Consider any single-attribute vN-M utility function defined over wealth. Incurring sunk costs on a project moves the investor down to a new point on his utility function. The shape of the utility function at that point -reflecting a new local risk attitude - will imply a new set of optimal decisions. 1.2 Sunk Cost Decisions Involving Two or More Projects : The Need for Multiple Attributes In actuality, investment decisions always involve multiple projects. Decisions concerning one venture will seldom be made in a vacuum, without considering alternative uses for the available funds. Even the simple decision to discontinue one project implicitly involves putting the remaining funds elsewhere - be it in a bank account. These alternative uses for the available funds constitute alternative investment projects. The prospect theory model of the sunk cost phenomenon has serious limitations when we try to extend it to the case of multiple projects. Consider two distinct projects, one of which has already been the subject of a (possibly substantial) financial commitment. If the outcomes (profits) from the two projects are aggregated into a single 'mental account'6, sunk costs in the committed project may have moved the 6Such "total profits" (for the week, month or quarter; for an individual manager, his division or the whole company) may well form the basis of a single mental account. If so, then the single-account explanation of prospect theory may well be appropriate. See Bowman (1982) for the application of this idea to the "risk-return paradox". 26 investor down onto the convex segment of the prospect theory value function. But under these conditions, both projects are treated equally, as their aggregation does not allow prospect theory to distinguish between them. As a result, the model will not systematically predict persistence with the committed project over the new one. Consider in particular the uncertainty interpretation of prospect theory. Risk seeking may hold if outcomes from the two projects are being aggregated, but as a rule will not always hold. Specifically, prospect theory cannot predict the choice of a less risky investment in the committed project over a riskier investment in a new venture. That is, unless the committed project is also the riskier of the two - which may not necessarily be the case, the risk seeking and self-justification (face saving with respect to the committed project) hypotheses make opposite predictions. The sunk cost effect actually results from having a risk attitude for the sunk project that differs from the risk attitude for the new project. As a result, multiple mental accounts are needed to capture the multiple project scenario. This line of reasoning leads to a general conclusion: No single attribute framework that aggregates outcomes from the different projects can properly capture the (multi-project) sunk cost phenomenon. This includes economic utility defined over total wealth or total profits, or even generalized expected utility models. By its very definition, the sunk cost phenomenon implies, ceteris paribus, a tendency for pursuing previously committed projects at the expense of other projects - at the cost of a net (expected) economic loss. In a utility maximization framework, this means that profits 27 from a committed (losing) project are therefore perceived as providing greater utility7 to equal profits from some uncommitted project. Profits resulting from the committed project will be evaluated not only on their economic value but also on the contribution they may make to other, psychological dimensions such as face saving, reducing cognitive dissonance or regret, etc.8 Because no utility function defined on aggregate profits alone can properly model the sunk cost effect, a multiattribute utility function that separates the different projects is required, and standard 'profit' considerations must be modified to account for the differential treatment of cash flows that arise in the two distinct projects. This paper proposes a multiattribute approach for modeling the sunk cost problem, and explores some of the behavioral ramifications - descriptive as well as predictive -of such an approach. Our aim is to develop a general, yet parsimonious model that explains the sunk cost phenomenon. We believe that a formal approach will help us understand and better predict its presence and intensity. Our preference for a multiattribute utility approach also reflects a choice in modeling philosophy. We must decide between a purely predictive model, and a more descriptive one, whose mechanics are transparent. Most of the generalized utility 'Unless specified otherwise, we employ the term utility in a generic sense, to represent both risky (vN-M) utility as well as deterministic value, for decisions under uncertainty and under certainty, respectively. *We underscore that conventional economic rationality must be relaxed in a model of the sunk cost phenomenon. This means that we must go beyond the utility of consumption (which implies economic utility only) and consider the utility of outcomes (to obtain psychological as well as economic utility). This distinction is critical to our approach. 28 models, that have been developed axiomatically to 'explain' the major paradoxes of expected utility theory, are predictive ones. Predictions are derived "as if' decision makers were maximizing some generalized expected utility function. We have chosen the other approach in developing an empirically-based descriptive theory of the sunk cost phenomenon, to make explicit the psychological motivations that drive choices. The paper is outlined as follows. In the next section, we present a multiattribute model of sunk cost decisions, distinguishing between the cases of certainty and uncertainty. We build up the model from its foundations, test behavioral assumptions and present the major conceptual results. Section 3 draws out the implications, both behavioral and theoretical, of the model proposed in Section 2. Section 4 discusses theoretical extensions to our approach, dealing with the sunk cost problem and beyond. Brief conclusions are presented in Section 5. 2. A M U L T I A T T R I B U T E UTILITY M O D E L O F S U N K C O S T B E H A V I O R The need for multiple attributes in modeling the sunk cost problem emphasizes the tradeoffs involved in sunk cost decisions. Committed projects may well be pursued, but only up to a point: the investor may cut his losses and invest elsewhere if the alternative projects offer much greater profit potential. This raises important questions, which are at the heart of the multi-project sunk cost problem: If utility9 is indeed project-specific, how do we combine the projects or trade one off against the other? What set of attributes best captures these tradeoffs? We now turn to these 9As before, this may consist of deterministic value or even risk attitude. 29 and related questions. In what follows, a basic 2-period allocation model is assumed. The decision of interest in the sunk cost problem is the allocation decision in the second time period, which occurs after some costs have been sunk (with little or no success) during the first time period. For simplicity, we focus on decisions involving two projects: project #1, which has already incurred sunk costs of s and whose revenues yield net profits of n1(c1,s) upon further allocation of cx; and project #210, for which an allocation of Cj produces revenues yielding net profits ofi^ c,)". See Figure 3. Our goal is to model the decision that takes place at time t^ , after s has already been sunk into project #1. — Insert Figure 3 here — In formulating a model to describe sunk cost decisions, the choice of attributes is critical. Not only should the attributes have a meaningful interpretation, they should also lead to a simple representation of total utility. Appendix A shows that the profits from the two projects ( I C 1 , T C 2 ) do not form an appropriate (separable) attribute set for "Project #2 can represent the "composite other" project, capturing all, or the best, of the investment opportunities outside of project #1. technically, we may have ^ ((^ .s) if there exist technical linkages between projects. But this is not critical, as only the final profits Ttj and will matter in the model which we develop here. 30 this problem. Any attribute set proposed as part of a multiattribute formulation of the sunk cost problem must, in particular, consider the dependencies in economic utility between projects or mental accounts. The decomposit ion approach which we now propose captures these dependencies, while remaining separable in its attributes. We construct our approach under certainty, and then extend it to the more common and realistic case of decisions under uncertainty. Throughout, we distinguish between the riskless and risky models, which are different in their axiomatic foundation, interpretation and (as we shall see) their functional representation.12 Because of the relationship between deterministic value and probabilistic utility, the model under certainty acts as a building block, as well as being a special case, for the analysis under uncertainty. As we shall argue in Section 3, deterministic value tradeoffs are necessary for the occurrence of the sunk cost phenomenon, even in a risky setting. 2.1 Decomposing Riskless V a l u e 2.1.1 The Case of a Single Project Whyte (1986) has argued that the prospect theory explanation draws its appeal from its ability to interpret the sunk cost phenomenon as the result of a framing effect, without appealing specifically to self-justification motives. The prospect theory value function may indeed be a practical ope rationalization of sunk cost behavior in the single-project case, but its failure to explain the sunk cost effect in the case of deterministic value measures strength-of-preference, while probabilistic utility does not. See Schoemaker (1982) and von Winterfeldt & Edwards (1986) for good discussions of the utility versus value distinction. 31 multiple projects indicates the need for a deeper understanding of the factors that actually underlie prospect theory or other single-attribute representations. A value function such as that of prospect theory, defined over a given mental account, aggregates the various considerations affecting choice into a single functional representation defined over monetary outcomes. But we live in a multiattribute world. Total 'pleasure'13 experienced from some economic outcome may actually consist of (at least) two distinct parts: the economic value of the contribution to one's total wealth and the additional psychological (or other) pleasure resulting from the outcome or transaction on the particular mental account concerned. Figure 4 presents total value decomposed into a sum of these two component parts.14 The economic $ function, defined over total wealth level and assumed to be concave in shape, captures the generally accepted concept of decreasing marginal economic value of money. The function y is the second half of the decomposition and is the psychological complement to the <J> function. It reflects how a model of total value for some mental account, which includes psychological or hedonic considerations, differs from the conventional economic one. \|/ captures any psychological considerations above and beyond those present in the economic $ function, as it could reasonably be argued that the concept of (decreasing) marginal economic value is partly a psychological one. 4> captures the (economic) value of consumption, while \\f captures the higher-level (in the sense of Maslow (1954)) psychological rewards from L3The value function of prospect theory views man as a "pleasure machine". l4Any function of a variable w can be expressed as the sum of two other functions of w. 32 a given outcome. — Insert Figure 4 here — In particular, the y function introduces a reference point w0 u , absent in the <J> function, that influences the psychological value (pleasure or displeasure) experienced from an outcome. The reference point can be interpreted as a "neutral stimulus", from which psychological value is measured. The shape of the y function, concave above the reference point and convex below it, reflects this stimulus interpretation. The psychological response to monetary changes, like the response to many other sensory or perceptual dimensions, is a concave function of the magnitude of the physical change (Kahneman & Tversky, 1979, p.278). The y function thus reflects the compressive nature of most stimuli, a finding well documented in psychophysics for over a century (since the days of Weber and Fechner (I860)). The location of the reference point also determines the way in which the decision situation is framed, which in turn drives the sunk cost problem. Any framing differences result in different behaviors in the face of sunk costs.16 Some care must be taken in giving $ and y distinct interpretations. It is quite reasonable to talk of economic value as separate from psychological value. But because both functions are defined simultaneously over the same argument (monetary "This reference point can be a target or aspiration level. 16Loomes and Sugden (1987) talk of the "convexity" of the combined value and regret function. This «*n be shown to be compatible with the compressive stimulus interpretation of our y function. 33 outcomes), they must be interpreted jointly: y(w) is actually \y(w) given <J>(w) (and vice-versa), so that one cannot be experienced without also experiencing the other. As a result, an alternative, more cautious interpretation of \j/(w) may be as a residual function rather than a direct psychological one: it represents the difference between a more psychological interpretation of value, based on gains and losses (as in prospect theory), and the purely economic #w) function.17 Adding <J> and y, both denned over dollar outcomes (w), produces the aggregate value function v. Specifically, we have: v(w) = <Kw) + vy(w) . Since our decomposition approach was motivated by the stimulus intuition that underlies prospect theory, it is not surprising that the prospect theory value function can be derived as a special case of this two-attribute approach. In Appendix B we determine the conditions under which our aggregate value function will coincide with the value function of prospect theory. The decomposition approach we have just outlined is at the core of our treatment of the sunk cost phenomenon. We extend the (<j>,\|0 decomposition approach to model sunk cost decisions involving multiple projects. 17It is clear that for any two functions v and <|>, there will always exist a function \p such that v = <tH-\y . 34 2.1J2 Extension to Multiple Projects: Tradeoffs under Certainty as a Model of the Sunk Cost Effect Consider total value denned over the profits from two projects, vOc )^. By employing the same approach as above, total value v can once again be quite naturally decomposed into <j> and y. As before, we let <t> represent the conventional economic value function, now defined on the total profits from both projects: ^in1+n2)16. The function y on the other hand captures the psychological explanations (self-justification, reducing cognitive dissonance, reducing regret) that compel the investor to persist with the committed project. The specific psychological factors that underlie the sunk cost effect stem from the prior commitment to and unsuccessful status of project #1 as of time tj. y thus captures those psychological factors in -\ that are not present in 7^, so that we define y as o function of %j only, yfaj) . There may of course be non-economic concerns affecting both projects, which suggests decomposing V ( % V K ^ into <(>(K1+7t2) and y ,^;^ ). We address this more general situation in section 4, below. Our analysis focuses on tradeoffs between the economic and psychological attributes. The presence of a second project introduces the potential for trading off profits18 in it, for those in %{. economic gains stemming from investment in a new project get traded off for psychological gains (saving face) resulting from investment 18Formally, this is tyyt 0+-.x+-^. But because w0 is fixed, we can define this simply as ^T^+Jtg). "Only in the multiple-project case are such tradeoffs possible. 35 in the committed project. The implicit tradeoffs between the two attributes will be the key to developing a model of the sunk cost phenomenon. The extent of the dependence between attributes, and the way in which they trade off, must be reflected in the functional form of the multiattribute model. The choice of an appropriate functional form has critical implications for the usefulness of a multiattribute approach in general. A simple functional representation, separable in its attributes, has clear benefits - in operationali zing tradeoffs, facilitating the utility assessment process, and in obtaining a parsimonious explanation of sunk cost behavior. Our purpose is to construct a conceptual model that is both descriptive and predictive. Our focus on the dependence between attributes is not to aid us in assessing the total value function v. We wish instead to see what our decomposition of v, and the reasonable shapes postulated for <fp and y, can predict for sunk cost choices. Having value that is separable in its attributes allows us to gain behavioral insights that would otherwise be masked in more complex representations - these insights being an important objective of using multiattribute value theory as a descriptive tool. Several sources review the major independence conditions that lead to an additive conjoint measurement model, the simplest (and most commonly used) multiattribute value decomposition under certainty (Krantz et al. (1971); Keeney & Raiffa (1976); von Winterfeldt & Edwards (1986)). We can test the validity of the key condition, the Corresponding Tradeoffs Condition in the context of our two-attribute model, to determine whether additive conjoint measurement, of the form v = , 36 adequately captures and represents the $ versus y tradeoffs of the sunk cost problem. Figure 5 presents a conceptual test of the Corresponding Tradeoffs Condition in the sunk cost setting. The reader can examine Figure 5 and judge whether he/she wishes to satisfy the condition: If the three heavy arrows correspond to indifference tradeoffs he/she is willing to make, then the fourth (shaded) arrow must also represent the appropriate tradeoff. If this is so for all such possible tradeoffs, then the Corresponding Tradeoffs Condition (necessary and sufficient for an additive conjoint representation (Keeney and Raiffa, 1976)) is satisfied. — Insert Figure 5 here — Testing the Corresponding Tradeoffs Condition, like other independence conditions, relies on an individual's subjective judgments. It would need further empirical substantiation through assessments from actual decision-makers. At a fundamental level, however, our two attributes (economic and self-justification) were chosen to be independent, with no significant interaction between them. Inspection of Figure 5 suggests this to be the case. As a result: 37 The Additive Value Model Meeting the Corresponding Tradeoffs Condition guarantees the existence of functions <f»v and y v such that the value function v representing riskless sunk cost choices has an additive conjoint measurement representation: vomica) = vOij+Ra, Ki) = 4»v(jc1+7t2) + Vv ^ i ) • fU This representation of value, additively separable in its attributes, captures the tradeoffs that underlie the sunk cost phenomenon. The existence of <t>v and \j/v, and of an additive form for total value, does not imply any specific conditions on the scaling (relative weights) of 4>v and y^  the shapes of <j)v or yv, or on the exact psychological content of yv. Additional conditions must be imposed to determine the characteristics of our two-attribute decomposition as it pertains to sunk costs. The shapes of $ and y that were posited in the (univariate) single-project case need not necessarily hold in the two-project case, for which v^,^) is now a bivariate function20. Our additive decomposition, however, does produce the following result: A sunk cost effect will occur as long as the investor is willing to trade off some 4>v for yr, regardless of the respective shapes involved. For any yT function that is not a constant in nv tradeoffs of $T for yv will generate an allocation that *°That is, v is now a three-dimensional surface defined over (% , Hj) space. 38 differs from the purely economic one. And for any \|/v increasing in 7^  (which is to be expected), the resulting allocation will favor the committed project (as compared to the purely economic allocation). These results are a direct consequence of maximizing (^Ttj+rCa) + vv(rc1) as opposed to a purely economic value function vd^ +rc,). Having yv increasing in nv for example, implies that the marginal value of 74 exceeds that ofn?, while in the purely economic case they are equal. For some people, tradeoffs of total profit n^i^ against K± may well take place only when the tradeoff involves bringing rtj back to breakeven or above, and not for tradeoffs which simply make % less negative. Figure 6 (successfully) tests the Corresponding Tradeoffs Condition in the case of tradeoffs which take TCx from the negative to the positive domain21. The result is that in such cases, \ J K T C J ) is continuous over losses, but the model is only appropriate (and should only be used) to capture breakeven situations. Indeed, this interpretation is quite compelling psychologically, as the compulsion for breaking even (a "breakeven effect") appears to be a main driving force behind sunk cost behavior. See Thaler & Johnson (1990) for a detailed discussion of the breakeven effect. 'Testing the Corresponding Tradeoffs Condition in this case requires the existence of some positive psychological value from an increase in TCx within the positive domain. Once additivity is established (through Figure 6) for this general case, it will also hold for the degenerate case represented in Figure 7. This is true even though the latter does not allow us to test the Corresponding Tradeoffs Condition for changes in 7^ within the positive domain. It is clear in the degenerate case of y=constant that only dp matters - which is still consonant with an additive representation of the form <t>+\j/. 39 - Insert Figure 6 here -Some reasonable postulates can be made concerning the shapes of <|>v and yv. Just as in the single project case, we can define $Ttobe concave over total wealth, to reflect decreasing marginal returns in economic value.22 yT, on the other hand, may vary from one type of situation to the next. In a sunk cost setting, the characteristics of yv and its psychological properties, which are at the heart of our model, have some theoretical support. yT, we submit, is increasing and convex in the domain of losses, relying as before on the argument that any stimulus or sensation is compressive, or sub-additive in intensity. Such a stimulus argument seems appropriate in the case of sunk costs, where the stimulus in yv is the amount of lost face, of regret, or of missed opportunity. In the domain of gains, however, these psychological considerations tend to vanish. Once project #1 starts earning positive profits or exceeds some profitability threshold (or reference point), the compulsion to justify sunk costs will likely disappear. This can be observed in Figure 7, which establishes tradeoffs between <J>V and \\fy One is unlikely to trade off any amount of total profit 7 ^ + % in order to increase % if % is in the positive domain - and vertical tradeoff arrows result. This implies that y(n1)=constant for nt in the positive domain (i.e. above some breakeven value). The resulting shape of yO )^ will thus display a kink and flatten out to horizontal at the TC1 breakeven point. Beyond that point, profits from both projects contribute equally because the magnitude of the gains or losses being contemplated in individual mental accounts will often be small relative to total wealth, the <j>„ function may be regarded as being approximately linear over that range. 40 to overall value. ... Insert Figure 7 here — The particular functional shapes presented in Figure 8 reflect the preceding line of reasoning. Economic value $T displays decreasing marginal returns, while yv takes the form of a convex stimulus in the domain of losses, which then vanishes (flattens out) in the domain of gains. The resulting additive value function in equation [1] describes the riskless sunk cost decision. — Insert Figure 8 here — The intensity of the sunk cost effect - the willingness to give up dollars for psychological satisfaction - will also be reflected in the relative scaling and slopes of the <|>v and \yv functions, respectively, indicating how much the investor values face saving or is prone to dissonance or regret. Shapes may also vary. Obviously, an individual's exact 4>v and yv functions can only be obtained by assessing his/her preferences directly. 2.2 Decomposing Risky Utility The presence of uncertainty obviously adds realism to the analysis of the sunk cost problem. Not only do real sunk cost decisions almost always involve uncertainty in outcomes, some would argue that sunk cost behavior is a direct result of the presence 41 of uncertainty, feeling that the potential for making a currently unsuccessful project profitable is what triggers the sunk cost phenomenon. We now extend our approach to formulate a model of sunk cost decisions under uncertainty.83 23.1 The Case of a Single Project As in the riskless case, we feel that the risk-seeking postulate of prospect theory does not constitute a fundamental explanation of the sunk cost phenomenon. Instead, risk-seeking is a by-product of more basic psychological considerations, such as the need for breaking even or for saving face, and of complex framing influences. What is referred to as "risk attitude" in a single-attribute framework may well be a composite of factors that translate into more or less risky behavior along that attribute. A risky utility function can therefore also be decomposed into its component economic and psychological functions. Our decomposition of riskless value in the case of a single project, presented in 2.1.1, extends to situations of uncertainty. That is, u(w) = $(w) + \|Kw) . The domains and general shapes of $ and y remain the same as in the riskless case, but the functions now have a different interpretation. The risky interpretation ssWe develop an expected utility model, which requires that we accept the assumptions of expected utility theory. Also see footnote 25. 42 of the economic function $ conforms to its conventional economic meaning of risk aversion. It is the convex psychological function y that makes decisions over losses risk seeking. The risky y does not represent a deterministic stimulus but captures instead the psychological impact of outcomes under risk. The graphs on Figure 4 can be given this risky interpretation. A reasonable interpretation of the y attribute in the utility model under risk may possibly apply only to gambles that involve the potential for breaking even — gambles offering only the possibility of reducing one's losses in project #1 may well produce minimal or no change in psychological utility. In breakeven-type gambles, as in the deterministic case, the convexity of y over losses yields a sensible interpretation. The presence of risk, however, introduces somewhat more complexity in the multi-project situation. 2J2J2 Multiple Projects: A Multiattribute Utility Model of The Sunk Cost Phenomenon The multiple project representation under uncertainty is a natural extension of the preceding approach. Again, we postulate two distinct components to total utility: an economic part C X T ^ + T C J , ) and a psychological part ydcj). Unfortunately, having an additive value function in the riskless case is irrelevant to the risky utility representation. Risky tradeoffs between economic and psychological factors must be 43 formally established, by testing independence conditions leading to the various representations of multiattribute utility. Keeney & Raiffa (1976) present the major utility independence conditions for two attributes, and give the resulting representation theorems for total utility. Additive utility independence, the most stringent independence condition, leads to an additive utility representation of the form Udtj , JCj) = ufai+JCj, , JCj) = (^(Jti+Jla) + y ^ ) . The additive decomposition has strong implications about behavior, and in particular about multiattribute risk attitude. Definition: [Richard, 1975] Consider the following 50/50 gambles defined over the pair of attributes (X,Y). Gl : {(xpyj) , (xg,y2)} and G2 : {(xvy2) , (x^y^) , with x2 preferred to x} and ys preferred to yt. Then a person who prefers Gl to G2 is said to be multiattribute risk seeking over (X,Y)\ one who prefers G2 to Gl is multiattribute risk averse over (X,Y); and one who is indifferent between Gl and G2 is multiattribute risk neutral over (X,Y). Additive utility independence implies (and requires) multiattribute risk neutrality over all possible pairs of outcomes (Richard, 1975). Figure 9A presents a test of additive utility independence in our sunk cost setting, which amounts to testing multiattribute risk neutrality. In managerial contexts, managerial reputation (or face 44 lost or saved) and income might be considered as (weak) substitutes, thereby suggesting multiattribute risk aversion between them, thus violating multiattribute risk neutrality. For many in fact, the certainty of receiving an intermediate outcome pair (the lottery on the right in Figure 9A) is not indifferent to a gamble involving "all good" or "all bad" outcomes (the lottery on the left of the Figure). As a result, the additive utility representation is not appropriate. A more general decomposition is required. — Insert Figure 9 here — M u t u a l m u l t i p l i c a t i v e u t i l i t y independence, a slightly milder condition, leads to a m u l t i p l i c a t i v e u t i l i t y representation, of the form The coefficient k is an interaction parameter, allowing the multiplicative representation to capture the interaction between the attributes, not captured in the additive form. Figure 9B tests multiplicative utility independence in the sunk cost context. It tests whether risk attitude over economic payoffs is independent of the level of psychological utility obtained, and whether risk attitude for psychological payoffs is independent of the level of economic utility obtained. 45 Multiplicative utility independence is somewhat problematic to test. Is risk attitude over income independent of the amount of face loss that one experiences? And vice-versa? It does not appear grossly unreasonable to answer yes. While some might wish to clearly violate multiplicative utility independence in Figure 9B (in which case the multiplicative utility representation would be inadequate to capture that person's sunk cost behavior), multiplicative utility is the simplest functional representation that appears "reasonable" in the present context. Any looser independence assumptions (although possibly more satisfactory) would lead to more complex representations of total utility (see Keeney & Raiffa, 1976), that are less parsimonious and likely the source of fewer insights. Therefore, inspection of Figure 9B suggests that although still restrictive, multiplicative utility independence appears reasonable here, over both the economic and the psychological attributes. However, verifying the validity of this condition empirically with actual decision makers would greatly increase our confidence in our use of the multiplicative (or any other) form. The added flexibility of the multiplicative form allows it to capture risky tradeoffs between our two attributes. As a result, we state the following: 46 The Multiplicative Utility Model Sunk cost decisions under uncertainty can be described by a multiplicative multiattribute utility model, of the form U ^ . T C J ) = uOti+Jia, Wj) = • „ ( W 1 + K 2 ) + V » ( « i ) + k<l>n(rci+*2)Vu(*i) • ^ This representation combines both the tradeoffs between the economic and psychological attributes and the risk attitude present in risky sunk cost decisions. The multiplicative form also imposes constraints on multiattribute risk attitude over attribute pairs (Richard, 1975). It implies a unique, strict multiattribute risk attitude (aversion or seeking) over every possible outcome pair - as dictated by the unique value of k. In the multiplicative form, multiattribute risk aversion implies -1 < k < 0 while multiattribute risk seeking implies k > 0 . Multiattribute risk neutrality, corresponding to an additive utility model, is a degenerate special case of the multiplicative model, for which k = 0. Empirical work by Fischer et al. (1986) has demonstrated a tendency toward multiattribute risk aversion for pure gains and multiattribute risk seeking for pure losses. The sunk cost problem involves two kinds of outcomes: profits, on the one hand, and cognitive dissonance (or loss of face), a negative stimulus, on the other. 47 If jCj+Ttj is negative 3 4, then the decision will be framed as a pure loss situation and we can expect multiattribute risk seeking. If J ^ + T C J , is positive, the decision will be framed as a mixed outcome situation. It is unclear which multiattribute risk attitude to expect over mixed outcomes. Both types may well be observed. As we shall see below, this will play an important role i n our model's predictions about sunk cost behavior. • A Note About Uncertainty Some explanations of escalation behavior have actually been grounded in probability biases. The saliency of a sure outcome, for example, results i n the "certainty effect", making a sure loss (resulting from letting go of a losing project) particularly aversive, and generating apparent risk seeking behavior. By formulating a multiattribute expected utility model, we assume the expected utility hypothesis (and its underlying axiomatic system), which implies linearity in probabilities.2 6 By doing so we do not wish to rule out alternative explanations, but instead seek to complement them with a model that focuses on utility considerations rather than on probability distortions. Sunk cost decisions will not always involve continue/discontinue choices, and as a result may not always be subject to a certainty "The concept of "negative" profits may also be a relative one, when profits fall below some reference point. ^Payne, Laughhunn & Crum (1984) found that Savage's sure-thing principle generally held, when assessed i n a simple multiattribute setting - lending some support to our approach of remaining within the Subjective Expected Utility (SEU) framework. Moreover, while a multiattribute SEU approach has the flexibility to accommodate behavior that may violate single attribute SEU models, the refutability/power of SEU is still greater than that of generalized SEU models (which incidentally have not yet been extended to multiple attributes, except in one minor exception (see Fishburn, 1984)). 48 effect. They will instead be influenced by utility concerns. However, for those situations that are subject to probability biases, the sunk cost phenomenon may well be exacerbated by the presence of both utility and probability effects. • 3. IMPLICATIONS OF T H E M O D E L 3.1 The Need for Deterministic Tradeoffs In some respects, the deterministic tradeoffs of money against psychological considerations, postulated in the riskless sunk cost effect (section 2.1.2), may stretch credibility. When presented with a clear choice between more profits or less, few will choose less, even though the lesser amount originates from the sunk project. Under uncertainty, however, a sunk cost effect is often observed. Because the riskless sunk cost effect requires a transparent tradeoff of more dollars against less, or of dollars against psychological considerations (or $ against y), we are made to wonder whether the sunk cost effect is not a by-product of the presence of uncertainty. We show below that under expected utility26, the occurrence of the risky sunk cost phenomenon implicitlv reouires such deterministic tradeoffs to actually take place, regardless of the risk attitudes involved. 'This argument also holds for generalized expected utility theories, which must also provide a consistent ordering over degenerate prospects. 49 The proof relies on the following key result: v and u Indifference Curves are Identical Lemma: A risky utility function u must produce the same preference ordering over detenninistic outcomes (when applied to degenerate prospects) as does a deterministic value function v. That is, v must be a special case of u, applied to outcomes under certainty. As a result, the u-indifference curves under risk must be identical to the v-indifference curves under certainty. This is a general result, extending beyond the particular functional forms in equations [1] and [2]. Proof: The equality of the v and u indifference maps can be formally established when we consider that udc^ x,) = ffvOi^jij)]. Using the following notation: Uj = du/^ Jij, i=l,2; v , = dv/DrCj , i=l,2; and £, = df7dv, the slope of a u-indifference curve at any point is Ua f; • va v2 which is the slope of a v-indifference curve at that point. For example, additive v and multiplicative u implies (von Winterfeldt, 1979) that u = e*^  = e"*1*"1*1'"****151 so that 50 U a e* • -k • v, va This lemma simply relies on the Hicks-Allen idea that only ordinal utility is needed to establish indifference curves. For a good discussion of this idea, see Hicks (1946). We can now establish the need for deterministic tradeoffs between money and psychological concerns. Theorem 1: The existence of a sunk cost effect under uncertainty implicitly results in a deterministic tradeoff that involves giving up greater profits TC, from a new project in favor of lesser profits % from the committed project. Conversely, such a deterministic tradeoff also implies the presence of a sunk cost effect under uncertainty for at least some possible gambles. Proof: Consider the indifference map in the , JT^) plane shown in Figure 10. — Insert Figure 10 here — Assume that deterministic decisions conform to economic rationality (and no deterministic sunk cost effect occurs), so that value is defined over total profits (itj+n^) only. Indifference curves will thus be linear and at a 45° angle in that plane. 51 However, the presence of a sunk cost effect under uncertainty, by definition, implies the existence of at least one indifference curve that is not linear and at 45° - the result of not optimizing over ( j ^ + T i j ) alone. Therefore there exist two points A and B as shown on the figure, such that A lies on a higher indifference curve in the deterministic v case, while B lies on a higher indifference curve in the risky u case. But this is a contradiction, as u must be order-preserving of deterministic preferences over degenerate prospects. Consequently, a sunk cost effect under uncertainty implies a departure from detenninistic economic rationality. The converse is also true, because of the equivalence of the u and v indifference maps, making this is an if and only if result. Note that this result occurs regardless of the specific functional forms in equations [1] and [2]. • Similarly, a different risk attitude in one project versus the other also implies deterministic tradeoffs of 4> against y. We see this by observing that indifference curves that are linear and at a 45° angle, corresponding to no deterministic sunk cost effect, also reflect uniform indifference between any gamble on one project versus the other. That is because any gamble on -\ (represented by the horizontal arrows in Figure 11) has outcomes that end up on exactly the same indifference curves as the equivalent gamble on (the equivalent gamble represented by the vertical arrows). But this implies identical risk attitude on profits from the two projects, as it reflects indifference between any two such gambles. Therefore, we have the following corollary. — Insert Figure 11 here — 52 Corollary: Different "risk attitudes" that result from framing the two projects differently implicitly require the presence of detenninistic tradeoffs of 4> against VJ/ as well. These deterministic tradeoffs between projects exist regardless of the risk attitudes involved. Our model, in particular our deterministic model, makes explicit the economic/psychological tradeoffs that are implicit in both the riskless and risky sunk cost decisions. 3.2 Characterizing the Indifference Curves Having established that both the riskless and the risky sunk cost effects require indifference curves that differ from the linear, 45° type, we can now use the particular forms of our u and v models to further characterize the indifference curves, capturing the exact tradeoffs between % and TC,. Because the risky and riskless indifference curves are identical, as argued above, we can use the simpler value model (eq.[l]) to derive most of our indifference results. Note that our indifference maps can be presented in either the (jtj, KJ) plane or in the (rti+TCa , plane. The results obtained in one can easily be transferred to the other through a simple axis rotation. In the sections that follow, we alternate between the two representations, depending on the particular analysis being performed. 53 We know that along any indifference curve yielding a constant utility level of U (vN-M utility or value), we get dU = U xdx + U,dy = 0 (i) so that the slope of the indifference curve at any point is given by f£ = (ii) dx U, We can compute the slope by using the information from our deterministic value model in eq.[l]. Along an indifference curve, where v = ^(jii+ J t a ) + V ^ ) = constant, the slope i n the (%, ic,) plane is 3<(> dy 3<|> <ty • ^  = ^ ^ _ = - ^  ^ _ <; -l always . v 2 d$ d$ die, dic^  This is arrived at by using the key result from our model in eq.[l] (which we will use several times throughout our development) that B^/STCJ = d^/dn2, and noting that each of the three terms i n the last expression are positive. This result is obviously verified for indifference curves for our risky utility model (eq.[2]) u = $»(ni+*2) + Vu(*i) + kr«(*i+*«)Yu(*i) = constant. In this case, we find 54 u x _ drCj drtj di^ Again, because dctk/dTCj = 3$/c>7CA , and dividing both numerator and denominator by [1+ky], this becomes = 3<J> + dy r l + k^-j , ^ -1 * .x a i w a y s . dt|) This inequality obtains because scaling requires that both $ and y be between 0 and 1, in addition to having k > -1 (always). As a result, the bracketed term in the numerator is strictly positive, thus making the slope of the indifference curves always < -1 . Hence under both models [1] and [2], the slope of the indifference curves in the (TCi, TCa) plane is £ -1 everywhere. This is a clear result of our value model in eq.[l], where more rtj will always be traded off against less nv because of the additional y value associated with The curvature properties of the indifference curves can also be established by using the curvature conditions postulated in our value model in eq.[l]. Specifically, 55 (differentiating (ii) above), along an indifference curve we have dV = dx2 dx L u , J U? L dx d x J where (from (i) above) dU, T T T T dy dx dx and ^1 = + u n * dx dx For U(x,y) = v(x,y) = v^,^) = ^ T C x + + yfai ) , we get: U y = v 2 = d<)> a2* + afy 371? dnf d2^ d 2^ both = This last point is important to note: v u = v^ = 4>u = 4>ia = 4>22 -87 We also make use 2 7This notation differs somewhat from orthodox mathematical notation. While (jK i^+J^) has only a single argument, i t can be read as ^[(ni+n^in^)], or as ( ^ T C^). The partial derivatives on $ should therefore be interpreted as partials with respect to the two arguments Tti and TCa, respectively. 56 of this later on in our development. Then, dV = ox2 ^ r V i i + v u drcj drcj r - f L We are interested in signing this expression. We can take out the squared term at the beginning (which will always be positive). Because d^ldK^ = cty/chtg and = v^ , we are left with signing 3<t> r — | v 11 T12 drtj d7Cx + v„ i - * r v12 + \ u — 1 dy L drc, J 3$ r aV - i _ d v ^ j - ^ j - 1 + d 7 t 2 - j 1 (iii) Each of the terms in the last expression can be signed. We know that dn^dn^, the slope along an indifference curve, is £ -1, so that [1 + ditj/cbij is negative (or zero). Both 4> and y are increasing in TCx, and therefore the sign of expression (iii) depends on the curvature of 4> and y. As a result, under both models [1] and [2], under the traditional economic assumption 57 that $ is concave: y concave implies that (iii) is positive and the indifference curves are all convex (the standard result in economics); y convex implies that (iii) cannot be signed (based on the available information), and the curvature of the indifference curves is undetermined.88 The latter implies, in particular, that we lose the potential for optimization that results from convex indifference curves. 3.3 Model Predictions 3.3.1 Riskless Case The predictions that result from these indifference curves can now be spelled out. For the deterministic case of eq.[l], the prediction is simple: We will observe a deterministic sunk cost effect - trading off more 1% in favor of less n1 — as long as the loss in $v is at least compensated by the gain in yv. In the case of a concave <|>v and convex yv, for example, such tradeoffs move us down 4>v and up yv, to steeper portions on both functions. Sunk cost behavior will depend on the relative slopes and particular tradeoffs involved. Some Comparative Statics We can characterize one's willingness-to-tradeoff <{>„ against yT as we move along *8These curvature properties were derived for the (n^) plane, but they also hold in the (TCx+TCs,^ ) plane, as curvature of indifference curves in unaffected by this axis rotation. Specifically, curvature in (TC^TC^) space is d^ Kx+jt,) = d [d(7t1+7c2)] = d [1+ d%] = d 8^ djif drtj ditj di^  (1% drc? 58 one of the two attributes. Consider first a horizontal cut (n^  = constant) of the indifference map, shown in Figure 12. The constant k in this case represents the level of iso-utility along a given indifference curve. — Insert Figure 12 here — Face Saving as a Function of Wealth Willingness-to-pay to save face increases as one becomes richer. This is the result of 4» concave and is independent of the shape of the y function. Proof: Along an indifference curve, #71! + Jts) + vCTCi) = k . Denoting T^+KJ as f ^ i ) , this becomes 4>[fk(iti)] + V(Jti) = k . Differentiating with respect to nt yields d d W +\|f'(7C1) = 0 (along an indifference curve) djij dTCj Differentiating further with respect to k gives + 0 = 0 dTCjdk Collecting terms yields d^rt,) = dk d*, < Q ftf^)] 59 To sign this, we use 4>'>0 and 4>"<0. As well, moving to a higher indifference curve while keeping n\ fixed requires that 4(7^) increase, so that the middle term is positive. And along an indifference curve, increasing 7^ means that fk(7Cj) decreases, making the third term negative. So as k increases, that is, as one gets richer and moves to a higher indifference curve, the rate of substitution between 4(7^) and 7^ decreases, i.e. ^(T^+T^) decreases (tke giope becomes more negative, steeper). dTCi This produces the conclusion: 4* concave implies that one 'unit' of y is worth more $ as ( T^+TCJ ) increases. This is a simple consequence of our additive value model. • We can also ask the converse question about the change in one's willingness-to-pay as the amount of y loss increases. This case, symmetric to the preceding one, corresponds to a vertical cut of the indifference map, shown in Figure 13. — Insert Figure 13 here — Face Saving and the Amount of Lost Face For y convex, as sunk costs increase, one is willing to pay less to have TCJ increased marginally - i.e. to regain one 'unit' of y. This is the result of y convex over losses and is independent of the shape of <j>. 60 Proof: As before, along an indifference curve we have which we can rewrite (with n^rc^ = Tt,.) as #*T) + VuJk(%)] = k • Differentiating with respect to % yields L : •'(%> + vig^n • = o drCf (1% Differentiating further with respect to k gives 1 : 0 + Vfote)] • i(gk(Jtr)) . + V-[gk(*r)] . = 0 dk dk d% dn^ dk Collecting terms, d2gk(ic,.) dk die. rt -B k ^ = ^ > 0 for v convex. drtrdk V/[gk(tr)] This is signed by using \|*/>0 and \|r">0 (for y convex). As well, moving to a higher indifference curve while keeping Ttj. fixed requires that g^fty) increase, so that the middle term is positive. And along an indifference curve, increasing % means that gk(TCr) decreases, making the third term negative. So in the case of \|/ convex, > 0 dn^ dk that is, as k increases (and we move to a higher indifference curve along a fixed level of TCp, d^i) also increases (becomes less negative). d(TC1+TCa) As Figure 13 shows, if losses on are increased (and we move down the \y 61 function in Figure 8), one is willing to pay less and less money to regain one marginal unit of v - as should be expected from y convex. This is again a direct result of an additive value model. • Through indifference curves, we can also trivially establish the economic cost of sunk cost behavior. This is most easily seen in the , TC,) plane (Figure 14), where the slope of any indifference curve captures the tradeoff of money against psychological factors. In the absence of a sunk cost effect, the indifference curves would be vertical straight lines, and an individual at point B on Figure 14 would not be willing to sacrifice any net money in order to reduce the amount of sunk losses experienced on project #1. The presence of a sunk cost effect produces the following. The Riskless Sunk Cost Premium Definition: We define the riskless sunk cost premium as the amount of money that is actually foregone because of the compulsion to persist with the committed project. Specifically, it is the amount of money that is foregone by maximizing v = $ v ( r c i + J t 2 ) + V v ( ^ i ) as opposed to maximizing v = ^ ( T C J + T ^ ) only. The horizontal distance between any two points (such as A and B) in Figure 14 constitutes the sunk cost premium paid in order to reduce the (vertical) loss amount for nv 62 — Insert Figure 14 here — 3.33 Risky Case We can now turn to the predictions of our model for the risky case. The risky context is richer, and the multiplicative model in eq.[2] less transparent, than its riskless counterpart. Preferences between risky projects will be a function of the specific characteristics of our multiattribute utility model and its individual components. In the risky case, the central question to be answered is: Under what conditions will a gamble on the sunk project (#1) be preferred to an equivalent gamble on project #2? (See Figure 15.) This question can actually constitute a formal definition of the risky sunk cost effect. Under conventional economic rationality, both gambles would be equivalent - the source of the revenues being irrelevant. But preferring to gamble on project #1 translates into sunk cost behavior, that of persisting with the committed project beyond what is economically rational. We can derive sufficient conditions for our model to predict such behavior, for gambles restricted to the negative domain of KV — Insert Figure 15 here — Under the multiplicative utility model udcx.Jtj) = (^TCi+TCg) + yinj + k^ +fCjhjKTO [2] 63 a gamble on nt has exactly the same economic (<(») impact as a gamble on rc2. Hence, the differential impact of the two gambles on utility comes only from the last two terms, or VCjc^ tl+k^ jc^ Jta)] . Comparing the differential impact of the two gambles on this expression yields - gamble on %: f ydi^ tl+k^ Oi,)] • ffoij d*^  = E(y) + kE(y«$) where y0 = X ^ T C ^ - S ) , which results from letting go of project #1 with losses of-s, and pursuing instead the gamble on project #2. The problem therefore reduces to comparing That comparison produces the following sufficiency29 result, which we show below: Theorem 2: For fair or favorable gambles of any size (restricted to the negative domain of 7^ ), \r convex over losses and multiattribute risk seeking over our two attributes (k > 0) imply a strict preference for a gamble on project #1 over an equivalent gamble on project #2. 89The stated conditions are sufficient but not necessary to preferring the gamble on project E(y) + kE(y«t>) versus \j/0 + ku/0 E(<{») [Rl] #1. 64 Proof. We show this result by first noting that Cov(y,4>) = E 0 M > ) - E(y)E(<|>) We also know that $ is increasing in nv so that exists and is also an increasing function, and hence Because y also increases in rij, y ° 4>_1 is therefore also increasing in its argument. Thus ydtj) is an increasing function of ^T^) , and as a result Cov (y,<|>) > 0 . 3 0 Hence E(y»<J>) > E(y)E(<|)). Now, for y convex: E(y) t y c for fair or favorable gambles, and therefore E(y«<|>) > E(y)E(<|>) £ y„E(<|>) for such gambles. Putting these results back into relation [Rl], when k > 0, yields the stated result. Any other conditions, in particular k < 0 or y concave, or unfavorable gambles, do not allow us to systematically establish relation [Rl]. • This result may not hold for gambles that involve outcomes in the positive domain of Ttj. Consider gambles centered at ~\=-s, where y0 = yfa -^s). As gambles get larger and upside payoffs for TCx become positive, they fall along the flat portion of y (see Figure 8). The expectation of these gambles produces E(y) that is more and more l i k e that of a concave function, in which E(y) £ y0. As a result, this may also lead to E(y*$) £ yoE(4>) . Substituting this into [Rl], we find in such cases that the preference for gambles on project #1 may disappear. Therefore, for fair, favorable or even unfavorable gambles, under the conditions conducive to a sunk cost "Alternatively, Cov (y,4>) > 0 simply because y and <|> are both increasing in TC l t so that 4 increases if and only if y also increases. 65 effect (y convex over losses and k > 0), the tendency toward a sunk cost effect decreases, and may eventually disappear, as the gambles get larger and involve positive values of rcr We can obtain additional results if we restrict the gambles to be relatively 'small', allowing us to approximate our multiplicative utility function through a Taylor series. Theorem 3: For a small gamble of positive expectation, convex y and k positive or zero will imply a preference for the gamble on project #1 -consistent with the result derived for gambles of any size. For a small gamble of negative expectation, concave y and k negative or zero will imply a preference for the gamble on project #2. In the case of a fair gamble (whose expectation is zero), both of these results are true. Proof. The proof is given in Appendix C. We have therefore identified the two main contributors to the sunk cost phenomenon in the risky case: the curvature (or shape) of the y function, and (the sign of) the coefficient of multiattribute risk attitude, k. In short, y convex, as well as multiattribute risk seeking (k > 0), will tend to generate sunk cost behavior. While neither condition is always necessary or sufficient to generate sunk cost behavior, both conditions will usually push preferences in the direction of a sunk cost effect. 66 The conditions under which the multiplicative utility model leads to sunk cost behavior were derived through gambles that involve either one project or the other (ie. along the vertical or the horizontal cut of the indifference map in Figure 15). However, the expected utility model also applies in investment situations involving mixtures of the two projects, and can be used to make predictions concerning investment allocations, and the impact of the sunk cost effect, in such cases. Because of the equivalence of the v and u indifference maps, the willingness-to-pay (comparative statics) results, derived in the riskless case, are also true for the risky case, even under multiplicative utility. We can also determine the risky sunk cost premium through an indifference curve analysis. The Risky Sunk Cost Premium Definition: We define the risky sunk cost premium as the expected amount of money willing to be foregone as the result of maximizing u = QJ.K1+K2) + yfjjtj + k ^ T ^ + T C a t y j T C i ) as opposed to u = ^ u C i C i + T C a ) only. While the indifference curves are identical in both the deterministic and the risky cases, the cardinality of individual curves matters in the risky case. With the tradeoffs postulated in our deterministic model, cardinal values for the indifference curves can be obtained simply through assessing <J>U, which gives us a cardinal 67 measure of risky preferences for Jij=0 - represented along the horizontal axis on Figure 16. Because there is a unique indifference curve going through any given point on the horizontal axis, assessing 4>„ therefore provides cardinal utility values for every possible indifference curve. — Insert Figure 16 here — Once cardinal utility values are obtained, for any lottery (say {A..5; B,.5) on Figure 16) we can find the indifference curve of utility equal to the expected utility of the lottery (the curve u=.3 in this case). The point at which that indifference curve cuts the horizontal axis (C dollars) represents the dollar amount - when loss of face is zero - providing that level of utility (u=.3). Now, consider the dollar amount (F dollars) whose utility corresponds to the expected utility of optimizing the same gamble on <J>U alone ({D,.5; E,.5}). The difference w between these two dollar amounts (w = F - C) is the risky sunk cost premium. The risky sunk cost premium is represented by the amount w on Figure 16. It is the expected difference in profits willing to be foregone from playing the (A3) lottery as opposed to the (D,E) lottery. In effect, it represents the (expected) cost of saving face. Parenthetically, the amount y on Figure 16 represents the traditional economic risk premium, that results from <J>U not being risk-neutral. Amount z is the expected 68 cost of saving face for a risk neutral agent. BA Empirical Issues Our model provides empirically testable predictions about sunk cost behavior, and helps establish the exact conditions under which a sunk cost effect will or will not occur. However, its success in predicting sunk cost behavior ultimately rests on empirical substantiation. Conceptual and theoretical arguments were used to postulate the generic shapes of the 4> and y functions. But their specific curvature for a given individual can only be established through a subjective assessment process. This gives rise to interesting assessment issues, in particular the assessment of the y function. Similarly, the specific functional forms of the u and v tradeoff functions for a given individual depend entirely on the tests of the various independence conditions that the individual appears to, or wishes to, fulfill. The conjectures made in this paper about the functional forms of v and u resulted from the apparent reasonableness of selected independence conditions, based on introspection. The independence tests in Figures 5 through 7 and in Figure 9 determined the additive form for v and the multiplicative form for u. More involved functional representations for v and u would seriously inhibit our ability to make predictions and draw implications from our models. Further empirical assessments of these independence conditions will be required to establish how appropriate our proposed functional forms for v and especially for u may 69 be, and if required to determine other more appropriate functional forms. Ultimately, the acid test of the sunk cost model(s) presented in this paper is to observe whether an individual's sunk cost behavior is consistent with his/her assessed utility function. Specifically, through the value and utility assessment procedures of decision analysis, the different independence conditions can be tested, the shapes of the 4> and y functions and the sign and value of k can be established. Comparing the predictions from the resulting value and utility functions with observed sunk cost behavior (in hypothetical or real sunk cost decisions) would then test the appropriateness of our model(s). These empirical issues also extend beyond the sunk cost problem, giving rise to the prescriptive versus descriptive tension, a problem common to economics and behavioral decision theory. Multiattribute utility theory, in particular, has been used primarily as a prescriptive tool. That is, an individual wishing to satisfy some set of independence conditions would maximize the resulting utility function. However, the descriptive application of multiattribute utility theory presents additional challenges. Independence conditions between attributes are necessary in determining appropriate functional forms for the tradeoff functions because the functions themselves (with the possible exception of the additive form) are not transparent. While these independence conditions are used to establish a methematical equivalence to a particular functional form, it is unclear whether the two will coincide (even approximately) in a descriptive setting. An individual's utility assessment may satisfy some independence condition, but (s)he may take decisions inconsistent with the 70 implied functional form. This is a caveat of using multiattribute utility theory as a descriptive tool. Exploring these empirical questions in the logical next step in substantiating our multiattribute model. This is the focus of ongoing work. 4. FUTURE DIRECTIONS - BEYOND THE SUNK COST PROBLEM A Behavioral Model of Project Selection/Budgeting Decisions The multiple mental account formulation, discussed in section 2.1, obviously touches on a broader "framing" issue, exceeding the boundaries of the sunk cost problem: that of making decisions in the presence of multiple mental accounts.91 In many managerial contexts, 'success' in allocation decisions is often measured with a yardstick that differs from the conventional economic one. Allocation decisions may not be taken solely to maximize the overall return of the portfolio of projects at hand, but may also be motivated by behavioral considerations relating to individual projects. Sunk costs are a case in point. Similarly, short-term losses on a project may incite a firm to abandon it, but managers will keep a 'pet project' going by trading off total 3lWhile the problem of combining multiple mental accounts is an important one in behavioral decision theory, little has been published on it. Thaler (1985) (see also Thaler & Johnson, 1990) proposed the "hedonic framing" theory, to describe the way in which outcomes from multiple projects are combined. According to that theory, multiple outcomes are either aggregated or segregated, to maximize total Value' as defined by the value function of prospect theory. 71 profits in order to get positive returns on that specific project. Alternatively, managers may simply wish to demonstrate their competence as decision makers by having all of their projects making money. These are cases where managerial incentives are not necessarily captured by economic 'reputation' effects. These problems involve - implicitly or explicitly - multiple attributes. Multiattribute utility/value theory provides a framework to study them. Our decomposition of value/utility into multiple attributes easily extends beyond the context of sunk costs into the more general decision problem of combining separate mental accounts, to describe allocation or choice behavior in decision problems involving multiple projects. We propose this approach • a general izat ion of the a p p r o a c h presented i n the case of sunk costs - as a behavioral decision model of project allocation, to predict choices in multi-project situations. This model will be a simple extension of our sunk cost model, incorporating similar psychological intuitions • such as commitment to an individual project - into the framework already developed for the sunk cost problem. Combining Multiple Mental Accounts Just as in the sunk cost context, the multiple mental accounts are once again subject to strong economic dependencies. It is not correct to simply postulate the multiattribute utility function to be the weighted sum of two mental accounts. As we did for the sunk cost problem, we must decompose total value or utility into its economic and psychological (or residual) attributes, and test the various independence 72 conditions between attributes, to obtain the appropriate functional forms that will reflect the actual tradeoffs between attributes and between mental accounts.32 Consider a situation where one is faced with two distinct sources of cash flows (or profits TCj and n^), which result from different projects or mental accounts. We can once again define the (total) economic contribution of these profits as ^TCj+rt,), a concave function of total profits. However, each project may now bring about more 'psychological' rewards: the pleasure or pain of having a won or lost on a given project, distinct from economic concerns. Total value/utility can therefore be decomposed into three distinct arguments: TCJ+TCJ , -\ and itj , and the three corresponding attributes which we designate as ^r^+TCa), Vidtj) and ^(TCJ), as shown in Figure 17. Our task is to determine the appropriate representation for this three-attribute model. — Insert Figure 17 here — Compelling evidence in support of additivity of psychological stimuli comes from the psychophysics literature. Ward (1989) summarizes a number of authors who found additivity of sensory stimuli in a variety of contexts. It is far from immediate whether this result can extend to our context, to the economic and the more cognitive psychological rewards (pleasure or displeasure) associated with outcomes in distinct mental accounts. In testing for preferential independence33, however, we find no significant interactions between different sources of pleasure or displeasure, so that ""This approach also extends naturally to the case of n>2 projects. "See Keeney & Raiffa (1976) 73 they would seem to combine additively. We do not posit that such explicit tradeoffs actually occur in choices between projects, but rather that individuals behave as if total value (being maximized) were an additive combination of 4>, V i and y 2 . This leads us to an additive value representation, of the form vfai.Jlg) = V(TC1+TC2,TC1,JC8) = tfr^+TCa) + y ^ ) + • Parallel arguments in the risky case lead us to a multiplicative utility representation,84 of the form udt^ TCa) = U +^TI^ TCj.TCa) = T^Cx+TCa) + y^) + y ^ ) + k<t>(7t1+7t2)y1(Tc1) + k^rc^ic^y^) + y1(Tt1)ya(Tc2) + kfyrc 1+ic2)y1(7c1)y2(7i2) This utility function provides testable predictions, in a number of areas. In addition to tackling the problem of multiple mental accounts, this model may shed Light on the problem of risk attitude in the domain of losses (via (<J>, yt) only), multiattribute risk attitude over different domains, and the framing of sequential versus parallel outcomes. Further theoretical as well as empirical work is required to understand these areas better. S^ufficient conditions for these and various other three-attribute (or more) value and utility representations are given in Keeney & Raiffa (1976). 74 5. CONCLUSION This paper has developed a model of the sunk cost phenomenon, and its underlying causes, within a utility maximization framework. It has provided a formal yet simple approach to the study of what has long been an important, yet largely overlooked, problem in decision theory. The intent of the paper was primarily conceptual, to show that multiattribute utility theory could be used to model behavioral decision problems. It is important to recognize that key independence assumptions underlie our use of conjoint measurement theory and expected utility theory to describe sunk cost behavior. While we believe them to be reasonable in the present context, it remains an empirical matter whether real decision-makers facing sunk cost situations will actually satisfy the assumptions that underlie our analysis. Ultimately, the value of our conceptualization rests or falls upon the empirical validation of the multiattribute independence conditions. The direction which we followed in this paper, of decomposing value or utility into separate economic and psychological attributes, may hold promise for a variety of other problems in behavioral decision theory, in which economic and psychological motivations are both important (as exemplified in section 4). We hope that this paper will encourage future work in this area. 75 REFERENCES Arkes, Hal R., & Catherine Blumer. (1985). The Psychology of Sunk Cost". Organizational Behavior and Human Decision Processes 35,124-140. Battalio, Raymond C, Carl A. Kogut, Owen R. Phillips & Michael B. Ormiston. (1989). "Sunk Costs and Opportunity Costs in Decision Making". Presented at the CORS/TIMS/ORSA Joint National Meeting, Vancouver, B.C., May 1989. Bowman, Edward H. (1982). "Risk Seeking by Troubled Firms." Sloan Management Review. Summer 1982, 33-42. Fechner, Theodor. (1860). Elemente der Psychophysik (Vols. 1 & 2). Leipzig, Germany: Breithopf & Hartel. Fischer, Gregory W., Mark S. 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Academy of Management Review 11,311-321. 77 APPENDIX A The Problems of Combining Separate Mental Accounts Directly Because the sunk cost phenomenon results from the differential treatment of cash flows that arise in the two distinct projects, it is natural to attempt to address this difference directly, by separating out the multiple mental accounts. We can define the profits resulting from project #1 (TCJ) as one mental account, and the profits resulting from project #2 (rtj) as a separate mental account. Each mental account can then be viewed as a separate attribute in a 2-attribute utility function, describing the investment decision following a sunk cost. This two-attribute set, consisting of prospective outcomes on each of the two mental accounts, contains all of the information upon which the sunk cost decision gets made. The utility of outcomes from project #1 can reflect economic as well as psychological considerations (such as self-justification) - the result of that project having incurred a sunk cost of s, while the utility of outcomes from project #2 can be economic only. The following example illustrates how multiple value functions from prospect theory could be used to represent multiple mental accounts. Multiple Mental Accounts and the Prospect Theory Value Function Consider the situation where each mental account is represented by its own value function. At time t^ , the mental account for project #2 would start at the origin of the value function, while the mental account for project #1 78 would start somewhere in the negative (convex) domain of the value function, reflecting the cost already sunk in the project. See Figure 18. — Insert Figure 18 here — The resulting two-attribute model would thus combine the prospect theory explanation with tradeoffs between the two projects, inherent in a multiattribute setting. The problem lies in determining how the two mental accounts are combined or trade off against each other. In general, marginal (economic) value of profits in one mental account will depend on the level of profits obtained in the other mental account. The marginal value of % will be different when 7^ =0 than when n?= $10 million. This makes the two accounts, and hence the two attributes, highly dependent upon each other. Similarly, risk attitude in one account will likely depend on the outcome obtained in the other account (consider risk attitude on TCx when 7^ =0 as opposed to when 7^=$ 10 million). The contribution of individual profits to the aggregate therefore imposes economic dependencies between the various mental accounts - so that utility will not be a function separable in the two projects. Decreasing (or simply non-constant) marginal value of total profits violates the Corresponding Tradeoffs Condition in the deterministic case, while non-constant absolute risk attitude over total profits violates both additive and multiplicative utility independence in the risky case. Only under unacceptably severe restrictions will value or utility be separable in the two projects: 79 - for Additive Value : if value is linear in $ - for Additive Utility : under risk neutrality over total profits - for Multiplicative Utility : under constant absolute risk aversion over total profits (so that total utility defined over aggregate profits is exponential). As a result, multiple accounts cannot easily formalize the preference tradeoffs between projects in either the riskless or risky cases.86 • "This lack of independence between the two mental accounts means that the multiple account approach is invalid for decisions that involve some investments in both projects, resulting in a mixture of and TCj. It may, however, be able to handle cases where the decision at tg is to choose between investing in project #1 or in project #2, but not in both (such as aU-or-nothing continue/discontinue decisions). The outcomes (and gambles) being evaluated would then be TCJITC^O versus JCJITC^-S . 80 APPENDIX B Prospect Theory as a Special Case of our Additive (<|>,y) Decomposition The shape of the value function postulated in prospect theory imposes conditions on the relationship between $(x) and y(x), when there is a single project or mental account. These conditions (on y) allow us to link the purely economic representation of value and the prospect theory value function. Two key conditions characterize prospect theory's value function: a. v convex over losses means that d V d84> d? dx2 >0 Vx„<0 *0 Concavity of the economic profit function implies d2<> < 0 Therefore, at any point in the domain of losses y must be more convex than <j> is concave, Le. dV d2<> dx2 > 0 Note that locally, this is a very weak condition, as $ for small losses will be 81 approximately linear. b. v 'steeper'for losses than far gains means that i.e. or dv dx dv > dx Vx,>0 d<}> + d v > d0 + d v dT dx" dx dx d<$> d<|> > d v dy d7 d7 dT *1 dx *1 -x, Global concavity of $ implies d<|> d<|> dx" dx Therefore, prospect theory's steepness condition is satisfied as long as we do not have d v d v dx" < < dx that is, as long as y over gains is not much steeper than y over losses. The steepness condition on v, also referred to as loss aversion, can result from <$> or y. But because 82 it takes place with small amounts lost or gained, where $ is approximately linear, it requires y to be steeper (locally) for losses than for equivalent gains. This was easily satisfied in our sunk cost model. These two conditions were initially formulated to conform to risky choice observations, and may lose their meaning in a riskless setting. There is some theoretical support from the psychological literature, however, to indicate that these conditions may hold even under a deterministic stimulus (strength-of-preference) interpretation of the value function. Convexity over losses results from the compressive nature of psychological stimuli - which exceeds the concavity of the economic function. The steepness condition reflects a systematic asymmetry in responses to stimuli, with negative stimuli carrying more "weight" than their positive counterparts. • 83 APPENDIX C Proof of Theorem 3 Consider the case of a gamble involving a possible gain of e with probability p, and a possible loss of 6 with probability (1-p), with both e and 5 small. The utility of the potential outcomes can then be expressed as u^+e,^) = uOc^ rca) + eujCrcj,^ ) + U ^ T C ^ ) + 0(e3) 2 with probability p / C\2 uO^-OfTCj) = uCTCpTCj) - Su^TCi.TCj) + U„(TC,.7C) + 0(63) 2 with probability (1-p) Similarly, ud^.jta+e) = utTtj.TCj,) + E U ^ I C ^ ) + U 2 2 ( T C X , T C 2 ) + CKe3) with probability p U d t t ^ - S ) = utTC^TCg) - S U J J ^ . T C J J ) + J _ _ U 2 2 ( T C 1 , T C 2 ) + (X83) 2 with probabiUty (1-p) This gives the expected utility equations EUfai gamble) = nin^) + [pe-U-ptfhi^,^) + [pe2. + ( l - p ^ u ^ i c ^ ) + (Xe 3^ 3) 2 2 and EU(7£a gamble) = nin^) + [pe-(l-p)6] u ^ i t , ) + [pe2. + (1-p® U ^ T C ^ X , ) + 0(e3,63) 2 2 Our multiplicative utility model gives the following: 84 and lire = + ky<t>22 = •Jl+ky] = •ntl+ky] Similarly, % « Y I + Y i + krVi + ky-yi = U j + yjl+ky] > u , a lways (as the bracketed term is always positive) and % = 4>u + Yn + k rVi i + M>iVi + kVvu + kr iVi * yntl+ky] + yu[l+kY] + 2k<t>1\)f1 = U a + Vud+ky] + 2kY 1Vi As the term in square brackets is always positive, the last equation yields: for y u > 0 and k > 0: u n > U22 for y u < 0 and k < 0: u u < u^ Putting these results back into the expected utility equations for the two gambles (above), and comparing these two equations term wise, produces the stated result. Note that this does not depend on the curvature postulated for The proof easily extends to more general gambles having more than two outcomes, as well as to continuous gambles. Only the terms in square brackets would change in the expected utility equations: the expectation of the gamble (the first bracketed term) and half its second moment (the second bracketed term). The stated results 85 remain the same under these more general gambles. • 86 FIGURES FOR CHAPTER 2 87 V $ (change in wealth) FIGURE 1: Prospect Theory's Value Function FIGURE 2: Riskless Value and Commitment to a Course of Action 88 1 1 K K 1 ' 2 t 1 s t 2 C ,C 1 2 FIGURE 3: The Two-Period Allocation Decision 89 0 Economic Value: A Typical ({) Function $ W (TOTAL WEALTH) + $A W (CHANGE IN WEALTH) o w 0 Psychological Value: A Typical \j/Function FIGURE 4: Decomposing Total Value 90 -150 -1000 " 150K 400 50 N 400 100? 50 100 1000 2500 FIGURE 5: Testing the Corresponding Tradeoffs Condition it. -500 -1000 \ \ 50 100 1000 2500 ic 1 +it2 FIGURE 6: Testing the Corresponding Tradeoffs Condition Breakeven-or-Better Tradeoffs 1 300 -600 •1000 " t t 4 » | \ 400 50 100 V W 2 1000 2500 FIGURE 7: Likely Tradeoffs in the Case of Sunk Costs 91 W o ' S W0 W0+7C1+7C2 s = amount already sunk on project 1 •fe - initial wealth level FIGURE 8: Representing the Sunk Cost Decision through Multiple Attributes 92 Say (0. -200) .5 (1000,100) .5 (1000,-500) .5^(0,-500) ~ .5^(0.1( 100) FIGURE 9A: Testing for Additive Utility Independence Pairs represent ( T C ^ ^ . T C ) . 5 ^ (100°. 0) Does the equivalence on (TCJ+TC ) remain the same Say (42P_,0) ~ <^ ^ ^ regardless of the value of n j (*o)2? Say TC =-S > -200? .5 ^(0,0) * 0 , " 3 0 0^ Does the equivalence on nx remain the same ~ g * » (o, o) regardless of the value of (TC^ %2) (*0)? Say (TC 1 + TC 2) = 500? FIGURE 9B: Testing for Mutual Multiplicative Utility Independence FIGURE 9: Testing The Independence Conditions for u 93 \ ^ : indifference curves for v, defined on(ic j-t- 7 r 2 ) vk = v(Tc 1+n 2 = k) (one-to-one value tradeoffs) r \ : indifference curves for u, defined on (it 1 , n2) U k ( 7 C i , 7 C 2 ) 7C, FIGURE 10: Showing the Need for Deterministic Tradeoffs 94 FIGURE 11 : Gambles in the Absence of Any Sunk Cost Effect 95 0 7T 1 + 7C2 FIGURE 12: Indifference Curves as Wealth Increases direction of increasing iso-utility k 7C 1 + n2 FIGURE 13: Indifference Curves as nx Increases 96 FIGURE 15: Gambling on Project 1 vs. Project 2 97 FIGURE 16: Determining the Risky Sunk Cost Premium 98 FIGURE 17: Decomposing Two Mental Accounts 99 FIGURE 18: Two Separate Mental Accounts 100 Chapter 3 MODELING THE SUNK COST PHENOMENON , ITS CAUSES AND SOME STRATEGIC IMPLICATIONS "The amounts invested in the past are sunk costs; neither they nor amortization of them are relevant to today's decisions." (Shillinglaw, Managerial Cost Accounting, 1982) 1. INTRODUCTION Economic analysis provides a clear-cut recommendation to the manager facing the sunk cost problem. If the objective is to maximize profits, then the allocation of funds at any point in time should be based exclusively on future (mcremental/marginal) costs and benefits. Economic models of sequential investments thus exclude the possibility of investment profiles which differ from the financially 'rational' one. Standard economic analyses, in evaluating decisions in the light of objective profit functions, have led to the popular label of the sunk cost fallacy. Yet the behavior of throwing good money after bad' persists. Throughout this paper, we will refer to the tendency of pursuing a previously committed project beyond what standard economic considerations would dictate, as the sunk cost phenomenon. The historical development of decision theory has taught us that a phenomenon stops being a fallacy' of rationality when enough rational' people consciously choose to behave in that way. The Allais Paradox (1953), for example, as well as other repeated violations of expected utility theory's independence axiom, have led many to re-define what constitutes rational' decisions under uncertainty. We believe that a 102 similar re-definition may also apply to the sunk cost phenomenon - that preferences may actually change following a sunk cost, and that conforming to these new preferences may be quite rational (in the "thin" sense of Elster (1983)). The important prescriptive issue of whether these new preferences are themselves, in some broader sense, rational (because of ego-defensiveness, reputation, or even survival value?) or irrational (maladaptive, preventing learning) will not be tackled here. However, in constructing a descriptive model of decision making, it is quite reasonable to rely on the preferences which are known to obtain in sunk cost situations - especially if these preferences can be systematically established. Our view, therefore, is that the sunk cost phenomenon is not always a fallacy, that it often results from a deliberate choice, based on the maximization of a utility function whose arguments differ only slightly from traditional economic ones. In other cases, it may still constitute a violation of the postulates of rationality, particularly when caused by systematic biases in handling uncertainty. The approach which we propose in this paper allows us to distinguish when the phenomenon results from fallacious reasoning and when it does not. To model the sunk cost phenomenon as 'rational' means that we must accommodate a slightly broader definition of rationality than the usual one. At the same time, however, we wish to be able to preserve the maximum formalism and power of traditional decision theory models. Our approach combines these two considerations. Through minimal departures from conventional notions of economic rationality, we will enhance the psychological content of the model of the manager's 103 decision making, and hence its resulting external validity. The key is obviously to identify the specific systematic departures from conventional rationality that will produce the sunk cost phenomenon. In this paper, we take the first steps towards formalizing existing explanations of the sunk cost phenomenon, as given in the psychological literature, within a utility maximization framework. We show how 'sunk cost' behavior can arise by allowing the decision maker's utility function to include considerations other than economic profits only. Our objectives are two-fold: 1. to derive the conditions on an investor's utility function which will produce 'sunk cost' behavior through utility maximization; 2. to use these basic conditions about the investor's utility function in more complex, applied environments, in order to generate economic predictions, as well as some normative prescriptions, for those situations. Our claim is not that so-called economic Violations' should be considered rational in some extended sense simply because they occur. It is not our goal to explain the sunk cost phenomenon through a self-fulfilling set of assumptions. Our wish is to model sunk cost behavior through a small modification of the concept of economic rationality.1 We believe that it is possible to demonstrate the presence of 'The analysis hinges on how far we need to relax traditional rationality to accommodate sunk cost effects, without offending the principle of an optimizing agent. 104 the sunk cost effect through very minor relaxations of traditional economic variables, thereby increasing predictive validity while preserving much of the rigor and elegance of current economic models of choice* Even if viewed as a fallacy, the importance and pervasiveness of the sunk cost phenomenon still justify its study in economic settings. As long as it is viewed as a systematic irrationality, the sunk cost phenomenon can form the basis of specific predictions. The conservative reader thus need not accept our broader definition of rationality to recognize the need for studying the economic implications of the phenomenon. Of course, escalation of commitment to a project can result from pure economic rationality for the firm or project - for example, as a result of moving down an experience curve, if switching costs are high or if sunk capital costs make a marginal additional investment worthwhile. What might first appear to be a sunk cost effect, a tendency for persisting with a committed project, may in fact be justified on purely economic grounds, based on marginal costs and benefits. The sunk cost phenomenon, as we have defined it, entails psychological costs of switching that exceed purely economic switching costs. In other instances, what appears to be a sunk cost effect can be wholly attributed to economic considerations on the part of the manager. As pointed out by "Along the lines of Popper (1959), we propose a model of the sunk cost effect which has some degree of refutability, in order for the resulting theory to be more powerful. 105 Staw & Ross (1987a), perseverance, especially perseverance in the face of adversity, is a quality highly valued by society. Perseverance with struggling courses of action, as well as "consistency" in decisions both contribute positively to the manager's reputation as a decision maker - especially under asymmetric information, where the desirability of persisting with a committed project is information privately held by the manager. In such situations, the manager's reputation (which influences his earning potential) becomes an important component of bis decisions. Under these conditions, a manager may well display the sunk cost effect and persist with a committed project beyond the point that is financially optimal for the firm. The sunk cost effect can therefore result from inappropriate managerial incentives: where the manager's self-interest3 clashes with the firm's economic objectives as they apply to the committed project. Differing incentives are not new to economic theory: they are at the heart of the principal-agent problem. In this case, reputation effects enter the manager's personal utility (Net Present Value (NPV) of compensation) function. In maximizing this utility function, the manager will often persist with the committed project, ensuring that he does not disclose the information which, from the firm's perspective, would have supported abandoning it. From the firm's position, a sunk cost effect results.4 Kanodia, Bushman & Dickhaut (1988) examine the sunk cost phenomenon in this light, as an effect driven by information asymmetries between principals and agents, and by "agency theory rationality" that 8This may include long-term reputation effects as well as short-term compensation. 4Of course, the firm may never know the (ex ante) economic merit of the decision to escalate. Because of information asymmetries, it can only observe that there was increased investment in the committed project. 106 includes reputation building on the part of the manager. The rational framework which we propose should help reconcile the behavioral and economic explanations of the sunk cost phenomenon. More generally, we hope that the methodology we present can be extended to bridge traditional lines of research in problems encompassing both rich behavioral and economic aspects, crossing the disciplinary boundary between psychology and economics. The paper is laid out as follows. The next section presents a typology of causes for the sunk cost phenomenon. This typology presents a number of psychological causes as complements to conventional rationality arguments proposed in the economic literature. Section 3 proposes a micro-economic definition of the sunk cost phenomenon within a simple two-period allocation model. We relate this definition to the psychological causes of the sunk cost effect and show that a utility maximizing, micro-economic framework can indeed incorporate departures from traditional economic rationality. In section 4, our utility maximization model is extended to two-person strategic games, to see how the presence of the sunk cost phenomenon affects the outcomes of competitive situations. Conclusions and future research directions are discussed in the final section. Mathematical proofs are given in an appendix. 'Staw & Ross (1987a, 1987b) discuss some of the organizational solutions, including appropriate managerial incentives, that can help mitigate the occurrence of escalation. However, optimal managerial incentives to reduce escalation behavior have not been formally established. This remains a potentially rich problem for agency theory research. 107 2. A TYPOLOGY OF CAUSES Some of the psychological causes of the sunk cost phenomenon were reviewed in the first chapter of this dissertation. These and other causes are shown in Figure 1, which summarizes the various ways in which an apparent sunk cost effect can take place. The classification breaks down additional commitment according to its degree of conformity to 'economic rationality'. It shows that individual rationality goes beyond the binary distinction of rational versus irrational, of optimal versus sub-optimal. Observed behavior may still be modeled as rational, even though it violates strict economic optimality. In all but the last line of Figure 1, we can model choices as resulting from utility maximization. This points out that we need not always impose additional economic factors to our models of choice in order to explain or predict behavior. Cases 1A and IB in Figure 1 represent pure economic rationality on the part of the manager, utility maximization based on economic arguments. Cases 2A and 2B model choices through utility maximization, but with different subjective parameters. In case 3, choices result from utility maximization, whose parameters are fallacious. Case 4 represents all other kinds of choices, falling outside of utility maximization. Choices in cases 3 and 4 are the only ones which we could qualify as 'non-rational'. Further knowledge concerning the basic psychology of the sunk cost phenomenon would be helpful in formulating an accurate economic model of the problem, as well as in identifying applied situations in which the effect is most likely to prevail. But even a coarse understanding of the psychology underlying the 108 phenomenon is sufficient to formulate a utility maximizing model of sequential investment, and to perform the resulting economic analyses in various applied settings. Conversely, it is our hope that determining the type of utility function that leads to a sunk cost effect can shed light on the behavioral determinants of the phenomenon. Finally, modeling the sunk cost phenomenon may help reveal the potential of a utility maximization approach for modeling general problems of behavioral choice. 3. A GENERIC MODEL OF THE SUNK COST PHENOMENON UNDER UTILITY MAXIMIZATION Consider an investment situation in which funds must be allocated over two competing projects. There are two time periods. At time t0, one must decide on the amount Sj to be invested in project #1. Project #2 is unavailable at t0. At time t^  the remaining funds are allocated over the two projects: c: and c^ 6 Revenues resulting from these projects are assumed to follow the functions ra = r^Si.Cj) for project #1 r8 = r^Cg) for project #2 All revenues are assumed to be received at the end of the second period. Profits for the two projects are therefore defined as 'This formulation can also accommodate the case of more than two projects at tlf by simply considering project #2 as a composite of all alternatives to project #1. Project #1 remains the focus, as it is the one into which costs have been sunk. 109 K ^ S ^ C J ) = r1(s1,c1)-81-c1 ,and The time-line in Figure 2 depicts the situation. — Insert Figure 2 here The total funds available for investment over both periods are F.7 With little loss in generahty, no time discounting between t0 and tt is assumed (which would be the case for very short time periods). The investor is seeking to maximize his utility function resulting from this 2-period project allocation. The key departure from a traditional neo-classical economic analysis of the problem lies in the arguments that enter his utility function, or more specifically in the way the arguments impact on his utility. In an analysis of the sunk cost phenomenon, it is critical to note that considerations other than just pure economic profits come into play. These other considerations, as well as the impact of economic profits, must be captured by the investor's utility function. Specifically, the investor's commitment to project #1 stems from the cost sx that has been sunk into it. 'Because TC, is an aggregate of all other possible uses for the firm's funds (i.e. an aggregate of all other projects), it is not unreasonable to talk of a budget constraint. Our strict representation of a budget constraint may also be valid in many organizational contexts, where divisions are allocated fixed pots of money and divisional managers are pretty much limited to those fixed amounts. Without a budget constraint (i.e., under unlimited access to financing) we may still have a sunk cost effect (e.g., chapter 2 has no budget constraint), but it then becomes difficult to define an observable escalation effect (below). In this chapter, we have a particularly extreme form of a budget constraint. A natural generalization of this is to have the firm borrow money. As long as the interest rate is increasing and other mild conditions are satisfied, this is equivalent to having a budget constraint. 110 The sunk cost sx therefore becomes a second argument in the utility function, along with economic profits. The investor's optimization problem, therefore, is: max uCjtjCs^c^TC^Ca), 6^ s.t. F - 8j - Cj - Cj = 0 max u f r ^ B ^ C i ^ B i - C ! + r ^ C a ) - ^ , s^  s.t. F - - Cj - Cj, = 0 8i>Cj,C2 In reduced form, this becomes: max ufc j .c^Si) s.t. F - sx - c x - Cj = 0 3.1 One-Period Analysis: The Decision at tx Let us decompose the problem and examine the one-period situation at tu where s1 = s has already been invested in project #1 at t08. The analysis that follows applies equally to deterministic utility maximization, in the case of a deterministic decision at tx, or as the reduced form of SEU maximization, in the case of a decision under uncertainty at t^  With s already invested at t0, the optimization problem at tj becomes: There may be advantages to early investment at t„. Early investment of s may generate greater revenues from project #1 at tx, with the resulting positive impact on the utility function. I l l max uCc^ c^ s) s.t. F - s - ct - Cj = 0 (0) Derivation of the comparative statics results for this maximization problem is presented in Appendix A l . The following results emerge: sign (dcj/ds) = sign (-uM + u^ + u u - U g . ) (1) and sign (dca/ds) = sign ( u u - u^ - u u + ) . (2) The purpose of deriving these comparative statics results is to determine the characteristics of the utility function that will lead to a sunk cost effect at tj. Letting cJ be the utility maximizing allocation to project #1 at tj, an escalation effect is denned as ^ > 0 . (3) ds This is our fundamental behavioral characterization of escalating commitment or persistence: the greater the amount sunk in a project at t0, the greater will be the subsequent investment in that project at tj. It is intended to capture the increased psychological commitment associated with an increase in s. But it differs somewhat from our previous definition of the sunk cost phenomenon as a further commitment to project #1 beyond what is economically rational. Neither definition implies the other: On the one hand, c\ need not be monotonically increasing in s for investment in a project to exceed the economically optimal point. Conversely, there may well be 112 cases in which dc^ /ds > 0 is based purely on economic considerations - for example, under significant intertemporal economies of scale in project #1. Under intertemporal economies, one is better off investing smaller amounts sequentially in the project, either because learning occurs or because congestion diseconomies make a larger one-time investment in the project at to uneconomical. Despite these differences, this comparative statics definition of an escalation effect provides an observable and operational representation of increasing commitment: where increasing the sunk amount changes the optimal allocation at tx in favor of the committed project9 (and reducing the sunk amount means a decrease in Cn) . A slightly different characterization of the escalation effect is simply u t a > 0 . (4) That is, as sx increases, the marginal value of investment in q increases. This is not a behavioral characterization but is based instead on utility considerations, and is neither necessary nor sufficient for (3) to hold. As we shall see below, however, the two representations of the escalation effect are closely related. "This result is assumed to hold for all possible levels of s, and thereby excludes realistic but more complicated cases for which c\ might first increase with s, but then actually decrease beyond some threshold value of s. However, our characterization need only hold locally, around the optimal allocation cj, for the ensuing analysis to be valid. 113 Our distinction between a "sunk cost" effect and an "escalation" effect points out the definitional difficulties and confusion which have surrounded the sunk cost problem. Loose intuitions about the sunk cost phenomenon give rise to different formal definitions and model-dependent operationalizations. Our continuous variable setting, for example, requires a different definition from a discrete 'continue/discontinue' decision at tj. A universal formalization of the sunk cost effect can only come from a behavioral model capturing the intuition of psychological commitment to a project beyond economic optimaiity. Such a model was developed in chapter 2, where we also established the formal link between that model and our comparative statics definition of escalation, above. Throughout the present chapter, our focus is on the escalation effect as defined above. Applying our previous comparative statics to (3), the escalation effect occurs when - U j a + U J B + U „ - UJJ. > 0. As part of our problem formulation, it is assumed that revenues for each project, r t and r^  are not directly influenced by allocations to the other project, so that we get r^ c^ s) and r^). In addition to this 'project independence', we also assume (for simplicity) the utility function to be additively separable, which implies = = 0 -- no mixed terms in the utility function. This means that the utility resulting from 114 a joint allocation can be expressed as the sum of a utility for project #1 and of a utility for project #2. In essence, this assumption requires utility to be linear in dollars - so that overall utility is additive in the two projects. Under separable utility, the escalation effect therefore arises if and only if u u + Uaa > 0 . Under the additional assumption of strict concavity of the utility function (which also results from symmetry of projects under |J|> 0), we have < 0. So in this case, not only do we need u u to be positive (consonant with our second characterization of the effect), but it needs to be large enough to overtake the concavity u^ if escalation behavior is to occur.10 These conditions are sufficient for an escalation effect (as we have defined it in (3)) to take place at tj. But it must be kept in mind that these conditions on u can also be the result of pure economic rationality on the part of the investor. In particular, economic (profit) considerations alone may lead to u^ > 0, or to u u > 0, and (3) may result. u u , for instance, measures how the marginal effectiveness of investment in project #1 (at tx) changes with the amount already sunk in the project. The example of intertemporal economies of scale in project #1, alluded to earlier, would imply u u > 0. Additional behavioral considerations about the sunk cost will 10This condition: |u u | > lu l^ , is necessary for the STRONG version of the escalation effect. See below. 115 simply be one more factor to enter into uu, pushing the decision at tj in the direction of the escalation effect. We must therefore interpret escalating commitment with care: our comparative statics definition of the escalation effect may not always be incompatible with traditional economic rationality, u^ is purely economic, while u u can be economic and/or psychological. Under the current formulation, condition (3) is somewhat stronger than we may like the escalation effect to be. A change in s imposes an income effect on the funds available for investment at tx, as can be observed in our budget constraint: Increasing s reduces the total budget (B) available for investing in CJ+CJ at tv thereby imposing an income effect which acts in the direction opposite that of the escalation effect in (3). c\ is therefore directly a function of s (because of the escalation effect), as well as of the budget remaining at tj, B, which is itself a function of s. Hence, we have q(s3(s)). Cj + C2 = F - s. Therefore, dT rani L p a a a a t e d + dc\ dB 3B ds (5) t total effect T substitution effect t income effect 116 Thus, while the escalation effect (substitution effect) may be present, unless it is strong enough, it may get erased in (5) by a greater income effect. The following definition makes the distinction clear. Definition: 1. An investor for whom dc) 37 comptnaatsd > 0 will be said to display the WEAK escalation effect. 2. An investor for whom dc] > 0 (total effect) will be said to display ds the STRONG escalation effect. The WEAK effect is a necessary but not sufficient condition for the STRONG effect to occur. Having made this distinction, we can use a comparative statics analysis to derive conditions on the shape of the investor's utility function that will translate into WEAK escalation behavior, just as we did for the STRONG version in the preceding In the WEAK effect, a change in s needs to be compensated by an equivalent change in F, such that F - s = constant, in order for (Cj+Cj) to remain constant. Our comparative statics characterization of the WEAK escalation effect (detailed in Appendix A.2) gives us the following result: analysis. 3cj 37 > 0 if and only if u t a - Ua, > 0 . (6) 117 This is necessary and sufficient for the WEAK escalation effect. Note that when utility is separable, then = 0 , and condition (6) simply becomes u u > 0 - which is our characterization (4)! Table 1 summarizes the conditions on the utility function leading to the two types of escalation effect, under the separable utility assumption. Effect STRONG Effect d C l > 0 YES UH+UJB > 0 ds NO Uu+Uja £ 0 U22 n o t « 0 Uaa « 0 is the dominant effect > 0 £ 0 Uaa » 0 U22 n o t » 0 Table 1 The key consideration throughout Table 1 concerns the relative magnitudes of u„ and U Q . These will entirely determine the occurrence of the escalation effect in our present formulation of the problem. Interpreting the case of dependent projects, or of non-separable utility (both resulting in u u *• 0), is substantially more tedious, and adds little to the intuitive 1 1 8 understanding of the sunk cost phenomenon. Suffice it to say that specific dependencies among projects, which can be temporal (in going from t0 to tr) or atemporal (between cx and C j directly), can create apparent escalation effects purely out of economic profit maximization. 3.2 Two-Period Analysis: Recursion to t„ Having characterized the sunk cost phenomenon (and its relation to an escalation effect) in the static allocation decision at t^  we can now examine the intertemporal allocation decision at t0 to determine the causes and implications of the phenomenon in a multiperiod setting. In a two-period model of utility maximization, we examine not only how the sunk cost phenomenon can arise, but also how planning for its occurrence can help mitigate its effects. We focus in particular on the relationships between perfect foresight, recursive rationality and the sunk cost effect. The FOC's in equations (A1MA3) can be solved to obtain the optimal investment profile at tj as a function of s: CI(B) and <£(&), whatever the specific value of s may be. Backtracking one period, the optimization problem at t0 now becomes max u"(c (^s1),c2(81)^ 1) s.t. Si £ F (sx £ 0), where the results of the optimization at tp under recursive rationality, form recursive inputs to u°. In reduced form, this becomes 119 max irXsj) s.t. B t S F 2 0 ) . It is important to note that u° need not equal u, used in the optimization problem at tj. u° must capture some advantages to early investment in project #1, BV For if there were no advantage to investing some amount into BV the total availability of funds F would simply carry over to and be allocated at that time. Any 'sunk costs' would vanish. Similarly, if B\ £ F, there are no funds left for allocating at tx and again, the sunk cost problem vanishes. The case of interest is therefore the one where the constraint in the optimization problem at t0 is non-binding, i.e. 0 < sj < F . The analysis that follows is restricted to this case. With no binding constraint, the decision problem at t0 becomes one of unconstrained optimization of u0^). At the maximum, we need du° n , dV A = 0 and < 0 . dfij ds2 The FOC can also be expressed as du° = du° dq + du8 del + du° = Q ( ? ) ds1 dcx dsj dej dsj ds! + + + + Assuming u° to be monotonically increasing in its arguments (the amounts allocated to the two projects), and under the Strong escalation effect, the signs of the various terms are shown above. 120 We note that under the Strong escalation effect, dc* > del Hs7 os7 because the change in c, must also include the income effect, which is in the same direction. As well, dc^ dst < -1. This can be seen by noting that we must have F-Sj = Cj+Ca . Increasing sx by e means that we reduce (F-sx) by e, which translates into reducing (q+Cg) by e. And since we know that the Strong escalation effect implies that cx increases with an increase in s1( for (cj-t-Cj) to decrease by e means that Cj must decrease by more than e. Little can be said about the relative magnitudes of the other terms, except perhaps that none of the three terms is likely to 'overpower' the other terms (as a condition at t0 for the Strong escalation effect to occur). 3.2.1 Modeling the Various Causes of the Sunk Cost Phenomenon This two-period analysis helps clarify some psychological issues, not captured by our formalization of the escalation effect in (3) or even in (4), that provide behavioral insights into the various causes of the sunk cost phenomenon. Particular parametrizations of the utility function help characterize these causes. In these parametrizations let TC represent the economic profit function, and x^ s.^ ) be the behavioral component of the utility function supporting the (Weak or Strong) sunk cost intuition. In the current structural formulation (as presented in Figure 2), where the revenues accrue at the end of the second period, we have the following 121 possibilities: Case 1: u° = u1 = jcCs.c^ Ca) In this case, recursive optimization does not allow for a psychological sunk cost effect to occur, and the dependence of u1 on s is purely economic (i.e. some early investment s in project #1 may be desirable because of discounting, for example). This is the classic economic problem, in which incremental economic optimization disregards sunk costs other than for their life-cycle, economic impact on TC (see Northcraft & Wolf, 1984; Tang, 1988). The preceding comparative statics analysis still holds, but has a purely economic interpretation. Case 2: u° = TcfoCj.Cjj); u1 = Tcte.Cj.Ca) + y(8,Ci) This is the situation where the utility function is actually modified at tj to reflect the psychological impact of the presence of the sunk cost s. As it is formulated here, the investor knows from the start that he will be psychologically influenced by any sunk cost and that he will exhibit a sunk cost effect - it is beyond his control, once sunk costs have occurred. All he can do is make the best of the situation by recursively incorporating this knowledge - about his tendency to display the sunk cost effect at tx - into his optimal selection of S j at t0, arrived at through a purely economic u°. This is in the spirit of the work on precommitment and self-control (Elster, 1979; Thaler & Shefrin, 1981; Schelling, 1984), which explores behavioral strategies for protecting oneself against future "weakness of will", and a changing utility function, 122 occurring under some states of nature. Case 2 has a strong prescriptive flavour. It suggests that investors who fall prey to the sunk cost effect should account for it by including that knowledge into their optimization problem at t0. Precommitment is simply the result of recursive rationality, which forms the basis of the dynamic programming solution to the multi period investment problem. The key is to recognize from the start that the utility function at t0, which reflects only economic considerations, will no longer be the appropriate utility function for tj. Our formulation allows for the decision being confronted at t„ to be either deterministic or probabilistic. But under the assumed perfect recursive rationality, the presence of a psychological sunk cost effect is premised on the investor obtaining a *bad' outcome at t0 - which suggests the need for some uncertainty to be present at t0.12 With that uncertainty, face saving, post-decision dissonance reduction and regret mitigation all become compelling psychological mechanisms supporting persistence with project #1 at tv to justify the unsuccessful initial allocation s.13 In "Akerlof & Dickens (1982) also identify precommitment contracts as a means of mitigating the effects of cognitive dissonance. "Other psychological causes of commitment or attachment to a particular project, such as Thaler's "endowment effect" (1980), will not be considered here. Formally, we allow uCc^ Cj.s), the utility function at tu to differ from the traditional economic uic^c^) only by the psychological factors that stem from sunk cost considerations (discussed in section 2), and not by any other psychological influences. A completely deterministic setting may admit these additional influences, but does not admit a commitment based on our psychological explanations of the sunk cost phenomenon. 13This holds true regardless of the direct economic influence of s on the payoff in the second period. 123 fact, all of the psychological mechanisms leading to the sunk cost phenomenon discussed in section 2 (even prospect theory arguments) are premised on the sunk investment at t0 resulting in an unsatisfactory outcome before iv Such an outcome will not occur in a world of certainty and perfect recursive rationality, where the result of investing s at t0 can be foreseen perfectly. The presence of uncertainty at t0 is therefore essential to the psychological sunk cost phenomenon, making the decision at t„ a probabilistic one (see Figure 3). — Insert Figure 3 here — The allocation problem thus far can therefore be framed as one having uncertainty at t0 which gets resolved before tx, and where the second time period is entirely deterministic. Maximization of the utility u° at t0 simply needs to be interpreted as SEU - rather than deterministic utility - maximization. • Our formulation can also accommodate an alternative situation, in which the decision at te is deterministic. This purely detenninistic, complete foresight 2-period case is much more difficult to justify as an actual sunk cost situation. Nonetheless, without uncertainty at te, our model can still capture important Variants' of the sunk cost phenomenon: specifically, situations in which some investment s is warranted, but where preference changes occur at tx as a result of the investment s. Consider the dilemma you face on a Sunday afternoon: you need to work on a paper, but would like to watch the first quarter of a football game on television. Your prior preferences are ordered as follows: watching one quarter >p watching no football >p watching the 124 whole game. In accordance with these preferences, you settle down to watch one quarter of football. The problem you face is that after Investing' your time watching the first quarter, your preferences change so that you want to invest just 'a few more minutes' to the game. After those few minutes, the process repeats itself, and you eventually become trapped. You end up watching the whole game - instead of only one quarter, and experience regret for having wasted away the afternoon. We could classify this situation as one of 'addiction' or habit formation. The change in preferences is not the result of justifying past investments of time. But even though the cause of the preference change is not rooted in the sunk cost phenomenon, the resulting observable behavior is the same - and can be accommodated by our model. The essence of this completely deterministic problem lies in the change in the investor's utility function that occurs after investing s. The premise of the two-period recursive analysis is that the investor knows at the start of tc that his utility function will be changing. While this assumption may be somewhat dubious in many empirical settings, it does permit the generation of specific predictions. More importantly, however, recursive rationality can be used as a prescriptive model, to help make precommitment decisions in order to satisfy the appropriate set of preferences. Say that you wish to satisfy your prior preferences - which are the ones under which the initial decision, at t^ , gets made. You can use the knowledge that your preferences will be changing after watching one quarter of football, to precommit to watching nothing at all - to avoid becoming trapped into watching the whole game. • The objection could be made that in a complete foresight case, the prior 125 knowledge of displaying the sunk cost effect at tj would preclude any investment into Sj at t0. But this is not necessarily so. An initial investment of s may be justified in SEU terms, even with the knowledge that there will be a sunk cost effect at tv [The same goes for detenninistic decisions at t0 : some non-zero investment s may be warranted, even though one recognizes beforehand his compulsion for 'overinvesting' in committed endeavours.] The amount of the investment 8 may simply be tempered by the knowledge that an unsuccessful outcome at t0 would result in a psychological commitment to that project. Case 3: u° = rcts,^ ,^ ); u1 = vrXsfi^) + y(8>ci) A somewhat different sunk cost situation is one where the manager 'inherits' a situation, at some time prior to tj, in which an investment of s has already been made at t0. The self-justification aspects are obviously absent from this case, and so may any sunk cost effect (yCs,^ ) = 0). Still, the investor may be compelled to pursue the committed project in order to salvage the investment, and may thus impose some sunk cost considerations (yte.q) * 0) on his decision at tv Alternatively, the investor may have plainly made a 'mistake', not optimizing on the true rcCs.c^ Cj) at t0 - in which case face saving aspects may be quite salient in his decision at tv Such a 'mistake' could have resulted from the blind allocation of funds to project #1, without having completely evaluated the full consequences of that allocation. The investor may thus persist with project #1 beyond what is economically rational, as a way of justifying his previous choice • trapping him into a sunk cost effect. We obviously cannot formalize 'making a mistake' (in general terms) in our model of the decision at t0. We simply state that the realization of having made a mistake can lead to a systematic sunk cost 126 effect. The Case of Myopic Decision Making A different category of decisions, falling under the umbrella of Case 3, can also trigger a sunk cost effect at tj. Consider a situation in which only the possibility of investment at te is known. The possibility of further investment at tx is not recognized. It becomes necessary in this case to assume that both projects are available at t0, i.e. that investment at t0 goes into sx and respectively (otherwise there is no decision at tc). Then at tv extra funds become unexpectedly available and a further allocation decision into Cj and Cg takes place. This second allocation may well be subject to a sunk cost effect, as a means of reconciling this allocation with the first. Revenues at the end of the second period will be a function of total investments: r i = ^ ( S i . C x ) and r2 = r^s^Cj). Figure 4 illustrates the situation. — Insert Figure 4 here — The resulting utility functions being maximized will be: u° = ifCsyS,) and u1 = jrt(s1,s2,c1,ca) + ^ . s ^ c ^ C a ) . The conditions for a sunk cost effect are less clear here, as there may have been investment into both sx and s2. Establishing these conditions via a comparative statics analysis (as above) would require a clear interpretation of sunk cost behavior when both Si and ^ are non-zero. In any case, the sunk cost effect will be present here if 127 V f e p S ^ c ^ C g ) * 0, and absent if yU s^^ c^ c,) = 0. Such myopic situations can lead to sunk cost effects. Some would argue that the possibility of obtaining further funds should be recognized and incorporated into the decision problem at te, making the initial allocation a recursive decision under uncertainty of future funds, rather than a myopic 1-period allocation. Prescriptively, this is obviously the case. However, just as having made a 'mistake' at tD can be a strong motive for self-justification, so can myopia, as it too can be construed as a form of mistake.14 3.2.2 More on Myopia: Failing to Foresee the Sunk Cost Effect The preceding two-period analysis, and in particular the decision at t0, rests on an assumption of perfect foresight: that any change in utility brought upon at tt by a sunk cost effect can actually be planned for in the decision at t0. But in many cases it is quite possible that the change in utility caused, for example, by self-justification or cognitive dissonance, may not be foreseen at the beginning of t„. In such cases, the perfect recursive rationality assumption, as exhibited in Case 2 above, must be relaxed to accommodate such 'utility myopia', thereby opening the door to very credible decision situations, even in deterministic settings. Consider a 'myopic' investor confronted with our 2-period investment problem. l4How common such myopic decisions are is an empirical question. 128 Suppose that he is currently at t0. He knows his economic profit function ic for both time periods, but doesn't realize that once at t^  bis utility function will be modified to include sunk cost considerations. Hence his allocation sx will be determined by recursion of his profit function n, rather than his actual utility function u1 = TC + y , into the decision at t„. The investment 8 l f which would have been optimal with respect to his profit function TC had the utility not changed part-way through, will no longer be optimal under u1. Not realizing that he would come under the influence of a sunk cost effect, the investor could not protect himself by planning ahead and decreasing his investment in BV The resulting allocation will be too heavily weighted towards project #1. The "price" of myopia - of not having anticipated a sunk cost effect - can be measured by computing the difference in TC obtained under the two competing allocation profiles. 3.3 Modeling the Presence of Uncertainty at tx The preceding analysis has provided conditions on the investor's utility function that lead to his displaying the sunk cost effect with a deterministic decision at tv Having laid down this methodological groundwork, we can now extend the analysis to account for the presence of additional uncertainty at tv Just as uncertainty at t„ is crucial to the presence of the sunk cost phenomenon, most realistic/common instances of the sunk cost effect also involve the presence of uncertainty at tx as well. Truly deterministic decision situations are rare indeed. In a thorough analysis of the sunk cost phenomenon, our stylized decision problem 129 formulation should therefore capture this important factor. A number of simple situations can be formulated around a common generic structure, capturing the uncertainty at tj. See Figure 5. There, rx and ra are probabilistic functions of sx, ct and c^ . Different situations may differ in their specific payoff structure (the timing of the payoffs or the time at which the uncertainties get resolved) and the nature of the uncertainties present (binary, discrete, continuous) -as was the case for uncertainty at t0. — Insert Figure 5 here — In the case of uncertainty at both time periods, the decision criteria become: att^ max SEU1 (s^ sXc^ s)) cl,c2 i which feeds recursively into att0: max SEU0 (a^ 81 The u functional in the previous analysis can be interpreted as a reduced form of the uncertainty case. The derivative conditions on u remain the same under uncertainty. However, the greater number of degrees of freedom in SEU models allow us to separate utility considerations - reflecting a change in preferences that occurs at ^ following a sunk cost - from probability considerations as causes of the sunk cost effect. The different components of SEU therefore provide or represent different 130 behavioral insights about the phenomenon. Exploiting the utility versus probability distinction may allow us to make more accurate predictions about the sunk cost effect. Utility effects have been the focus of most of the prior work on the sunk cost problem. We will not dwell upon them here, as they were the focus of chapter 2, in which we proposed a new behavioral decision model of the sunk cost phenomenon. Instead, we concentrate here on probability aspects, and on their impact on the sunk cost effect, when combined with a conventional utility function. Modifying Beliefs: Modeling the Sunk Cost Phenomenon as the Result of Non-Bayesian Learning Experimental evidence supports the contention that a sunk cost effect can result, in whole or in part, from systematic probability biases at tx15 (Knox & Inkster, 1968; Arkes & Blumer, 1985, p. 130; Staw & Ross, 1987a, p.70). Two distinct intuitions may be seen to contribute especially to these probability distortions: a) Consider the case of two independent sources of uncertainty: one at t0 and one at tv Not recognizing the independence of the uncertainty in the two periods, the investor may exhibit the gambler's fallacy. The fallacy results from the local application of a long-run concept: that luck' has a tendency of catching up with you. 16The psychological causes that would lead to adjusting/biasing beliefs rather than preferences are not clear. In our deterministic analysis, we could only modify the utility function. In the probabilistic case, post-decision dissonance reduction can affect both subjective payoffs as well as subjective probability estimates. 131 The resulting view is that chance is a self-correcting process (Kahneman, Slovic & Tversky, 1982). The fallacy can systematically bias probabilities positively or negatively: failures will be judged more likely to follow a series of successes; while in the wake of past failures, subsequent successes will be judged to be more likely. The sunk cost situation arises at tj because of previous failures. The investor may therefore inflate his chances of success at tj, thinking that project #1 is "due to turn out well". b) Wishful thinking may act to inflate the subjective chances of successful outcomes. Here, cognitive dissonance is reduced by changing beliefs, just as it was reduced by modifying preferences in the preceding analysis, in which subjective payoffs got inflated following sunk costs. Wishful thinking may also result from an "illusion of control" over the uncertainty, which psychologists (for a summary, see Wortman, 1976) have often found to accompany involvement in uncontrollable risky activities. Obviously, systematic probability biases can also result from the many heuristics which are regularly used in handling uncertainty (see Kahneman, Slovic & Tversky, 1982). The simulation heuristic, for example, may be especially active in generating both the gambler's fallacy as well as wishful thinking biases. While the gambler's fallacy can be viewed (and modeled) exclusively as a probability effect, wishful thinking relies on an explicit dependence between posterior beliefs and the sunk amount s. This dependence makes it difficult to formulate an 132 exact model of wishful thinking, although some comparative statics results can be obtained. Beliefs get modified in the direction of increased probability of'success' for the committed project. The magnitude of the wishful thinking bias in beliefs can be postulated to increase with the amount of the sunk investment s. Under that assumption, we can characterize the resulting change in the subjective belief function as a first-order stochastically dominating shift in the probability distribution of outcomes. This is a rather mild yet powerful characterization. Even if wishful thinking results in increasing the subjective probability of a single successful outcome, the effect will be a first-order stochastic dominance shift in the outcome distribution.16 Through comparative statics, it is relatively easy to demonstrate, for a large family of situations, that an escalation effect (as we have defined it in (3)) results from such a probability distortion. The expected utility maximization problem at tj is: max fyriu(c1,x;c2,y^ )dF(x^ )dG(y) C x , C j (9) s.t. F - s - Cj - Ca = 0 In this formulation, u is now a vN-M utility function. It is a function not only of the investment levels clf Cg and s, but also of a random variable x capturing the uncertainly in the return for project #1 and of a separate random variable y capturing 16The stochastic dominance shift arguments also hold for the gambler's fallacy, although the magnitude of the shift may not necessarily increase in s, which is required in the following analysis. 133 the uncertainty in the outcome of project #2. Variables x and y can represent the uncertain returns per dollar invested in each project - the case of stochastic constant returns to scale (Arrow, 1971). This assumes that x and y are independent of q and Cj, respectively17. We also assume x and y independent of each other.18 Variable x has density dF(x;s), s being present to account for biases in subjective beliefs, e.g., wishful thinking. Variable y has density dGXy). Since the comparative statics result in (1) is valid as a generic representation of the uncertainty case, we can use it as a starting point for comparative statics under uncertainty. We get: sign (dcx/ds) = sign ( -u^ + + uu - u^ ) Six separate terms therefore need to be signed. This is done in detail in 17In the more general case of x(cx) and jKcj), the lack of separability between the amounts invested and the random returns also makes it impossible to sign the comparative static without making a number of additional assumptions. Without independence, the second order parti als in (10) become quite complex integral expressions. "Assuming correlated risks (x and y) requires additional assumptions in order to sign the comparative static. = sign (-ffu12dFdG + ffu^dFdG + f [/(uudF + UldF.)]dG -/[/(u2ldF + uadF.)]dG) = sign (-ffu^dFdG + ffu^dFdG + ffuudFdG + ffUjdF.dG (10) 134 Appendix A31 9. The resulting comparative statics equation ((A20) in Appendix A3) is: sign (dq/ds) = sign (-ffuudFdG + ffUadFdG + ffuudFdG + / / u ^ . d G 0 0 + - //ua.dFdG - //uadF.dG). (11) 0 0 So in the case where there is no escalation 'utility' effect, the stochastic dominance shift in the distribution of x has to be large enough to overtake the curvature u^ in order for a STRONG escalation effect to occur. We note that our characterization of the WEAK escalation effect in (A15) also leads us to a weaker condition in the probabilistic case. Our deterministic condition u u - U j , > 0 is equal to only the last four terms in (10) above. Under our assumption of separability, a positive fourth term implies the WEAK escalation effect. Therefore, any change in beliefs resulting in a stochastically dominating shift in the distribution of x will cause a WEAK escalation effect under the present set of assumptions.20 Obviously, if a 'utility' escalation effect is also present, then a stochastically dominating shift in x will contribute to an even greater (Weak or Strong) escalation phenomenon. 19Signing this requires the additional assumption of a strictly concave utility function, separable in the two projects. "fey symmetry, if s results in a stochastically dominated shift in dG, the distribution of y, the results just obtained still hold true. 135 4. ANALYSIS OF SOME TWO-PLAYER STRATEGIC IMPLICATIONS Some key research questions concern the strategic implications of the sunk cost phenomenon. Specifically, can one exploit an opponent's sunk cost effect to gain a strategic advantage and improve one's position? Conversely, is it always strategically undesirable, in terms of purely economic profits, for a player to display the sunk cost effect? We now turn to these and related questions. There are several 2-player structures that extend the 1-player structure of Figure 2. The basic 2-player situation which we will examine is portrayed in Figure 6. — Insert Figure 6 here — In this case, Player B has no control over the amount sunk into s by Player A. Under the assumed perfectly recursive Nash solution, B can only use his knowledge of A's failure to ignore sunk costs, in his Nash utility optimization at t1. Final outcomes will depend on the form of both players' utilities entering the Nash solution. [Note: We can think of sA as determining which of several Nash games will be played at t}. Because of the recursive determination of s* from the Nash solution at t lt Player B can only mdirectly influence A's choice of s through his allocation decision at tj. But because B cannot precommit or signal any departure from his Nash allocation prior to his decision at tx, he will have no choice but to play his Nash move in the game chosen by A through A's choice of s\ Player A therefore enjoys a clear first-mover 136 advantage.] From Player A's perspective, the problem is structurally similar to Case 2 of our 2-period, single-agent analysis. The only difference is that Player A now recursively feeds back his Nash allocation at t» rather than his constrained single-agent optimal allocation, into his optimal determination of s at t0. A single-period analysis (at t^  of the two-player situation will help shed light on the strategic advantages resulting from Player A displaying a sunk cost effect. In order to perform the 2-player comparative statics analysis, we will simplify Player A's situation by incorporating his equality budget constraint [F - s = cx + aj directly into his utility function (i.e. by substituting C j = F - s - Cj ) , transforming it to an unconstrained problem. The same can be done with Player B, so that he too in effect has a single decision variable in an unconstrained utility maximization problem. [Although B's problem may be unconstrained to start with.] This helps keep the number of variables down, although by the same token we may lose some comparative static information. We therefore examine the situation at tj, in which s has already been sunk into project #1 by Player A at t0. The resulting optimization problem at tj is: for Player A: max u*(a,b*,s) = 7C*(a,b\s) ( + \|Ks,a) if the sunk cost a effect applies) for Player B: max uB(a*,b,s) = jr^ a'.b.s) b 137 where a represents Player A's investment in project #1 at tj, and b represents Player B's investment in project #1 at tv [Project #1 is common to both players (e.g. a joint venture or a competitive project), while project #2 is not, i.e. represents a different project for A and B.] A comparative statics analysis of the Nash game played at tj provides insight into the impact of the escalation effect on the resulting equilibrium allocations. See Appendix A.4. We get: for downward sloping reaction functions: da* > 0 and db* < 0 ; ds ds for upward sloping reaction functions: da* > 0 and db* > 0 . ds ds These results have a nice intuitive interpretation. As Player A's sunk costs in project 1 increase, A's tendency to persist with project 1 also increases - accompanied by a shift in his reaction function. B's profit function, on the other hand, and hence his reaction function, are unaffected by a change in s. Hence, an increase in a* leads to a decrease in b* as we move down B's downward sloping reaction function, or to an increase in b* as we move up B's upward sloping reaction function. 138 4.1 Sinking Costs as a Precommitment Strategy: Using your Sunk Cost Effect to your Advantage We can illustrate the implications of these comparative statics results in the context of a simple Cournot duopoly signalling example.81 Consider a situation in which Player A has sunk s into the development of a product which, at tx, he will sell in a duopoly along with Player B. Moreover, Player A can be of one of two types: Type N : Displays no sunk cost effect Type S : Displays a sunk cost effect. Type being information private to Player A, Player B must start the game off by assuming a probability distribution about A's type. B then observes the amount s that A sinks into the development of the product, and with this information updates his beliefs about A's type. Using this updated (posterior) distribution, B then goes on to play a simultaneous Nash (Cournot) output game with A. The situation is portrayed in Figure 7. — Insert Figure 7 here — The price of the (jointly produced) product is: p = y - 6Xa+b) , (y,8 > 0). Costless production is assumed (for simplicity). "For the fundamentals on mcomplete-information games of this type, see Harsanyi (1967-68). 139 We can solve for the equilibrium solutionis) of this game recursively, in three distinct steps: Step 1: Solve B's Output Game Let p be p(s), B's posterior about A's type (p also known to A). Then B's output decision is to Max [y-6(a+b)]b (12) b s.t. A plays argmax [y - 8(a+b)]a with probability (1-p) a and plays argmax [y - 5(a+b)]a + a(s)a with probability p a (a(s)*0; do/ds>0)22 Player B's optimal allocation can be determined as follows: FOC for Player A of Type N: y- 25a -8b = 0 (SOC is satisfied) which gives a^  = y - 5b 25 FOC for Player A of Type S: y - 25a - 6b + ct(s) = 0 (SOC is satisfied) which gives % = y - 6b + a(s) 25 Player B must therefore take Player A's (uncertain) production to be 82oc(8)a is a particular parametrization of y(s,a), capturing our idea of escalation - where an increase in s encourages increasing a. 140 a* = (1-p) aN + pas = y-6b + pot(B) 25 (13) This is shown in Figure 8. — Insert Figure 8 here — This graph shows the optimal reaction functions for Player A of Type N, of Type S, and for Player B, and the resulting optimal production for B (point P*) given the uncertainty about A's type. Point P* is located at pPN + (l-p)P8 . Player B's own FOC from eq.(12) is: y- 5a -26b = 0 . (SOC is satisfied) which gives b* = y - 6a (14) 25 Solving equations (13) and (14) simultaneously for b* yields b* = y - pais) , which is decreasing in both p and oc(s). 35 Note that b* £ 0 requires that y k pa(s). This constrains the parameter values in the problem. Step 2: Solve A's Output Game If A is of Type N Max it* = Max [y - 6(a + b)]a a a Taking Player A's FOC and solving simultaneously with b* (found above) yields 141 a" = 2y+ pais) , which is increasing in both p and o(s). 65 Substituting these values of a* and b* back into the objective functions, we get that for Player A of Type N: U * = it* 4f + 4pyoc(8) + pVte) [Tinctfs)] (15) 365 JC 8 = 2f - pycrts) - p2a*(s) [lina(s)] (16) 185 If A is of Type S Max uA = Max TC* + cc(s)a = Max [y • 5(a + b)]a + ct(8)a a a a In this case, we obtain a* = 2y + (3+pkx(8) , which again is increasing in both p and a£s). 65 Therefore, for a Player A of Type S we get: uA = 4^  + (12+4p)ya(s) + (p+3Ws) [Tineas)] 365 TC8 = 2f - (3+p)yo<s) + (3p-p2)c^ 8) [iina(s) (over the allowable range of 186 y£po(s))] 142 or, expressed differently, 2f - p7o(s) - pMs) Spcfts) - 3yo(s) (17) + 185 185 The interesting result for ^ concerns TC*, the economic profit part of uA: ic* = 4f + 4pYo(s) + pV(B) ofts) (18) 365 45 In this case, any ais) < 4py/(9-p8) will increase TC*. Hence, Player A can actually be better off financially at tj than in the case where A is known to be maximizing TC* only, even though (s)he displays the sunk cost effect - a positive by-product of B's uncertainty about A's type. This occurs because B adjusts (in this case, reduces) his Nash production to account for the possible sunk cost effect of A Note that (15) > (18) but that we may get (16) < (17) or (16) > (17) . Step 3: A's Sunk Cost Decision At this stage, we have not yet addressed the question of whether Player A should sink s into development of the product at t^  to begin with. The previous results only address the impact of the sunk cost effect as of tj, once s has already been committed. The fundamental question we must address is: Is it profitable for Player A to make a deliberate investment of s at t0, in order to then use his sunk cost effect at tx to his competitive advantage, making him better off even at t0? We can find out by 143 comparing the profit function at tc with and without a sunk investment s. Assuming no discounting between periods, Player A's profit function at t0, when investing s, is obtained by adding one term to eqs. (15) and (18), respectively: For A of Type N: TC*, = 4y* + 4pya(8) + p'cfts) - s 365 For A of Type S: TC* = 4^  + 4pya(s) + D 2O?(B) - efts) - s 365 45 Note that for any positive s and the associated positive a(s), TC£ > TC* . When s = 0 and hence aCs) = 0 , TC* = TC* = y795 . The equilibrium (optimum) s* depends upon the specific values of the parameters in the problem. Characterizing the equilibrium requires that we consider 3 possible parameter scenarios. These are illustrated in Figure 9. — Insert Figure 9 here — Case 1: TC* and TC*. are both maximized at s*, = s8 = 0. This is the equilibrium. Case 2: TC*; is maximized at s*, > 0 and TC* is maximized at s*, = 0. Then any s > 0 signals with probability 1 that A is of Type N, so that p = 0. Hence both types of A are best off playing s = 0. This is again the equilibrium. 144 Case 3: a* is maximized at s£ > 0 (and because n£> n% Vs, n£ is maximized at % > 0). This is the richer, more interesting (non-degenerate) case. It occurs when 4pyco(s) + p'cfts) - efts) - s > 0 (for Type S) 365 45 (and hence, automatically 4pifa(s) + p2a*(8) - s > 0 (for Type N) ). 365 Here, both A Types N and S have an incentive to increase p, which yields greater profits. Hence, it is to A's economic advantage (in terms of purely economic utility, or profits), regardless of his type, to put himself in a sunk cost situation at t0 - a first-mover advantage. He then benefits from an increased a* in equilibrium, under the threat that he may be maximizing a utility function in the Nash output stage that includes a sunk cost effect component. The following analogy conveys the intuition in effect: Intentionally "burning money" (literally) for no apparent reason may convince an opponent that you may not be a perfectly rational adversary in subsequent time periods - and this is something which you may be able to exploit.23 "For a discussion on the strategic role of burning money and the stability of equilibria, see van Damme's (1989) work on forward induction. 145 The following results characterize the equilibrium of this game: Non-Existence of a Separating Equilibrium Because T C * * > rc* * > yV98 (the latter holding when s=0), there exists no s>0 that would make Type S better off than s=0 while making Type N worse off than 8=0 (see Figure 9, Case 3). Therefore, a Type S can never shake himself free of a Type N trying to mimic him - which a Type N will always want to do (to increase p), as any S N * s*| would signal that A is of Type N and would push p to 0. Uniqueness of a Pooling Equilibrium Because s*, maximizes TC* given p , it also maximizes p (it signals that the amount s being played is the best move for a player of Type S). From the preceding paragraph, 8*, is also the best move of a Type N. Hence, the unique optimal s for both types of A is Sg . This is a nnn.infnrmative allocation, so that Player B's posterior about A's type = p = B's prior about A's type. Hence, p is an exogenous parameter which, in conjunction with the particular values of y, 8 and cc(s), will determine which Case (1, 2, or 3) is being played. A's sunk cost, regardless of A's type, will be = 0 in cases 1 and 2, and =s*i in case 3. The subsequent equilibrium output allocations of A and B will then be made, as outlined in steps 1 and 2 above. Note that a nonzero s* invested (in case 3) by Player A of either type makes him better off, while making Player B worse off than if s=0. 146 This characterizes the equilibrium of this signalling game. Special Cases of this Signalling Example Perfect Information: A is of Type S. and B knows it (o=l) In this fully informed special case, we get: Player A: max [y - 5(a+b)]a + cc(s)a a Player B: max [y - 5(a+b)]b b We obtain: a* = 2ct(s) + y ~~35 b* = y - a(s) 35 The objective functions at tj are: uA= 1 [y+2o(s)]2 ttincx(s)] (19) 96 T C 8 * 1 [y-o(s)]2 [iino(s) (forySote))] (20) 95 and 7C* = 1 ty* + ya(s) - 2a2(s)] (21) 95 A positive a(s) is financially beneficial when ya(s) > 2a2(s), i.e. for a(s) < y/2 . That is, a sunk cost effect of intensity a(s) < y/2 will make Player A better off as of tx in 147 profit terms than if he displayed no sunk cost effect at all ( a(s) = 0 ) - the result of B reducing his production to account for A's sunk cost effect. The optimal "intensity" of the sunk cost effect, the one maximizing A's profits, will actually be of the level o(s) = y/4 . Note that Player A need not "pretend" that he displays a sunk cost effect: he actually does display the effect, and Player B knows it in the deterministic game played at t^  As of tj,, we get: 1 If + Yo(s) - 2a2(s)] -s (22) 95 Without a sunk investment s, A's profit function at t0 is Y8 (s=0, cc(s)=0 in eq.(22)). (23) 95 We can establish whether some investment s is justified simply by comparing the last two equations. Specifically, (22) > (23) when ya(s) - 2a2(s) -s > Q (24) 95 We must have y > o(s) (for b* £ 0), and so for (say) a proportionally large y, it is quite possible for ya(s) > 2CC\B), and for (24) to hold. The optimal amount s can actually be determined by maximizing (22), which will also maximize (24). Assuming an interior solution, and assuming the SOC to hold, the FOC leads to s* such that ya'Cs*) - 4a(s*)or'(8*) - 95 = 0 . This s* would be the equilibrium level of s for this two-period game. 148 Perfect Misrepresentation: A is of Type N, but B thinks that A is of Type S (o->l) A variant of this situation, and an extreme case of our signalling example, is when Player A is not subject to a sunk cost effect, but B believes that he is*4. In this case, B gets "faked out" into adjusting (reducing) his Nash production at ^ to account for A's apparent sunk cost effect Player A can then cash in on B's adjustment by playing his optimal strategy based on his purely economic TC* function. The key, of course, lies in B's belief that A is subject to the sunk cost phenomenon. Hence: Player B determines b* based on the (erroneous) belief that o(s) * 0 . Player A knows that ot(s) = 0 , and determines a* from that. Under these conditions, we get: b* = y - a(s) 36 That is, B computes the same equilibrium as in the previous case. Player A then uses this b* in determining his optimal a*: max [y - 5(a+b')]a a which gives : a* = 2y + OC(B) ( O£B) as perceived by Player B, not A's 65 actual ais)) "Player B's incomplete information, leading to his uncertainty about A's type (as portrayed in Figure 10), is necessary if any misrepresentation of A's preferences is to occur. In the extreme, however, B's uncertainty about A's type can actually become a false certainty - as it is in the present case. 149 This (a\b*) pair yields: uA= TC*= [2y+a(8)P 366 TC8 = 27 s - yais) - efts) 186 [T in a(s)] [ i in a(s)] (25) (26) We note that for any sunk cost effect ocCs), rc* is always greater here than in eq.(21) above: A's profits are always greater here than in the perfectly informed case, at both ^ and t0. This is quite consistent with intuition: B employs exactly the same strategy as before, whereas A is now maximizing TC* rather than uA. At t0, A's profit function becomes: [2y + otvs)]2 - s 366 With s = a(s) = 0, this becomes: y* 96 We obtain (27) > (28) when 4ya(s) + efts) - s > 0 365 If (29) is satisfied, equation (27) is maximized at the value s* such that 270V) + a(sV(8*) -185 = 0 (assuming the SOC to hold). (27) (28) (29) Comparing the problem of misrepresentation with that of an actual sunk cost effect 150 (addressed previously), we see that (29) represents a broader class of cases than (24). As a result, even though both can be beneficial to A, misrepresentation offers a greater likelihood for exploiting B's beliefs than does displaying a sunk cost effect. This is again consonant with our intuitive expectations. Other Degenerate Special Cases A of Type N and B knows it (o=0) Then s=0 , and uA = TC* = y798 TC8 = y795. This is the perfectly rational equilibrium, where misrepresentation is neither possible nor desirable. A of Type S and B thinks A of Type N (o-*0) Then ic* = y* - cr*(s) - s , which is I in ct(s). 98 ~48~ Clearly, s* = 0 . Therefore, even though A displays a sunk cost effect, B does not adjust his output to account for it. As a result, there is no opportunity for A to earn profits in excess of those from 8=0. • 151 As the preceding analysis shows, the sunk cost effect provides Player A with an interesting means by which to gain a strategic edge. By sinking money into project #1, Player A of Type S precommits himself to displaying a sunk cost effect in the ensuing game - and in effect, to behaving irrationally at tj. To quote Schelling (1960): " It may be perfectly rational to wish oneself not altogether rational" (p.18). While Schelling's statement was made in the context of making threats credible, it also applies here, to the case of sunk costs. If Player A can successfully convince Player B that he is subject to a sunk cost effect and play what - from Player B's perspective - appears like an irrational strategy, then A can gain a strategic advantage. To do so, A must precommit himself to sinking s into the product at t„ and must convince B that the effect of this sunk cost will be a(s) in his utility function. Of course, in order to convince B it may be necessary for A (of Type S) to actually fall prey to a sunk cost effect - a strategy in the spirit of true precommitment. In that case, no misrepresentation occurs: the advantage to A results because of, and in spite of, A's sunk cost effect. An even broader family of situations in which Player A uses his sunk cost effect as part of a precommitment strategy can be represented generically as a game in extensive form, via the game tree in Figure 10. — Insert Figure 10 here — 152 Player A must first decide how much of a cost s, if any, to sink into a project. Some uncertainty then gets resolved: If successful, Player A can then reap monopoly profits - having pre-empted Player B's involvement in the project. If unsuccessful, Player A loses the initial allocation of s and then enters a simultaneous Nash game with Player B. It is the unsuccessful resolution of the uncertainty which drives the psychological motivations leading to a sunk cost effect for Player A - and the resulting change in his utility function. Player A, which may not have perfectly anticipated his reaction to sunk costs (hence his prior q*), ends up in one of two utility states (i.e. with one of two utility functions) following these sunk costs. Player B does not know the utility state of Player A, as this is A's privately held information. He only has a prior probability estimate, qB. A and B then proceed to play the Nash game of the second period along the lines indicated in the bottom half of Figure 10 (assuming discrete strategies26), yielding the equilibrium allocations. The payoffs at the bottom of the figure reflect A's different utility functions. Arkes & Blumer (1985) recognized that the sunk cost effect can be used to one's advantage. They quote an argument made by Do wie (1981) in the context of nuclear energy. He suggested that if construction of power plants can be secretly initiated, sunk cost arguments can then be brought up when the public finds out, to argue that it is too late for construction to be stopped. While this specific example may have been somewhat cynical, it does point out the potential for Player A to impose a sunk cost - either to himself or to Player B - as a strategic move that permits him to get his a6The approach obviously extends to continuous Nash games as well - subject to the standard measurability conditions. 153 way. Imposing sunk costs on oneself demonstrates resolve for persisting with the project Imposing sunk costs on someone else (which would be the case if public funds were used in construction of the power plants) transfers the sunk cost effect to the other playeKs). This recognizes sunk costs as an important strategic tool in delegation or principal/agent situations. This is an important problem, with great potential for analysis. 4.2 Exploiting an Opponent's Sunk Cost Effect26 We now turn our attention to the problem of exploiting an opponent's sunk costs. Under what conditions will one player be better off because of another player's sunk cost effect? That is, when will: • u^ Nash^ ) > u^Nash^), where Nash,,, represents Player A displaying a sunk cost effect, while in Nash^ he does not; • or equivalently, thi (Nash) > ^ ^  . e ^ greater the value of s* (Player A's sunk cost), the greater the final utility for Player B. Partial answers can be found in our comparative statics results from the beginning of section 4, obtained for an escalation effect. MThere is an ongoing debate concerning the (lack of) dynamic consistency of non-expected utility agents, and how they can be exploited in economic decisions under uncertainty. For a thorough review of this debate, see Machina (1989). While not concerned with the same type of behavior, our present context of changing preferences following sunk costs raises some similar philosophical issues. 154 In cases of downward sloping reaction functions, we are moving southeast along B's reaction function, assuming it remains unaffected by a change in s. For such functions, and where the direction of increasing profits is towards the monopoly solution, as in many Cournot duopoly situations, we obtain duB(Nash)< 0. ds That is, it is not to B's advantage for A to increase his sunk cost commitment s. The previous Cournot duopoly analysis, interpreted from the perspective of Player B, falls in this category: A's escalation effect does not make Player B better off. In the case of upward sloping reaction functions, whether Player B ends up better off depends on the direction of increasing profits along his reaction function. However, situations where the decision variables are quantities produced, or further investments in a project, are unlikely to exhibit upward sloping reaction functions. Such functions generally arise in Bertrand-type problems, where the decision variables are prices - situations somewhat removed from our 2-period investment setting. There could, however, conceivably be cases in which Player B is actually better off with an increase in the sunk amount s.27 In more general cases, the impact of A's escalation effect on Player B will depend on the particular economic problem being studied28. 87See Milgrom & Roberts (1990) for different economic examples of upward-sloping reaction functions. F^ew will actually be Cournot duopoly situations. More economic structure will therefore be required in order to determine whether B actually becomes better off. 155 • In our Cournot duopoly example, because A's sunk cost increases A's commitment to that project, it is natural that under conventional Cournot assumptions, B cannot profit from the situation in what is essentially a single project setting (i.e. where the returns on the second project are constant). But by extending the situation to a Cournot duopoly with two distinct projects at tj, there now is the possibility for B to exploit A's increased commitment in project #1 (and away from project #2) by focussing his investment on project #2. This type of situation has been called "strategic complements" by Bulow, Geanakoplos & Klemperer (1985) in their economic analysis of multimarket oligopolies. Also see Milgrom & Roberts (1990). We now work out such a two-product example. As before, Player A has sunk s into the development of product #1 which, at t^ , he will sell in a duopoly along with Player B. But there is also another product, whose demand is independent of the first, which A and B also sell in a duopoly. At tj, Player A has an amount A to invest and Player B has B. Player A puts a into product #1 and A-a into product #2; Player B puts b into product #1 and B-b into product #2. The price of product #1 is: p = y - 6(a+b) ,(y,6 > 0). The price of product #2 is: q = 6 - c[(A-a)+(B-b)] ,(8,o > 0). Once again, no costs of production are assumed, so that the optimization problem is: Player A: max [y - 5(a+b)]a + [9 - o(A+B-a-b)](A-a) + cc(s)a , (a(s) £ 0) a Player B: max [y - 8(a+b)Jb + [9 - o(A+B-a-b)](B-b) b 156 FOC's: y-25a-8b - 6 + 2oA + oB-2oa - ob +a(s) =0 y - 25b - 5a - 9 + 2oB + oA -2ab - aa =0 (SOC's for a maximum are satisfied.) Solving the FOC's simultaneously yields: a* = (Y-9) + 3oA + 2a(s) 38 + 3a b* = (Y-9) + 3oB - a(s) (with a(s) sufficiently small to have b* and p* £ 0)29. 38 +3a We see that a* is increasing in a(s), while b* is decreasing in cc(s). Substituting a* and b* back into the two players' utility functions, and some tedious algebra (for simplicity, we assumed that y=B), yields: uA= A [Y5 + ya - o6(A+B)] + 9cAo(s) + 4a2(s) S+o 9(6+o) and TC* = A [76 + ya - o5(A+B)] - 2cfts) 5~+c 9(S+o) While u* is increasing in a(s), rc* decreases in a(s), so that Player A's sunk cost effect reduces his total profits at tv More importantly for Player B, we find: uB = TC 8 = B [76 + YO - o5(A+B)] + efts) 5+0 9(6+o) Player B's profit increases in a(s), so that B is made better off by Player A's sunk 29There are also conditions on the sign of (y-9) to get a* and b* £ 0 . 157 cost effect In this situation, Player A suffers from a first-mover disadvantage, which Player B can then exploit. • In the preceding examples, developed within the structure of Figure 6, any advantages to Player B are purely by-products of A's sunk cost effect, as B has no control over the amount s sunk by A at t,30. But from the perspective of Player B, the sunk cost effect presents yet another set of opportunities. For Player B, the question becomes: What are the conditions under which he can actively encourage and exploit Player A's sunk cost effect. To do so requires a different problem structure, in which B can actively influence A's choice of a sunk amount s. Figure 11 presents such a structure. — Insert Figure 11 here — Many sequential games can be portrayed in the way of Figure 11. Our focus is on games in which B can actually get A to commit himself to sinking a cost a° at t0, in order to exploit the advantages of that commitment in period t^  We can briefly outline several stylized situations that can be modeled along those lines. They are either direct examples of the sunk cost effect, or variants of the sunk cost which rely on similar psychological explanations. "unless he too can mis-represent his true preferences at tj - an unlikely situation, which we will not address here. 158 ADDICTION Consider the problem of addiction, or of habit formation. At t^  Player A would get some utility out of consuming small amounts of a product (say heroin), but is averse to consuming large amounts. After consuming a small amount at t0, however, A's preferences change so that he now wants to consume more.31 If A has not foreseen this change in his preferences, Player 8 then has a chance of exploiting the situation by essentially 'giving away* a small amount of heroin to A at t0, in order to sell him greater quantities at a premium at tv once he has become addicted. Such bait offers can be quite commonplace in various settings involving the possibility of addiction. SUNK COSTS IN AN ONGOING BUSINESS RELATIONSHIP Many relationships in business are not one-time affairs. Suppliers and buyers interact on an ongoing basis. In any situation where benefits occur only after a sequence of individual transactions (which is often the case for large scale projects), there is a possibility for one party to exploit the other party's sunk cost effect. The strategy is similar to the one just presented in the case of addiction: to bait one's counterpart into making early favorable investments or expenses, only to raise prices in later transactions. Consumers can use the sunk cost phenomenon to their advantage in bargaining with a sales representative over a good being purchased, such as a car. Having the salesperson devote, or sink, a substantial amount of time toward making a sale may 81In section 3.2.1, we argued in the context of watching a televised football game that knowing thin change in his preferences, Player A would want to precommit to consuming nothing at t0, in order to protect himself against ending up consuming a large amount. 159 create a sunk cost effect that the consumer can take advantage of, by asking for a low price. If the consumer comes across as lukewarm about the purchase or displays indifference about buying it elsewhere, the salesperson will often be willing to cut prices in order to make a sale, to justify the large time investment that went into that customer. This can be seen as the symmetric situation to low-bailing, below. LOW-BALLING and THE FOOT-IN-THEDOOR PHENOMENON Psychological research on compliance has found that the low-ball sales technique can be quite successful in producing compliance on the part of customers. Low-bailing, often used by automobile dealers, consists of inducing the customer to make an active decision to buy a product at an extremely good price, and then to remove the price advantage in one of a variety of ways32. Research findings (Cialdini et al., 1978) suggest that the rate of acceptance of a higher price following a low-ball offer is higher than the rate of acceptance for an immediate offer at a higher price33. We can talk here of a sunk 'cognitive commitment', rather than a sunk cost, situation. A variant to low-balling, also designed to produce compliance, is the foot-in-the-door technique (Freedman & Fraser, 1966). Asking for a charity donation of $2, followed by an revised request of $5 produces a better chance of compliance to the $5 request than if the full request had been made initially. As such, and unlike low-balling, the foot-in-the-door technique starts off with a small request (or offer) and s^uch as "checking with the boss" who turns down the deal, saying that they'd "be losing money"... ^This may be the result of mental accounting in relative terms, where the additional expense is considered an inconsequential supplement to the aggregate amount, rather than being evaluated in relation to zero. 160 builds progressively towards the final, much larger stakes. LOSS LEADER PRICING Loss leaders are products being sold at greatly reduced prices, perhaps even below cost, in order to attract customers who may then buy other, related products at their higher, regular prices. The purpose is simply to get clients "into the store". The experience of the Polaroid Land Camera also constitutes an example of loss leader pricing. The camera itself was sold at a very low price, but the film was priced high. At the time of purchasing the camera, any uncertainty concerning future film prices, or the esalation of future film prices, may well make it rational for a consumer to actually purchase the camera while at the same time entraping him into purchasing the film, even at unreasonably high prices. The consumer's decision to persist with the loss leader product can be explained in economic terms as a result of the high switching costs. We believe that an alternative explanation can be formulated around a sunk cost argument: that purchasing a new camera is aversive beyond purely economic switching costs, because of the belief of having V/asted' the initial purchase. We can thus talk of 'psychic', as opposed to economic, switching costs. BAIT AND SWITCH STRATEGY As a means of attracting customers, a store may advertise limited quantities of a product at a low price. Customers who had come to purchase that product may then be swayed into buying a more expensive version of the product, by arguments that it is of higher quality, has more desirable features than the product on sale, etc. 161 Alternatively, customers may have to turn to more expensive substitutes once the product runs out. Economic arguments relating to transaction costs may explain the finding that many people would still buy at the higher price - even higher than in other stores. But the psychology supporting low-balling (or foot-in-the-door) may also apply here. Even though customers knew that there was a risk of the product being out of stock, the initial commitment to buying the product (albeit at a lower price) will make them more likely to purchase the more expensive substitute. Extensive form representations of each of the games previously described are shown in Appendix B. These situations all share a common feature: after some initial commitment - financial or psychological - at t^  Player A's preferences (utility function) undergo some modifications at tJt which serve as the basis for making the decision at tj. These modifications, as in the case of the sunk cost phenomenon, favor continuing in the direction of the committed course of action. In some situations, the utility change can be foreseen and planned for appropriately at t0. In others, it is not foreseen and leads to more extreme cases of 'entrapment'. Figure 12 presents the game tree common to all of these situations. — Insert Figure 12 here — In Figure 12, nature first endows Player A with a reservation value Zj, with probability p,. This value is known to A but not to B. B only knows the probability 162 distribution of reservation values for the population, ps, i=l,...,n. At te, B first makes a price offer, which A accepts or rejects, based on his reservation value and on his expectations about future events, occurring further down the tree. The critical nodes in the tree are the uncertainty nodes that follow A's acceptance of B's initial bait offer. In the general representation of Figure 12, there are two uncertainty nodes occurring in sequence.84 The first represents technological or market uncertainty, relating to the 'success' (or sufficiency) of the initial commitment made by A This is primarily an uncertainty for A, as its outcome is under B's control (although in some instances it may also be an uncertainty for B). The second is preference uncertainty, and represents the chances that Player A will have new preferences at following the 'failure' of his initial commitment at t„. For neither uncertainty is it necessary for Players A and B to have identical expectations, so that p* need not equal pB and q* need not equal qB. Indeed, it is those information asymmetries and differing expectations that will offer the greatest opportunities for B to take advantage of A's change in preferences. B will usually get the most out of a sunk cost situation if A is 'myopic', in the sense that A does not realize at tQ that his preferences will be changing at t} in favour of the committed course of action. But this condition is not necessary for A to display a sunk cost effect, or for B to be able to exploit that effect. It may still be optimal for A, knowing that he will be subject to a preference change at tv to commit himself to S4There may also be instances where one of the two uncertainties is actually a certainty for both players, making one of the nodes superfluous. 163 a course of action that will make him vulnerable to an unfavorable preference change - Sinfavorable' when viewed in light of the preferences at t0. This is especially true in the presence of uncertainty at tD, regarding the success of the initial decision. Figure 13 presents a specific illustration of an extensive form game for the low-balling situation. In this example, Player A walks into a car dealership to buy a new car, of specific make and characteristics. He has a well-defined reservation value (max WTP) for this car, which Player B (the dealer) ignores. B only knows the probability distribution of reservation values in the population of car buyers, which range from $9,000 with probability pt to $11,000 with probability pn. B must decide whether to offer the car at $10,500 right away (for a profit of $2,500) or low-ball the customer by making an initial offer of $10,000 which, "upon verification with the sales manager", will get revised upwards to $10,500.35 — Insert Figure 13 here — If B offers the car at $10,000 and A commits himself to buying at that price, two sources of uncertainty will influence and help determine the equilibrium outcome. The first is the uncertainty of $10,000 actually being the striking price - which B knows will not be the case. The second is the uncertainty concerning A's change in his preferences, i.e. in his reservation value, once the $10,000 price has been raised to $10,500. As was mentioned earlier, A and B need not share identical probability MIn this stylized example, it is assumed that the dealer cannot make a lower counter-offer upon rejection of a price of $10,500 by the customer. No bargaining takes place. 164 estimates for either of these uncertainties. A's probability estimates determine A's expected utilities and decisions, while B's probability estimates determine B's. The equilibrium solution combines the decisions of both players. Obviously, the player with the better calibrated probability estimates will possess a competitive edge. In recursively "rolling back" the tree to determine his optimal response at tc, Player A faces an important conceptual issue. A may or may not know in advance that he will undergo a change in preferences after committing himself to buying the car at $10,000. At t^  in the present example, A estimates that he has a .1 probability of experiencing a change in preferences, that will raise his reservation value from $10,300 to $10,600. At t^  where the reservation value of $10,300 applies, A can in some sense "protect himself' against the influence of this anticipated preference change by rolling back a utility payoff of -200 (dollars), based on a reservation value of $10,300, rather than a utility payoff of +100, based on a reservation value of $10,600. This will bias A's decision at t0 toward the rejection of the initial $10,000 offer! But if A commits himself at t0 to the initial offer of $10,000 and moves down the tree to the decision node where he must either accept or reject the higher offer, his new reservation value will be in effect and he will choose to accept the higher price, with a "new" utility payoff of +100. The stylized game can be solved to obtain the equilibrium strategies for both players. Low-balling is actually the dominating strategy for Player B, as there is no downside to low-balling in our example. A then accepts the low-ball offer, accepts the higher offer if his reservation value increases, and rejects it if it does not. While the 165 equilibrium solution to this game may appear trivial, the simplicity of the game allows us to articulate precisely the issue of preference changes at tv 5. CONCLUDING THOUGHTS In this paper we have addressed a problem which, despite its economic importance, has been largely ignored thus far in economic models of decision making. The sunk cost phenomenon - the tendency to overinvest in previously committed projects - has been widely observed and documented. But there have been few attempts made at systematically modeling its causes or its implications. We have introduced a formal analytical framework for studying the sunk cost phenomenon, allowing us to identify specific causes and to predict its economic implications, and even provide prescriptive advice to an agent faced with the sunk cost effect, individually or in a strategic situation. 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Hillsdale, N.J.: Erlbaum. 170 APPENDIX A s Mathematical Proofs 171 A.1 Derivation of the Basic Comparative Statics Results The optimization problem at tj is given by the equation: m a x ute^c^s) s.t. F - s - cx - Cj = 0 (0) Forming the Lagrange an and differentiating yields: L = UCCJ.CJ.S) + X [F - s - Cj -Cj] First-Order Conditions (FOC's): L x = 0 <=> Uj - X = 0 Lj = 0 <=> Ua - X = 0 Lx = 0 <=> F - s - cx - Cj = 0 Totally differentiating the FOC's gives the comparative static equations: (Al) => Ludcj + L^dcj + L^ dX + L d^s = 0 (A2) => L21dc1 + Ljedca + L^ dX + L d^s = 0 (A3) => Ljudcj + L^dcj + L^ dX + L d^s = 0 We also know that: L u = -1 , L^ = -1, L^ = 0 and L^ = -1. Substituting these and dividing everything through by ds gives L u L* -1 L* La -1 -1 -1 0 (Al) (A2) (A3) (A4) (A5) (A6) dcj/ds dcj/ds = -L* (A7) dX/ds 1 172 Cramer's rule gives ds - L i , - L * L * 1 -1 -1 -1 |J| _ -L12 + 1^22 + Lu " La, m We know by the second-order condition that |J| > 0. Therefore, sign (dc/ds) = sign (-L^ + + L ,^ - L )^ (A8) Similarly, dca _ dT = sign ( -Uja + Uaa + u u - Uj.) ^ -La. -1 - 1 1 0 (A9) = ' L j , H- La. - f - LaX PI (A10) and sign (dca/ds) = sign ( u u - Ug, - u u + u^ ,) (All) Second-Order Condition (SOC) The second-order condition sufficient for a maximum is that the bordered Hessian determinant, which equals the Jacobian determinant, be positive. That is, 173 I * -1 L*x L^ 1 -1 -1 0 The SOC assumption thus translates into u u + u^ < 2uu . [ This is consistent with a comparative statics condition for both projects to be normal goods, le. dc/dF^O and dcJdF £ 0.] Under project independence and additive separability, the SOC becomes u u + Uja < 0. In this case, symmetry between projects suggests that both u u < 0 and u^ < 0 . Note that the SOC in no way contravenes the intuition underlying the sunk cost phenomenon. • A3 Comparative Static Analysis for the WEAK Escalation Effect Paralleling Chiang (1984, pp.406-407), our equation (A6) becomes LjjdCi + L^dcj + LxxdX + L d^s + L^dF = 0 (A12) 174 Budget compensation (s.t. F-s = constant) also implies: = -1, L -^ = 1, and ds = dF . Substituting gives LjjdCi + L^ dca + ~Lu.dk - ds + ds = 0. (A13) Note that (A4) and (A5) remain intact since F does not appear in their FOC's. Thus, (A7) becomes W 1^ 2 -1 -1 -1 0 dq/ds dcJds = -La. dX/3s 0 (A14) Cramer's rule gives 9 C i 5T -Lu L , 2 -1 -La. Laa -1 0 - 1 0 Lu - La. oompenMtad Hence, dcx 3T > 0 iff u u - Ua, > 0 (A15) 175 A.8 The Escalation Effect as a Result of a First-Order Stochastic Dominance Shift in the Probability Distribution of Outcomes We need to sign the following expression: sign (-ffuudFdG + ffu^dFdG + ffuudFdG + //UjdF.dG - ffu^dFdG - / fu,dF.dG). Separability of the utility function in the two projects, as we had in the deterministic case, implies that u1 2 = 0 and U g , = 0 everywhere, so that the first and fifth terms vanish. The SOC (see the deterministic analysis) in this case becomes Strict concavity of u, which can result from symmetry of the two projects in our SOC, gives The second term is therefore negative.86 The third term simply captures escalation effects which are caused either by purely economic considerations, or that are modeled as a 'utility' effect37. Because our present goal is to demonstrate that the sunk cost phenomenon can arise MdF and dG being densities, they are always positive. 8 7A 'utility' effect in this probabilistic (vN-M) case will (after integration) produce results similar to those obtained from a 'utility' effect in the preceding deterministic case. (A16) (A17) 176 exclusively from a probability effect, we will assume u u to be uniformly zero, so that there is no 'utility' escalation effect. The third term thus vanishes. The fourth and sixth terms can be signed by integrating by parts. The fourth term, after integration by parts on x, becomes: / [ / U i d F / x ^ l d G = /[uxF.(x;s) | - - / u ^ x ^ ^ l d G . (A18) F,(x;s) represents the change in the cumulative distribution function, evaluated at x, brought about by a change in s. It can be reasonably assumed that at the integral bounds, dF(x;s) = 0 for all s, so that at these bounds, F,(x;s) = 0, making the first part of the integral vanish. As for the second part, we know that a first-order stochastically dominating shift in dF(x;s) translates as F,(x;s) £ 0 everywhere (Vx). Combined with u u > 0, which is true for cases in which u is increasing in cx (e.g. stochastic constant returns to scale, u(q x)), the inside integral becomes negative, and the fourth term is therefore positive. A similar approach permits us to sign the sixth and final term. Integration by parts yields: f[/UadF.(x^)]dG = /[UaF.tas) | " - f u^/xjs^dG . (A19) Again, F,(x;s) = 0 at the integration limits, and the first part thus vanishes. The second part also vanishes, because the separability of the two projects, and of the random variables from the amounts invested, implies that U g , = 0 everywhere. The sixth term therefore vanishes. 177 We thus have sign (dcyds) = sign (-ffu^dFclG + JJu^dFdG + ffuudFdG + ffUjdF.dG 0 - 0 + - /f Ua.dFdG - //UadF.dG). (A20) 0 J0 • A.4 Derivation of the Two-Player Comparative Statics Results The optimization problem at t, is: for Player A: max u*<a,b*,s) a for Player B: max uB(a*,b,s) b The conditions for Nash equilibrium are: FOC's: Player A: uA I b . b . = 0 Player B: u8. | M . = 0 The Nash solution will be the pair (a*, b*). SOC's: Player A: uA. | ,.>b. < 0 PlayerB: u B „|^ > b .<0 and uA.uBb - uAbuBb | ..^ > 0 . Additional conditions on cross-partials are a function of the shape of the reaction functions: 178 Downward sloping reaction functions require: uAb, uBb < 0 and u{|, £ 0 , while Upward sloping reaction functions require: uAb, uBb > 0 and ub, £ 0.8* Differentiating the FOC's totally with respect to s gives us the system of comparative static equations: (A21) uAb da* " -uA. " u*b dT •uL db* dT From Cramer's rule, we obtain da* ds" 1 A -uA. uAb -uS. u?b I (-uA. uBb +uAb U B . ) A + - - -+ + + > 0 (A22) To help us sign this, we know that: A > 0 , u^ < 0 by SOC uAb < 0 , uf, < 0 for downward sloping reaction function uA. > 0 by escalation effect. Under these conditions, we get da* > 0 ds (A23) Similarly, "In cases of 1-period Nash equilibrium, where s has no explicit influence on profits at tj, we get u^ s=0, which keeps our comparative statics results (below) unchanged. 179 db* ds~ 1 A ul, -u|. = L (-uA. U B . + U J . uBD) A - - + -+ - <0 (A24) Here, we know that: A > 0 , u*. < 0 by SOC uB, < 0 , uB b < 0 for downward sloping reaction function > 0 by escalation effect These conditions imply that db* < 0 . (A25) A similar comparative statics analysis can be performed for upward sloping reaction functions. In that case, comparative statics results imply: daVds > 0 (still), while db'/ds > 0. • 180 APPENDIX B Extensive Form Representations of Specific Strategic Games 181 w.p. Pi w.p. Pi w.p. 2 ' Pi w.p. B B offers offer r B B reject accept reject accept (0,0) failure (0,0) success [PB] 1-pA [1-P*] (z'-s, s) B offer s+c AU no AU accept z"-z'+k [ q B ] z 1 reject accept (2z'+k-2s-c,s+c) (z j -s,s) (2z*-2s-c, s+c) (z j -s,s) [1-qB] reject (z ' - r . r ) FIGURE BI: ADDICTION 182 w.p. Pi w.p. Pi w.p. 2" Pi w.p. Pn B B offers B offer r B reject (0,0) accept reject failure lPB] (0,0) success 1-pA accept [1-pB] (z'-s, s) B offer s+c A U no AU z'-z' + k [ q B ] accept reject 1-qA accept +k-s-c,s+c) reject (-s,s) (z'-s-c,s+c) (-s , s) (z !-r, r) FIGURE B2 : SUNK COSTS IN AN ONGOING BUSINESS RELATIONSHIP 183 w.p. Pi w.p. z 2 P2 w.p. Pi w.p. ZB Pa B B offers B offer r B reject accept reject accept (0,0) failure (0,0) success IPB1 1-pA [1-PB] (z'-s, s) B offer s+c A U no A U accept z"-zj+k [q B] z' reject accept IHB] reject (p+k-s-c, s+c) ( 0 , 0 ) (z'-s-c, s+c) ( 0 , 0 ) (z'-r,r) FIGURE B3: LOW-BALLING 184 w.p. z1 f>l w.p. 2' f>2 w.p. 2' P i w.p. zn Pn B B offers B offer r B reject accept reject accept (0,0) failure (0,0) success [PB] [1-pB] (z'-s, s) B offer s+c DO AU accept z^z'+k [qB] 21 reject accept reject (z'+k-s-c,s+c) (-s,s) (zj-s-c,s+c) (-s,s) (zj-r,r) FIGURE B4 : THE FOOT-IN-THE-DOOR PHENOMENON 185 w.p. z 1 w.p. P2 w.p. Z' Pi w.p. B B offers B offer r B reject (0,0) accept reject accept failure (0,0) success [PBJ 1-p* [1-pB] (z'-s, s) B offer s+c A U no A U accept z^z' + k [ q B ] l-o/ reject accept [1-qB] reject (z'+k-s-c, s+c) (-s, s) (z'-s-c, s+c) (-s, s) (z ' -r .r) FIGURE B5 : LOSS LEADER PRICING 186 w.p. Pi w.p. P2 w.p. z1 Pi w.p. Pn B B offers B offer r B reject (0,0) accept reject accept failure (0,0) success [PB1 1-pA [1-pB] (zj-s, s) B offer s+c no A U accept z'-'z' + k [q B l z' 1-qA reject accept (z'+k-5-c,s+c) [i-q B] reject (0,0) (zj-s-c,s+c) (0,0) (z'-r,r) FIGURE B6 : BAIT AND SWITCH STRATEGY 187 FIGURES FOR CHAPTER 3 188 ++ economic rationality IA. financially rational for the project? I (no I 4 IB. financially rational for the manager? I |no I I (including principal-agent issues, information asymmetries, reputation effects with economic implications for the manager) 2A. subjective parameters of u (or SEU) maximization modified following sunk cost? | (changes in risk attitude (as in prospect theory); |no beliefs and preferences get modified to reduce | cognitive dissonance; wishful thinking) i 2B. new attributes present in the utility function? (such as regret or | self-presentation attributes) |no 3. cognitive biases? (in probability updating • e.g. the gambler's fallacy) I |no I i 4. non-maximization decision rules (such as "hope',...) — economic rationality Figure 1 Further Investment in a Committed Project: A Typology of Causes 189 1 1 r ,r 1 2 t 0 s 1 I t 1 c ,c 1 2 Figure 2: The Two-Period Allocation Decision r ,r 1 2 t 0 s 1 1 1 t 1 c ,c 1 2 some uncertainty gets resolved -new information updates prior beliefs about payoffs Figure 3: The Importance of Uncertainty at t 190 1 r ,r\ • 1 2 I I r ,r 1 2 t 0 s ,s 1 2 t 1 c , c 1 2 Figure 4: The Case of Myopic Decision Making ' 1 r ,r 1 2 t 0 s 1 i t 1 c ,c 1 2 some uncertainty gets resolved -new information updates prior beliefs about payoffs r and r are also probabilistic 1 2 Figure 5: The Presence of Uncertainty at t 191 Player A I A s I A A C ,C I 1 1 2 A A r ,r 1 2 I 1 1 Player B t t 0 1 B B c ,C 1 2 B B r ,r 1 2 I * project #1 is common to both players Figure 6: The Two-Player Allocation Decision 192 B h a s prior a b o u t A's t y p e A s = 0 B's p o s t e r i o r Nash Output Game s > 0 B's p o s t e r i o r Nash Output Game Figure 7 Game Tree for the Signalling Example 193 Figure 8 Player B's Output Decision via Reaction Functions 194 Figure 9 The Three Parameter Scenarios for the Signalling Game 195 sinks doesn't costs success failure [P8] monopoly profits q * A U no A U [qB] B 0 B 0 ( 1 & U & ) (u&ufc) (u4+k°,u?0) [ l -q B l B 0 B (uft+ki.u?,) (uplift) <u&,uft) (uMJJ (uft.u*) Figure 10: Detailed Game Tree for Sunk Costs as Precommitment 196 Player A P, r H—-Player B t b Figure 11: Generic Structure in which B Can Influence A's Sunk Costs 197 w.p. Pi w.p. P2 w.p. z 1 Pi w.p. z n B B offers B offer r B reject (0,0) accept reject failure (0,0) success tPB] 1-pA [1-PB] (z'-s, s) B offer s+c A U no A U accept z'-z'+k [qB] reject z' l-q* accept (z*+k-s-c, s+c) [1-qB] reject (-s,s)* (z'-s-c,s+c) (-s, s)' accept (z ' - r . r ) Figure 12: Generic Game Tree for our Various Commitment Examples • In the case of only a psychological commitment at t^ these are (0,0) rather than (-s,s). This applies to low balling and bait and switch. Addiction is also different. There, p A =p B = 1 (no market uncertainty), and the final payoffs at the end of tj are, respectively: (2z j+k-2s-c,s+c) (z'-s,s) (2z'-2s-c,s+c) (z '-s,s) 198 w.p. 9,000 B w.p. 9,500 Pi res'n value w.p. B offer car reject at $10,000 10,300 Pi w.p. 11,000 B offer car at $10,500 accept reject B car costs dealer $8,000 accept (0,0) failure (0,0) success [PB] = 1 [1-pB] = 0 (300,2000) B offer car at $10,500 AU no AU rv. $10,300-=.1 accept $10,600 rv: $10,300 S 5 i * reject accept (100,2600) (-200,2600) at ^ [l-qB] = J 5 reject (0 , 0) (-200,2600) (o'.o) (-200,2500) Figure 13: Low-Balling Example 199 Chapter 4 ESCALATING COMMITMENT AND THE M A R K E T IMPACT OF DISCONTINUATION DECISIONS A n E m p i r i c a l Study 200 1. INTRODUCTION Extensive laboratory research on the sunk cost phenomenon, or escalating commitment, has been conducted over the past decade. This research has focussed on the extent of persistence in a course of action as a function of various situational or personal factors, and on ways to mitigate this effect in organizational contexts -thus addressing the causes of sunk cost behavior as opposed to its implications.1 The pervasiveness of the sunk cost effect in the laboratory, combined with agency considerations favorable to sunk cost effects, suggest its presence in field settings as well. But data requirements make it difficult to show whether the escalation of commitment in the field is ever truly "irrational". Doing so would require detailed estimates of future costs, benefits and the corresponding subjective probabilities of success at every point at which additional investment occurs. In the absence of such detailed data, the presence and magnitude of the sunk cost phenomenon outside the laboratory remains at best a stylised fact. Conventional economic arguments can be used to postulate that the consequences of persisting with a (losing) course of action should be equal to the opportunity cost of the "good" money that gets thrown after bad. With this question "resolved", little empirical work has been devoted to address the implications of sunk cost behavior. From the firm's perspective as well as in practice, however, the consequences of sunk 1Refer to chapter 1 of this dissertation for a review of previous work on escalating commitment. 201 cost behavior extend well beyong this simple characterization of opportunity cost. If properly defined, opportunity cost should of course include all the downstream consequences resulting from having reduced assets, a weaker strategic posture vis-a-vis competitors, etc. on top of the direct cost of missing out on alternative opportunities. But how can all these factors be captured? Measuring and combining their consequences is no simple task, making it difficult even to approximate the implications of the sunk cost effect. Fortunately, "efficient" capital markets provide an environment which captures all of these factors and combines them into a single, economic measure - the value of the firm. This single measure can then be used as a basis for inferring the opportunity costs associated with escalating commitment. This paper addresses the problem of escalating commitment, and its implications, in the field, by studying the stock market's reaction to discontinuation decisions made by firms. In an ideal efficient and noise-free world, one would measure the economic impact of a firm's escalation of commitment to a division or project by observing the firm's share price reaction to the escalation decisions. But escalation of commitment is usually an incremental, everyday event, unlikely to generate a discernable share price reaction. For publicly traded firms, the presence and implications of escalating commitment can instead be determined by observing the share price reaction to firms' decisions to divest or abandon8 a significant division or project. Divestiture decisions are often one-time, non-incremental decisions of some significance, that are made "Discontinuations are often referred to as divestitures or abandonments. 202 public and trigger an immediate stock price reaction. Under the semi-strong form market efficiency assumption that stock prices capture (on average) the net economic effects the announcement of a decision has on the firm3, an increase in share price upon the announcement of a divestiture signals the market's positive reaction to that divestiture. The market may, among other things, have viewed the escalation of commitment to that division or project as not having been in the best interest of the firm and its shareholders, and expected that escalation of commitment to continue in the future. The operationalization of looking at share price reactions to divestiture announcements therefore allows us to infer the presence of a sunk cost effect without having to deal directly with a chronological profile of divisional or business unit cash flows.4 The following example provides a vivid illustration of this. After accumulating losses for years on its L-1011 commercial aircraft, Lockheed announced in December 1981 that it would finally kill the project. The market reacted very positively to this news, Lockheed stock jumping 18% the following day. It did so not because of a sudden change in the fundamental economics of the company or its environment, but rather *Under semi-strong form efficiency, stock prices are based on all of the available public information about the firm's activities (Roberts, 1967; Fama, 1970; Brealey and Myers, 1984, ch.13). Strong form market efficiency states that all of the published information as well as information private to the managers or other insiders (such as specialized security analysts) determines the stock price of the firm. In the present case, the strong form assumption is not required in order to test our hypotheses. 4Other proxies to share prices could be used, such as evaluative reports from industry analysts or the amount of internal equity holdings following the decision (an increase reflecting the positive nature of the termination decision). Increased internal holdings are likely to help reconcile management actions with shareholder interests - although at the extreme, owner-managers may display a stronger sunk cost effect as they are playing with their own money! 203 at the thought that Lockheed management would finally stop throwing good resources after bad into this losing project. Relevant Past Research Some important sunk cost issues have been addressed in the few studies that did employ field data5. Shefrin and Statman (1985) studied the "disposition effect" -the tendency for shareholders to sell winning stocks too early and hold on to losing stocks too long. Their results were consistent with prospect theory (Kahneman and Tversky, 1979) -- including mental accounting, loss aversion, and aversion to regret -- combined with tax considerations. Subsequent studies of trading volume by Lakonishok and Smidt (1986) and by Ferris, Haugen and Makhija (1988) also found strong support for the existence of a disposition effect in stock markets. In the context of managerial decisions, Hearth, Melicher and Gurley (1990) used a financial event study and found that decisions to cancel partially completed nuclear power plants resulted in significantly negative abnormal stock returns - consistent with the belief that (nuclear power plant) cancellations are generally negative NPV decisions. Their results offered no evidence of a positive market reaction to the cancellations to account for managers' sunk cost effect. Elsewhere, using share price movements in reaction to both plant completions and cancellation announcements, De Bondt and Makhija (1988) found mixed results on the presence of a sunk cost effect in nuclear power plant investment decisions. Stock returns associated with plant BRoss and Staw (1986) [1986 World's Fair], and Tang (1988) [US Steel Industry] both looked at the causes of escalating commitment using field data. 204 completions supported the presence a sunk cost effect, while those at cancellation announcements did not. Overall, they could not conclude in favor of the joint hypothesis of a rational stock market and a "powerful" sunk cost effect. Statman and Sepe (1989) cast a broader net and analyzed the reactions of stock prices to termination announcements of losing projects in a wide variety of industries. In contrast to the preceding studies of nuclear power plant terminations, they found significant evidence in favor of a sunk cost effect. They concluded that on average, shareholders consider project termination announcements as good news, as reflected by the increase in average share price - the market reacting positively to the idea that management will now stop throwing good money after bad. The Statman and Sepe work is of particular interest because it represents the first empirical demonstration of a strong and systematic managerial sunk cost effect, and of the stock market implications of sunk cost behavior. A substantial body of laboratory and anecdotal case evidence, along with conceptual arguments and compelling intuitions all point to the widespread nature of the sunk cost effect Yet the few formal tests we have just outlined of its presence in field settings have produced mixed results. This rather unconvincing empirical evidence leaves many fundamental questions about the presence, magnitude and (financial) implications of the sunk cost effect still unanswered. Extending the Statman and Sepe methodology — which produced the strongest field results yet in support of a sunk cost effect — to address additional issues will hopefully shed more light on these fundamental questions about the sunk cost phenomenon. 205 Objectives In this paper, we test the behavioral hypothesis of a "sunk cost effect" on the part of managers, by empirically examining firms' share price reactions associated with two distinct types of discontinuation decisions: terminations (where the assets of the division remain within the firm), and sell-offs (where the assets of the division are sold to outsiders). We employ a financial event study methodology. Replicating the approach of Statman and Sepe (1989), we first examine the reactions of share prices to project terminations. In a second part, we extend their work and test for the presence of a "disposition effect" on the part of managers, by testing for the presence of an asymmetry in share price reactions to sell-offs of winning versus losing divisions. 2. THEORETICAL CONCERNS AND HYPOTHESES Normative and behavioral theories make different predictions about the impact of discontinuation announcements on the share values of firms.6 The Normative Prediction for Terminations The normative model of managerial behavior assumes that managers pursue projects offering the highest Net Present Value (NPV). Under this model, any information the market possesses to indicate otherwise would quickly lead either to a change in the projects being pursued by management, or to revised shareholder beliefs consistent with management actions. In either case, shareholder beliefs and hence share prices 'This section draws heavily upon Statman and Sepe's theoretical development. 206 quickly become consistent with the assumption that highest-NPV projects (on average) are being pursued. Therefore, a termination announcement indicates that the NPV of continuing in a project is lower than the NPV of terminating it, lowering shareholder expectations about the NPV of the project, and of the firm. The normative model, based on shareholder expectations, therefore predicts a decrease in share price (or at best no change if an equal-NPV alternative project exists) to accompany a termination announcement, as termination is viewed as bad news by the market. The exception to this is when information about some new project accompanies the termination announcement, showing that the new project offers a higher NPV than the current one. In that case, an increase in share price is expected to accompany the announcement of termination of the current project in favor of the new one. Hence, the normative model aligns shareholder expectations perfectly with managerial behavior. By construction, any agency considerations are explicitly excluded from the normative model. The Normative Prediction for SeU-Offs Two distinct normative hypotheses can be made concerning share price reactions to sell-offs ~ an information and a synergy hypothesis. Under the information hypothesis, the division is either undervalued by the seller and its shareholders or is overvalued by the buyer (as in the "winner's curse"). The sale of the division therefore increases the value of the seller's shares. The synergy hypothesis on the other hand 207 states that the target division is more valuable to the buyer than to the seller. The sale would again have the result of increasing the seller's share value. Empirical findings are consistent with these normative hypotheses: Sell-off announcements are indeed usually accompanied by an increase in the share values of the selling firms (see among others, Hite and Vetsuypens (1989), Hite, Owers and Rogers (1987), Kim and Schatzberg (1987), Jain (1985), Alexander, Benson and Kampmeyer (1984), Hearth and Zaima (1984), Linn and Rozeff (1984), and Hite and Owers (1983)). We should note, however, that neither the synergy nor the information hypothesis would predict that stock price reactions would be different in sell-offs of "winning" or "losing" divisions. The Behavioral Prediction for Terminations and Sell-Offs An alternative, behavioral hypothesis - the sunk cost hypothesis - makes a different prediction. This behavioral prediction applies equally to terminations and to sell-offs. The sunk cost hypothesis states that managers are reluctant to terminate losing projects, even when better (higher NPV) alternatives are available. This is the sunk cost effect. Managers fail to discontinue divisions in accordance with the maximization of NPV, which goes against shareholder interests. This behavior may stem from any number of psychological causes such as face saving, regret minimization or psychological attachment to a particular division or project, or from agency effects on the part of managers.7 7Escalating commitment need not be "irrational" to go against the best interest of shareholders. "Rational" actions on the part of management may still clash with shareholder interests, as is the case in agency problems. Kanodia, Bushman and Dickhaut (1989) employ an agency theory framework to derive conditions under which managerial reputation and future salary potential drive self-interested, economically rational managers to display a sunk 208 Management's reluctance to dispose of a losing division can usually be tied to the retrospective (or hindsight) evaluation of the division's performance. A manager's reputation and rewards are often closely tied to his division's performance. Disposing of a losing division more or less constitutes an admission of failure, which for many managers may entail loss of managerial reputation, loss of face, or loss of income. Alternatively, managers whose divisions have been experiencing losses may become more risk-seeking, and persist with a struggling division in the hope of turning it around Managers may also be subject to common cognitive biases such as wishful thinking, where the success of the division is truly believed to be "right around the corner". A comprehensive discussion and analysis of the various causes of the sunk cost effect is presented in chapters 1,2 and section 2 of chapter 3 of this dissertation. Under the behavioral hypothesis shareholders recognize the presence of managers' sunk cost effect, whatever its causes might be, but find it costly or difficult to enforce their views on management. The expectation that managers will throw good money after bad is therefore included in the stock's price. The termination of a losing project conveys good news by signaling that less good money than expected will be thrown after bad. Thus with some prior public information about the poor prospects of the project, termination conveys both b a d news — the prospects for the project are worse that expected, and good news - managers did not become entrapped any longer into a sunk cost effect. Note that in the case of the market possessing full information about cost effect. 209 the prospects of the project, termination would convey only the good news. Similar arguments apply to the case of sell-offs. A sunk cost hypothesis argues that managers of losing* assets delay sell-offs - the managerial equivalent to the stock market's disposition effect. In such cases, the expected waste of good money on losing divisions will be incorporated into stock prices — systematically lowering the stock value of the firm to allow for expectations about managers' sunk cost behavior. Since this type of behavior is not expected in the case of winning divisions, it will not influence the stock values of firms selling off winners. Sell-offs of losing divisions would therefore convey this extra good news to the market - that managers are finally walking away from their sunk costs in a losing division. Therefore under our behavioral hypothesis, sell-offs of losing divisions would be accompanied by larger gains in share prices than sell-offs of winning divisions. In cases where the poor prospects of a division were not disclosed to shareholders prior to a termination or sell-off announcement, the tendency toward a sunk cost effect would not be expected8. Then only the normative hypotheses would apply. Terminations should be accompanied by a decline in stock price, while sell-offs of winners and losers should result in similar stock price reactions. 8or at least, it would not be expected to be as likely. 210 Hypotheses In summary, the following hypotheses emerge from the preceding theoretical issues: Hypothesis 1: Under the joint hypothesis of a rational stock market and normative manager behavior: (a) Terminations of losing divisions should be accompanied by a decrease in share prices. (b) Sell-offs of winning and losing divisions should generate similar share price reactions. These normative predictions are independent of whether the market possesses any knowledge about division performance prior to a divestiture announcement. Hypothesis 2: Under the joint hypothesis of a rational stock market and a sunk cost effect on the part of managers, for divisions whose financial performance was known to the market prior to any divestiture announcement: (a) Terminations of losing divisions convey good and bad news to the market. Share price increases should accompany those termination announcements having a large good news component - whose escalation of commitment was expected to be the greatest. (b) Sell-offs of losing divisions should generate larger positive increases in sellers'share prices than sell-offs of winning divisions. 211 3. EVENT SELECTION M u c h of the empir ical work consisted of carefully selecting, interpret ing and classi fy ing the f inancial events that would constitute our f inal sample for analysis: those f i rms whose stock price reactions could be l inked unambiguously to specific terminat ion or sell-off announcements. 9 The f i rst step was to identify firms that were candidates for a sunk cost effect Th is was done by ident i fy ing firms from the COMPUSTAT Annual Industrial Tape and from the COMPUSTAT Research Industrial Tape that reported "signif icant" losses or gains from discontinued operations (data i tem 66) for the years 1967-1987. Specif ical ly, firms whose losses or gains from discontinued operations exceeded 10% ( in absolute value) of operating income of the firm i n that year were chosen. These firms were believed to have discontinued operations "signif icant" enough for the discontinuation announcements to prompt share price movement. In a l l , 2,034 f i rms 1 0 fu l f i l led this in i t ia l requirement. The Wall Street Journal Index was then used to obtain the announcement dates of the decisions to discontinue (i.e., terminate or sel l off) operations of projects or divisions for the 2,034 firms and years identi f ied above. Terminat ions were usual ly announced only once — the first announcement to discontinue operations being the signif icant event of interest to us. Sell-off announcements were often more gradual : first intent I n order to be able to compare our results directly w i th those of S ta tman and Sepe, we closely followed thei r event selection methodology. 1 0 To be more precise, we should say 2,034 "f irm-years", as several of those 2,034 observations include mult ip le occurrences of the same firm over different years. 212 to sell off a division, then negotiating the sale, then reaching a preliminary agreement on the sale, and finally sold. Each of these announcements conveys information on the increased likelihood of an actual sale, becoming a certainty with the sold announcement. Hence, each of these announcements may prompt share price movement. The initial announcement, however, is the one which conveys management's willingness to let go of the division. We can therefore expect the market to react most positively to the initial intent to sell announcements of losers versus winners. Announcements of discontinued operations reported in the Wall Street Journal did not always take place during the fiscal year reported on COMPUSTAT. Some announcements were made up to a year before the fiscal year in which the accounting numbers were reported on COMPUSTAT, while others were made months after the accounting numbers had been reported for the fiscal year of interest. To account for this latitude in reporting, a three-year window around the fiscal year from COMPUSTAT was searched in the Wall Street Journal for each firm. The magnitude of the discontinuation and the fiscal year of its reporting were often absent from Wall Street Journal announcements, creating ambiguity about the size (hence significance) and sign (gain or loss) of many of the announcements. At times, the linkage had to be inferred from the magnitude of the dollar amount and lead time to discontinuation alluded to in the Wall Street Journal. Other times, no discontinuation announcement could be found in or around the fiscal year of interest. In all cases, when the linkage between a Wall Street Journal announcement and the 213 initial COMPUSTAT screening could not be clearly established, these firms were deleted from our sample. Similarly, firms often had several announcements of discontinuations in or around the same year which then got aggregated into a single number (data item 66) on COMPUSTAT." In most cases, the Wall Street Journal did not report the size of these discontinuations, making it impossible to determine the linkage back to the COMPUSTAT event of interest. These discontinuations were also excluded from our sample. Observations with simultaneous announcements introduce potential confounding causes for a single share price reaction. Most of these involve earnings announcements. Because of our inability to discriminate between these multiple causes, any observation involving simultaneous announcements was deleted from further consideration. A few discontinuations involved prior Wall Street Journal announcements of a recent management change. Cases of recent management change (within the last year) were deleted from our sample, as the expectation of a discontinuation and the associated stock price reaction may have largely accompanied the management change "In fact, firms who shed operations or divisions were often firms in financial difficulty, undergoing several discontinuations in the same year. A large segment of our initial COMPUSTAT sample thus consisted of multiple discontinuations by the same firms over one or several consecutive years. 214 announcement12 Moreover, new management may frame or perceive divisions as "winning" or "losing" differently from old management, making it difficult for us to properly classify sell-off events.13 In summary, the sample screening process and the resulting event deletions were as follows: firms not on the CRSP tape - 73 firms not found in the Wall Street Journal Index search - 211 firms for which no discontinuation announcement was found — 678 firms having multiple discontinuation announcements in the same year - 419 firms with confounding announcements on the event day - 97 event dates or comparison period window not on CRSP - 24 miscellaneous deletions because of untraceable name changes, CUSIP number changes, or discontinuation announcements straddling multiple fiscal years — 13 This left us with 131 terminations and 388 sell-offs. These are listed in Appendices A and B, respectively. All 131 terminations resulted in write-offs (losses). Of the 388 "Some discontinuations may involve cases where there has been a recent management change that was not accompanied by a public announcement, and hence assumed to be unknown to the market at large. In such cases the stock price will react as it would in cases of no management change, which for the purposes of this analysis is all that really matters. 13Our test of sell-offs examines the market's reaction to sell-offs of what it perceives to be winners versus losers. The "sunk cost" hypothesis assumes that the manager's discontinuation decision is unfluenced by bis perceptions of a division's status, but ultimately it is the market's perception of the division's status that drives our test of the sunk cost hypothesis. 215 sell-offs, 228 resulted in losses, while 160 resulted in gains. Many sell-offs involved several announcements, raising the total number of events associated with sell-offs to 656. Separate analyses were conducted for terminations and sell-offs. A list of our initial 2,034 firms (along with event years and other details) is given in Appendix C. The list also shows which firms were discarded at each stage of the sample selection process, along with the firms that comprise our final terminations and sell-offs samples. Potential Sample Biases This winnowing of our original 2,034 firms was a necessary step in constructing our final sample. The stock return data must be available and reflect an unambiguous relationship to a particular announcement of interest. Cleaning up our sample therefore becomes a crucial part of the study. However, in reducing our sample size from 2,034 to 519, we must be careful not to introduce any systematic biases, by eliminating subsets of events biased in a given direction. If there is compelling evidence that a clear direction of bias in the remaining data would be introduced by the deletion of specific subsets of events, these events should not be removed from our sample. Two potential sources of biases may be introduced by the sample screening process: management-related biases and market-related biases. These potential sources of biases were examined before each subset of events was deleted from the sample. 216 Firms not on CRSP tape present no particular bias, although if the firms got de-listed, we might expect a slight market bias toward a negative stock price reaction. Firms not found in the Wall Street Journal Index search will likely be smaller firms. Discontinued divisions in these firms may be a proportionally larger fraction of these firms' total size, hence more important to them. In these cases, while we expect a significant management commitment to these divisions (hence a sunk cost effect, with an increase in stock price), discontinuation of a large fraction of a small firm may signal its imminent demise (the firm not having the strength to withstand the shock of the discontinuation), with a (market driven) decrease in stock price. For purposes of our analysis, we believe that no systematic bias is being introduced by deleting these events. Firms for which no discontinuation announcement was found should be reasonable sized firms, but with proportionally small discontinuations. No particular market bias is expected, and likely minimal management bias, so that the size of any effect is expected to be minimal here.14 Firms having multiple discontinuation announcements in the same year were also deleted. It may well be that these firms get used to discontinuing divisions, thus reducing the management bias toward a sunk cost effect, and reducing the expected "Alternatively, these discontinuations may have been quite important ones but which were not made public by the firm when they occurred - for strategic reasons or for fear of a negative stock price reaction to the announcement. This could bias our sample of remaining firms somewhat in the positive direction. 217 increase in stock price. Discarding these might therefore bias our sample in the direction of higher returns. On the other hand, as we discuss later on, the market may react more positively to discontinuations when they take place in multiples, these being interpreted as the firm "cleaning house" of its losing projects. Discarding these would therefore bias our sample in the direction of lower returns. These combined effects are expected, a priori, to result in minimal or no bias with respect to our hypothesis. Firms with confounding announcements on the event day may also be problematic. Some firms may hold off on announcing a discontinuation - for "window dressing" purposes - until they have other news (primarily earnings announcements) to announce at the same time. Such window dressing can be expected to take place in order for the total effect of the combined announcements to make the firm better off than if the announcements had been made separately. A positive discontinuation can be used to prop up a bad earnings announcement, or a positive earnings announcement can be used to prop up a negative discontinuation announcement. This symmetry makes it hard to identify a particular bias, so we expect little bias to be introduced by the deletion of these events from our sample. Luckily, there is only a small number of such events (97) that were discarded from our sample.16 lsWe can nonetheless attempt to make Borne conjectures. From management's point of view, terminations will likely be deemed as negative events, and get padded by positive earnings announcements. If the "really" bad escalation cases are the ones that get padded (these being the ones that should generate the most positive stock price reactions!), our remaining sample may therefore be biased in the negative direction. Management may view sell-offs as positive, and use them to pad other more negative announcements. In such cases, our remaining sample would exclude these highly positive sell-off events. 218 Announcements whose event dates or part of their comparison period window were not on CRSP were also deleted from our sample. No bias is expected for newly listed firms, although delisted firms may have more negative returns. Our remaining sample may be slightly positively biased. Finally, for other miscellaneous deletions (which are very few), we expect no systematic bias. For example, name or CUSIP number changes (resulting from takeovers, etc.) can be positive or negative. Overall then, each of the deletions that were made were thought to produce either no systematic bias or slight biases that (partially) cancel each other out. 4. ANALYSIS OF TERMINATIONS Daily stock returns were obtained from the CRSP tape for a fixed period around the termination announcement date for the 131 firms in our sample of terminations.16 Returns for 71 days were obtained: the Wall Street Journal publication date of the termination announcement [day 0] and the 70 days preceding the publication date [days -70 to -1]. A termination or sell-off announcement will usually be reported on the Dow-Jones News Wire on the day it is made [day -1] and appear in the next day's Wall Street Journal [day 0]. The effect of that announcement on stock prices will therefore occur in day -1 or in day 0. Days -1 and 0 thus represent the "announcement period". The cumulative market-adjusted returns over these two days are compared with the average cumulative market-adjusted return from a control period of 30 two-day 16Our terminations testing methodology replicates that employed by Statman and Sepe. 219 windows [days -70 to -11], the observations from the pre-announcement period. The nine days preceding the announcement period [days -10 to -2] were excluded from the comparison period to reduce the chance of contamination of stock prices by rumors of an impending discontinuation announcement. In testing the behavioral hypothesis, two different approaches can be used to test for the presence of significant positive abnormal returns in the announcement period. Both approaches were shown (by Brown and Warner (1980) and (1985)) to give very similar results. We tested the hypothesis directly on market-adjusted returns, calculated by subtracting the CRSP value-weighted market index returns from the daily returns of the individual stocks. The test was performed on the difference between the announcement period market-adjusted returns and the pre-announcement period market-adjusted returns.17 The test statistic is: t = Ra - Rc [1] s[l+(l/30)]6 where Ra is the announcement period's mean market-adjusted return (over all firms), Rc is the comparison period's mean market-adjusted return (over all firms and 30 two-day intervals), and s is the standard deviation of the comparison period's 30 two-day 17Market-adjuSted returns do not adjust for differences in systematic risk of individual stocks. In using market-adjusted returns, we are making the implicit assumption that the average market risk for each of the two samples in [1] (as well as in [2], [3] and [4] below) are equal. This assumption allows the differences in the mean abnormal returns of the two samples to be tested directly, without requiring the use of market model adjusted returns. The assumption seems justified here as each sample is similar in its composition, encompassing firms of different sizes spanning a variety of different industries - leading to similar average market risks for both samples. 220 mean market-adjusted returns.18 Under a strong behavioral hypothesis, we would have Ra > Rc so that the difference Ra-Rc would be significantly positive - violating the normative hypothesis that a termination announcement conveys negative or neutral information. A large abnormal positive return over the termination announcement period indicates the market's satisfaction with the termination, signalling its belief that commitment to the division had escalated to a point contrary to shareholder interests. Returns were also adjusted according to the market model. Details of this approach are given in Appendix D. Similar results were obtained with market model returns as with market-adjusted returns, leading to identical conclusions. Results for Termination Announcements The full terminations data set (n = 131) for the period 1967-1987 produced the following results: Ra = -.00396, Rc = -.00190, s = .00361. We have Ra < Rc, which is in the direction opposite to our behavioral hypothesis. While not statistically significant (t = -0.561), these results instead are consistent with the normative hypothesis of negative abnormal returns associated with termination announcements. 1BThe assumptions underlying our difference in means tests [1] through [4] require independent random samples from populations of normally distributed (two-day) returns. In addition, test [1] assumes equal population variances for the announcement period and pre-announcement period (two-day) returns. This assumption is not totally satisfied but appears reasonable. The 30 comparison period cross-sectional standard deviations ranged from .035 to .054, while the cross-sectional standard deviation for the announcement period was .062. This standard deviation is higher for the announcement period, by an average of about 25%. However, the conclusion from test [1] remains unchanged by this difference. 221 These results are quite different from the Statman and Sepe (1989) results who found significant support for a sunk cost hypothesis. Their results for n = 70 were: Ra = +.0124, Rc = -.0014, s = .0040. Using the same test statistic, they concluded that Ra > Rc at the a - .01 level. In order to compare our results more directly with theirs, we re-tested our hypothesis with a reduced data set that matched their period of analysis, 1969-1983. With n = 109 events, we obtained: Ra = -.00614, Rc = -.00163, 8 = .00413 - yielding the same conclusion as we had before: no support for a sunk cost hypothesis, contrary to the Statman and Sepe results. This surprising difference in the two sets of results bears closer examination. Section 5 examines why we observe these significantly different results in the two studies, and reveals several reasons why this is so. Recognizing these, we stand by our conclusion of a lack of support for the sunk cost hypothesis in our full sample of terminations. An alternative explanation for the absence of a sunk cost result may be the absence of public knowledge concerning the past difficulties of terminated divisions. Indeed, our behavioral hypothesis (2a) is contingent on the market knowing of a division's difficulties prior to the termination announcement. This is the issue to which we now turn. The Impact of Prior Information on Termination Announcements As was argued earlier, if the poor performance or prospects of a division were unknown to the market prior to the termination announcement, then the announcement should trigger a decline (or at best, no change) in stock price, in 222 conformity with the normative hypothesis19. We therefore expect larger (i.e., less negative or even positive) abnormal returns resulting from terminations of divisions previously known to be struggling, compared to divisions whose financial status was not known publicly. Statman and Sepe (1989) indeed found much larger positive abnormal returns when it was public knowledge that the project or division was struggling. To test this conjecture, our sample was divided into two groups: - the "information" group — divisions for which news of their financial (or other) difficulties had been published in the Wall Street Journal, or had appeared on the Dow Jones News Wire, within 3 years prior to the termination announcement;20 and - the "no information" group — all other divisions, not meeting the preceding criterion. Under a sunk cost hypothesis, divisions in the "information" group should have announcement period abnormal returns that exceed the announcement period abnormal returns of the "no information" group. This is also tested statistically by a difference in means test, with a test statistic of: ieand this, even though there may be a strong sunk cost effect on the part of managers. 20Two sources were used to obtain this information. The Wall Street Journal Index was searched for the period 1967-1978, and the Dow Jones News Retrieval Service (whose coverage starts in 1979) was used for the period 1979-1987. The latter was searched for references from the Wall Street Journal and from the Dow Jones News Wire. When the division's status changed during these 3 years, the most recent announcement made prior to the termination announcement was used to classify the division's status at the termination announcement date. 223 t= Ri-Rn [2] where Ri (respectively Rn) is the announcement period's mean market-adjusted return for the firms in the "information" ("no information") group, s" (s2) is the variance of the "information" ("no information") group's returns, and % (nj is the number of firms in the "information" ("no information") group. Results of Prior Information on Termination Announcements From our total sample of n = 131, we found = 18 firms in the "information" group and n,, = 113 firms in the "no information" group. Detailed announcement period returns are given in Appendix E. The following results emerged: for the "information" group: Ri = .03295, 8 { = .07345, 12 positive and 6 negative returns; for the "no information" group: R„ = -.00984, 8 n = .05870, 48 positive and 65 negative returns. The resulting t-statistic is t = 2.35, significant (in our one-sided test) at the a=.01 level. We therefore find significant support for our sunk cost hypothesis in this case, as terminations in the "information" group actually produce (statistically) significantly higher abnormal returns than terminations in the "no information" group.21 The "information" group also contains a greater proportion of positive returns thfin the "no information" group, substantiated at the a=.05 level of significance.22 We find 21For their sample of 70 firms, the Statman and Sepe results were: npll, iv=59; R-.0404, 8i=.068; R .^0072, sn=.043, leading to a difference significant at the a=.05 level. ""This was obtained via the normal approximation to the difference in proportions test: z = (12/18) - (48/113) = 1.91 [(60/131) (71/131) (1/18 + 1/113)]* 224 ident ical conclusions us ing market-model adjusted returns. 5. T E R M I N A T I O N S : A C O M P A R I S O N W I T H T H E R E S U L T S O F S T A T M A N A N D S E P E Ou r basic empir ica l design and methodology closely follows that employed by Statman and Sepe (1989). Therefore, i t was quite surpr is ing to observe such a marked difference between the two sets of results i n test [1]. Some key differences between our two methodologies were as follows: (i) S ta tman and Sepe focussed on projects w i th a history of substant ial losses, by ident i fy ing those f i rms on C O M P U S T A T that reported losses from discontinued operations (data i tem 66) which exceeded 10% of operat ing earnings for that year. They obtained n= 1,172 f i rms. We also used the same threshold of 10%, but broadened the net to also include projects or divisions who experienced gains from discontinued operations. (Our f ina l sample of terminations, however, ended up containing only divisions experiencing losses from termination.) We obtained n= 2,034 f irms from this in i t ia l screening for the period 1967-1987. F o r the Statman and Sepe period of 1969-1983, we obtained n= 1,415 firms. One possible reason for the difference between our results may be the difference i n our respective C O M P U S T A T firm retr ievals. The C O M P U S T A T A n n u a l Industr ia l Tape contains only firms that are st i l l i n operation (possibly i n some restructured form) as of that year. Del isted or bankrupt firms get transferred to the C O M P U S T A T 225 Research Industrial Tape. We used both tapes to retrieve our initial sample of firms. Therefore, our results should show no bias toward either successful firms or unsuccessful ones. On the other hand, Statman and Sepe retrieved firms off the 1984 Annual Industrial Tape only. Hence, their sample may have been biased toward "successful" companies (which were still in business at the end of 1983). This selection bias implies a better overall stock performance for these companies than for companies who stopped operating (or went bankrupt) in the interim - including better average returns for most every type of announcement. In particular, these successful (or surviving) companies were likely less vulnerable financially at the time of discontinuation announcements. They were likely viewed by the market as being more salvageable, causing them to display a better stock performance, on average, at the discontinuation announcements. (ii) Statman and Sepe focussed exclusively on unambiguous terminations, which then reduced their sample size to 111 observations. None of these observations involved any mention that the motivation behind the terminations was to transfer the assets to another, more profitable project (as such cases would have constituted exceptions to the "bad news only" hypothesis under the normative model). According to one of the authors23, this selection of the 111 terminations involved a fair amount of subjective interpretation, particularly in selecting terminations as opposed to sell-offs. We experienced the same concerns in selecting our sub-samples of terminations and sell-offs, as many Wall Street Journal Index announcements used phrases such as "plans to "based on a telephone conversation with Meir Statman, March 1991. 226 divest itself of, "is abandoning", "will discontinue", "is disposing of, or "is considering liquidating" a given unit or operation. We were left with 283 terminations after this stage (232 for the period 1969-1983). (iii) Statman and Sepe then deleted all observations with confounding announcements (mostly earnings announcements). They also deleted observations for which return data for the announcement period were missing. This left them with a final sample of 70 observations - concentrated in no particular industry or time period. Our sub-sample of terminations, when put through this same screening step, left us with a final sample of 131 termination observations (109 observations for the Statman and Sepe period of 1969-1983), also spanning a wide range of industries and distributed over the full time period examined. The remainder of the Statman and Sepe analysis, specifically returns used, days in the announcement and pre-announcement periods, abnormal returns and test statistics, were the same as those used in our analysis. Any remaining differences between our two sets of results therefore stem from the subjective aspects of the sample selection process, and in particular the interpretation of events, in points 2 and 3 above.*4 "The 70 firms in our sample of 109 with the highest announcement period abnormal returns did allow us to conclude in favour of a sunk cost effect. These 70 firms produced: Ra = .02995, Rc = -.00170, s = .00376, and a resulting t-statistic of t = 8.28 . Clearly therefore it is possible for a partial set of 70 of the firms in our sample to generate the conclusion of a significant sunk cost effect. 227 Examination of the exact 70 events in the final Statman and Sepe sample (which they graciously made available to us) reveals surprisingly little overlap between our respective samples of terminations, and shows how sensitive our test of the competing hypotheses is to the subjective sifting process involved in sample selection. Only 21 events were common to the two samples. These 21 events contributed very strong positive abnormal returns to both samples. The average announcement period abnormal return (Ra-Rc in [1]) for these 21 events is equal to +.025. Twenty of their final events were not part of our 2,034 initial COMPUSTAT events. These were not picked up in our initial search because of a slight difference in our initial firm selection criteria. We selected firms whose income from discontinued operations was at least 10% (in absolute value) of operating income before depreciation (COMPUSTAT data item 13), whereas Statman and Sepe used a ratio of at least 10% of operating income after depreciation. This different denominator resulted in their capturing more firms with their 10% criterion than we did. These 20 events produced Ra-Rc= +.010. Of the remaining 29 events in the Statman and Sepe sample, we rejected 5 because of confounding announcements at the event date. This subset of 5 events produced Ra-Rc= -.025. We also rejected 6 of their events because they were actually sell-off announcements, or because of ambiguity as to whether the division was being terminated or sold off. For these, we found Ra-Rc= +.009. All of these divisions, in fact, ended up being sold off following the initial discontinuation announcement. 228 The remaining 18 events were part of multiple discontinuation announcements in the fiscal years in which the terminations took place. These were absent from our final sample because of the resulting ambiguity about the sign and magnitude of these terminations. These 18 events contributed an average announcement period abnormal return of +.019 — a surprising result, which we address further in our discussion section below. Conversely, the 109 terminations in our sample over the 1969-1983 period includes 88 events not captured in the Statman and Sepe sample. Exactly why these 88 events never found their way into the final Statman and Sepe sample cannot be answered completely. Careful review of these events reveals them to be bona fide terminations. Of course, our use of both the COMPUSTAT Annual and Research Industrial Tapes obviously gave us access to more firms than Statman and Sepe who only used the Annual Industrial Tape. Also, because of the different definitions of operating income used in our initial COMPUSTAT screening, we likely selected more firms with a negative operating income before depreciation than did Statman and Sepe. Consequently, these two factors combined gave us sole access to many of these 88 events. The resulting Ra-Rc for these 88 events was -.011, thus making our average announcement period abnormal return negative over our full sample. Therefore, even though very similar, the two sample screening processes may have biased the two samples in slightly different directions by including a significant number of different events. We are confident of the conclusions which we obtained using our empirical methodology, which looked both at active as well as bankrupt 229 firms - thereby avoiding a major potential source of bias in the sample. 6. ANALYSIS OF SELL-OFFS A very similar empirical methodology was used to test our sunk cost hypothesis in the case of sell-offs. The major test in this case was whether abnormal returns in the announcement period were significantly greater for sell-offs of "losers" than for sell-offs of "winners".26 Defining 'Winning" and "Losing" Divisions in the Case ofSell-Offs The basic behavioral hypothesis is that managers will have a tendency to "throw good money after bad" in divisions that are losing money, and resist selling off divisions that are incurring losses. This suggests focusing on divisions currently incurring operating losses. But there may be other criteria that would make a manager frame a division as a "winner" or a "loser". It is important that these criteria be made explicit, to allow us to properly classify the events used to test our hypotheses. Sell-offs raise particular concerns in this respect, as the total income from a sold division consists of the operating income plus the disposal income resulting from the sale of the division. A division whose sale would result in a write-off may be less likely to be sold than one whose sale would result in an extraordinary gain (net of book value). This suggests that disposal income may also enter into the definition of winners versus losers. Therefore, we can ask: Will managers be reluctant to sell off 2£This test was proposed, but not investigated, by Statman and Sepe. 230 a division when it is mcurring operating losses, when the (anticipated) disposal value of the division would lead to a disposal loss, or when the sum of these two values would result in a loss? Moreover, will the stock market (whose expectations about managers' tendencies to throw good money after bad are built into the stock price) have the same definition of a losing" division as the managers do? This requires further exploration. The psychology of the sunk cost effect is driven by the idea of somehow "breaking even". Obviously, incurring losses on both operations and disposal poses no classification problem. Neither do gains on both operations and disposal. The more difficult cases to classify are the ones where there is a gain on operations and a loss on disposal, or vice-versa. In these cases, the sum of the operating and disposal values may be positive or negative. We need to determine which measure best captures the manager's "breakeven" motivations in such cases. Various conjectures can be made. The complete history of the division could be used to "objectively" determine whether the division is a winner or a loser. A full retrospective evaluation would include all of the division's past cash flows, including initial capital outlays, as well as disposal value, entering in the assessment of the division's performance. All of the cash flows (or discounted cash flows) since the division's inception could then be added to yield a net (present) value, representing the current balance in the "mental account" for the division being sold off. Complete histories of divisional cash flows, however, are not available from public, or even proprietary, sources. 231 A (direct) managerial compensation explanation (i.e., bonuses based on the division's total income) would likely be associated with the sum of the year's operating and disposal incomes. In such cases, the manager has an economic incentive to hold on to a "losing" division until the total of the operating and disposal incomes becomes positive. A managerial reputation / face saving explanation could go either way. We could argue, on the one hand, that the current operating success of the division determines the manager's reputation as an effective decision-maker. Alternatively, the net change in the unit's performance or value since the manager became its head can determine reputation. The same could be argued about the division's disposal value, as the manager's reputation might sometimes be based on whether the division was sold for a profit. Or we could even argue that the manager's reputation is assessed on the basis of the sum of operating and disposal incomes,' as was the direct managerial compensation explanation. Because of all these considerations, test [3] was performed for different definitions of "winners" and "losers": winners versus losers on operating income from the last year's operation of the discontinued division - which we believe to be the primary determinant of a manager's sunk cost effect; on the division's disposal income; and on total (operating + disposal) income from the discontinued division. Income from discontinued operations (COMPUSTAT data item 66) is a single number that captures both the income/loss from the operation of the division for the fiscal year 232 in which the discontinuation took place and the gain/loss on the disposal of the division (net of book value). Moody's Industrials were used to look up the income from discontinued operations separated into its operating and disposal parts, respectively. The breakdown into these two numbers was reported in Moody's only for about 43% of the firms in our sample of sell-offs.86 The test of our hypothesis for sell-offs was done by testing the difference in mean market-adjusted returns for the 2-day window (days -1,0) around the initial intent of sale announcement, between "winning" sell-offs and "losing" sell-offs. The test statistic is: t = Rl-Rw [3] tsf/n, + af/oj5 where Rl is the announcement period's mean market-adjusted return for "losers", s2 is the variance of losers' returns in that period, and n, is the number of losers; Rw is the announcement period's mean market-adjusted return for "winners", s2 is the variance of winners' returns in that period, and n, is the number of winners. Results for Sell-Off Announcements The different variations of our basic test of sell-offs of "winners" versus 'losers" produced the results summarized in Table 1. These are the results of our test for the different definitions of "winning" and "losing" divisions. Also, while the market's 26Only from Sept. 30,1973 onwards did accounting standards require that discontinued operations be a separate accounting item. Prior to that date, income from discontinued operations (both operating and disposal income) was usually aggregated with other "Extraordinary Items". Footnote information had to be used to retrieve discontinued operations from extraordinary items, and in some cases this breakdown was not even contained as part of the footnote information in Moody's. 233 strongest reaction to a sell-off usually occurs at the very first announcement of intent to sell, it also reacts to further developments concerning a possible sale. We therefore performed our test for two different types of sell-off announcements: "intent to sell" and "sold". Note that when no intent of sale announcement was made, the "sold" announcement became the initial sale announcement as well. — Insert Table 1 here — These results all lead to a similar conclusion: the complete absence of any evidence in support of a sunk cost hypothesis. In fact, most of these results (the t-statistic as well as the percentage of negative versus positive returns) lean the other way, although not significantly. This lack of significance is consistent with the normative hypothesis about sell-offs, which predicts no significant difference in abnormal returns associated with sell-offs of winners and losers. As in the case of terminations, however, we must consider the role of the market's prior knowledge of a unit's performance before we can conclude anything about the sunk cost hypothesis for sell-offs. The Impact of Prior Information on Sell-Off Announcements Sell-offs of divisions previously known to be struggling should generate higher abnormal returns than sell-offs of divisions known to be profitable, or of unknown finnnHal status. In fact, previous information is particularly important in the case of sell-offs, where the operating status of the division as well as its disposal value are 234 often unknown until reported in financial statements, well after the sell-off announcements have been made. As a result, prior information about a division's performance may be the best (if not the only) way the market has to classify winners versus losers. Our sample of sell-offs was therefore separated into three groups, as a function of the information publicly available about divisions' operating incomes: group 1: the "known losers" group - divisions for which news of their financial (or other) difficulties was published in the Wall Street Journal or on the Dow Jones News Wire27 within 3 years prior to the initial sell-off announcement;28 group 2: the "known winners" group - divisions known to be earning positive profits prior to the sale, as published in the Wall Street Journal or on the Dow Jones News Wire within 3 years prior to the initial sell-off announcement; and group 3: the "no information" group - all other divisions, not meeting the preceding criteria. Under a sunk cost hypothesis, divisions in the "known losers" group should have announcement period abnormal returns that exceed the announcement period abnormal returns of the "known winners" or of the "no information" groups. The test 27As in the case of terminations, the Dow Jones News Wire was only searched for the period 1979-1987. S8When the division's status changed during these 3 years, we used the most recent announcement made prior to the initial Bell-off announcement to classify the division's status at the sell-off announcement date. 235 statistic for comparing groups 1 and 2 is: t = Rl -R2 [4] tsX + sl/nj-5 where Rl (respectively R2) is the announcement period's mean market-adjusted return for the firms in group 1 (group 2), B\ (B 9,) is the variance of the group 1 (group 2) returns, and nx (ns) is the number of firms in group 1 (group 2). A similar test statistic was used to test group 1 against group 3. Results of Prior Information on Sell-Off Announcements Reactions to the initial sell-off announcements produced the following results: for known losers: Rl = .00415 , sx = .05833 , nx = 42 (18 positive, 24 negative returns) for known winners: R2 = .02458 , &j = .07103 , = 34 (23 positive, 11 negative returns) for no information firms: R3 = .01655 , Sg = .07480 , n3 = 294 (162 positive, 132 negative returns). The t-value for test [4] in testing group 1 versus group 2 was -1.35, which is in the direction opposite to our sunk cost hypothesis. A similar result is found in testing group 1 versus group 3 (t= -1.24). Detailed announcement period returns are given in Appendix E. These findings indicate that selling off known losers does not result in a greater stock price reaction than selling off known winners or divisions whose 236 performance was not publicly known. Our results clearly fail to demonstrate the presence of a sunk cost effect in the case of sell-offs. 7. DISCUSSION Terminations and sell-offs draw an inconsistent picture of the market's expectation and response to managers' sunk cost behavior. Together, these results offer mixed support for the joint hypothesis of an efficient stock market and sunk cost behavior on the part of managers. Our termination results support this hypothesis, while the sell-off findings, although not strongly significant, are in the direction opposite that predicted by our behavioral hypothesis. Terminations The termination results on "information" firms, while based on a modest sample size, provide some evidence to support the sunk cost hypothesis, under an efficient capital market assumption. When combined with the lack of any significant result for the full terminations sample, the interpretation seems clear. Consistent with our behavioral hypothesis (2a), the difficulties experienced by a division must be publicly known prior to termination if the tendency toward managerial sunk cost behavior is to be built into the market's expectations, on average. Our data therefore support the conjecture that unless it knows of the prior difficulties of terminated divisions, the market does not (on average) seem to anticipate any strong sunk cost behavior on the part of managers. When the difficulties experienced by a division are known to the market prior to the division's termination, a significant expectation about managers throwing good money after bad is built into these firms' stock prices. Consistent with our behavioral 237 hypothesis, and unlike the findings of Statman and Sepe who found a sunk cost effect on their full sample of firms, our results highlight the importance of prior public knowledge about a division's performance as a critical determinant of the market anticipating sunk cost behavior on the part of management29. In testing all firms together in our test [1], the presence of a sunk cost effect for the "information" firms gets diluted by the absence of any such effect in the "no information" firms, resulting in the lack of any sunk cost results for the full sample of terminations. This is not to say that there is absolutely no market expectation of sunk cost behavior on the part of the "no information" firms. We must recall that under our behavioral hypothesis, termination provides bad news (information downgrading the expectations about the division's profitability which in turn lowers the NPV expectations for the firm) and good news (that managers are finally letting go of a losing division). For the "no information" firms, we find no evidence to support our hypothesis of a STRONG sunk cost effect - that the total effect of the good and bad news is positive. But we cannot rule out the possible existence of a WEAK sunk cost effect — that some good news accompanies termination announcements (on average), but that the positive effect is small in relation to the negative (bad news) part of the termination. Using stock prices only allows us to observe the total effect of a termination announcement -- which may potentially hide the presence of a smaller yet significant "good news" 29Tbia is subject to the sample selection biases discussed in section 5. We do not believe that these biases in any way obscure the interpretation of our results. 238 component to termination announcements.1 An alternative explanation of the terminations result may be one based on the market's low tolerance for uncertainty. Under this explanation, the market doesn't like uncertainty, and in particular doesn't like the ambiguity or uncertainty surrounding the status of a struggling division. Termination of the division provides closure to the market by eliminating that uncertainty, which generates an increase in share price. Note that this explanation is observationally equivalent to our sunk cost hypothesis. It therefore receives no support in our full sample of terminations, but is in agreement with the results obtained in our "information" versus "no information" test. Moreover, without further refinement of our tests on terminations, the two explanations cannot be separated, as they both make predictions in the same direction. Our termination results also allow us to speculate about the economic or financial consequences of sunk cost behavior. In our "information" group of terminations, we found that stock price jumped an average 3.3% upon termination of a division, whereas it fell 1.0% in our "no information" group. This 4.3% difference can be viewed as a lower bound on the average "cost" of escalating commitment for firms who persist 30Because all terminations may actually involve both good and bad news, quasi-experimentation to control for the bad news and observe the effect of the good news only is extremely difficult to perform in the present field setting. The occurrence of a recent management change may be one variable that could be used to control for the "good news" part of a termination announcement. Unfortunately, there is little that can control for the lowered expectations about a firm's NPV, the "bad news" part of a termination. Experimentation under the more controlled conditions of the laboratory would be necessary to identify the presence and extent of any WEAK sunk cost effect. 239 with losing divisions. One obviously has to be careful in making such an inference, but using an inductive argument we can conjecture that this 4.3% would have been added previously to the value of these firms' shares had the market not anticipated any future escalation of commitment in these losing divisions. This 4.3% represents one economic implication of escalated commitment, capturing the average future cost of not "pulling the plug" on a division. The actual average cost is likely to be greater than that. Because market expectations about future managerial behavior are probabilistic, the 4.3% figure would likely be greater if the market were certain of continued future escalation of commitment in a losing division. Moreover, past costs of persisting with the division, captured by decreases in share prices over recent months or years, likely add to the total. Sell-Offs The results for sell-offs paint a different picture. In examining sell-offs of losing divisions, we did not find any hint of the market expecting a managerial sunk cost effect. Our results point instead in the other direction, as divisions known to be making money produce a greater stock price increase upon sell-off than divisions known to be struggling. Why might sell-offs of winners provide the market with better news than sell-offs of losers? A winner's curse explanation would postulate that divisions sold off to the highest bidder should generate a positive reaction to the selling firm's stock because of the buying firm's overvaluation of the division, but would not formally predict a greater stock price increase for sell-offs of winning as opposed to losing divisions. 240 Might winning divisions somehow generate oueroptimism in the market about their future earnings potential, not present for losing divisions? Perceptions about winners may indeed be biased differently from those about losers; however, no economic explanation would produce such a result. We can nonetheless make some conjectures about market expectations that would support different perceptions about winners and losers. Without additional information, the market may perceive that a known loser is either being sold off out of necessity, or because it is natural for the firm to do so, as the division is simply not working out and the firm feels that its money can be better spent elsewhere. The market reacts somewhat indifferently to the news of the sell-off, as if it were expecting it to take place. Note that this is the opposite to a sunk cost explanation of the market's reaction. The sell-off of a winner on the other hand may come somewhat unexpectedly, and may convey to the market that if this winner is being sold off, then the firm must have significantly better alternative uses for this money. Especially if management is risk averse31, giving up "a bird in the hand" ( B e l l i n g off a winner) must be for really good reasons. This may even contribute to a stock market overreaction to the good news nature of these sell-offs. Much of this runs counter to our terminations results, which supported the sunk cost and efficient market joint hypothesis. Conceptually, our sunk cost intuitions should affect sell-offs as well as terminations, which makes these disparate findings 81firms hedging, purchasing corporate insurance, and managers seeking job security all convey management's risk aversion. 241 somewhat puzzling. Sell-offs do however offer more potential sources of stock price reaction, making it more difficult to isolate a sunk cost effect component associated with a sell-off announcement. A WEAK sunk cost effect may indeed be present, but gets overwhelmed by these other factors. Clearly, further investigation is required to carefully isolate the appropriate factors that may be present. Further Speculations Repeated laboratory experiments, as well as casual observation, point to the pervasive nature of the sunk cost effect. Might managers who sell off divisions somehow be immune to this phenomenon? The ever-present doubts about the external validity of laboratory findings, and in this case about the sunk cost effect, only get strengthened by the (non-)re8ults we obtained for sell-offs. The sunk cost hypothesis presented in this dissertation is compelling not only because of laboratory findings but also because of a strong intuition about its pervasiveness that stems from introspection about sunk cost situations, which most of us have had to face in our personal or business lives. Still, it is legitimate to ask whether actual management practice differs from laboratory studies of the sunk cost effect, and if so, how. Managers who persist with a loser too long may be subject to economic discipline on the part of their employer - thereby mitigating the sunk cost effect. This also raises concerns about managerial incentives, discussed in section 6 above. If a manager's compensation is based on the outcome of a major project, then we can expect the manager to display the sunk cost effect, because a negative outcome for the project translates into a low compensation level for the manager. If, on the other hand, the 242 manager is rewarded on the quality of the decision process used to allocate funds to the project, we might expect to see the sunk cost effect mitigated, because in these cases managers are likely to be penalized for throwing good money after bad. T^amincr ig also critical. Managers who face many sunk cost decisions in the course of their career may eventually learn the value of pulling the plug at the right time. They may find it easier to employ economic rationality, to detach themselves emotionally from their investment decisions and make peace with their losses. A more aggregate mental accounting, thinking of division-wide profits as opposed to individual project profits - thereby aggregating several sunk cost situations into a single mental account, may also help mitigate the effect. Alternatively, their business school training may have taught them that only marginal costs should matter. Because of these reasons, there may be significant differences between practicing managers and laboratory subjects. These and other possible reasons should be explored as part of further empirical research into the causes of sunk cost behavior. The sell-off results in this study indicate a lack of empirical support for the joint hypothesis of a rational stock market and a sunk cost effect on the part of managers. This lack of an asymmetric market reaction to sell-offs of winners versus losers (in the direction predicted by the behavioral hypothesis) may instead stem from the failure on the part of the market to account for, and react efficiently to, managers' sunk cost behavior. 243 An alternative hypothesis to explain this finding may indeed be that the market falls prey to the same behavioral tendencies as managers do when evaluating the level (and escalation) of commitment to a division or project.32 In particular, shareholders may themselves be subject to "wishful thinking" (see chapter 3) in evaluating the likelihood for success of a struggling division. Discontinuation (specifically, sell-off) then results in the market's "disappointment" that the firm was unable to turn the division around, and results in a decline (or the lack of an increase) in share price. This explanation would be consistent with the nuclear power plant cancellation findings of Hearth, Melicher and Gurley (1990) which show greater stock price declines when sunk costs, relative to the market value of the utility company's equity, are greater. However, it does not explain why we reached different conclusions in the case of sell-offs and terminations. On a different note, as pointed out in section 5, Statman and Sepe's 18 firms who had multiple discontinuations in a given year had, on average, large positive abnormal returns at the discontinuation announcements. This surprising finding suggests a slight variant on the way we can expect the market to react under our sunk cost hypothesis. Under our behavioral hypothesis, one would expect the market to react positively to the first termination announcement as the "good news" that management is finally letting go of a losing project. But it is also possible (or as this result suggests, likely) that firms who are terminating or selling off multiple divisions over a short time span are revealing a pattern of "cleaning house" of losing projects, and S^hefrin and Statman (1985) did identify a tendency for stockholders to display a sunk cost effect (a "disposition effect") in deciding when to sell and buy stock. 244 that this pattern only gets revealed at the second (or third, ...) in a series of discontinuation announcements rather than at the first. The market may view the first announcement as an isolated case, or forced upon the firm by exogenous forces. This is an important question for future research to address. Another important set of questions involve the issue of management tenure. The sunk cost phenomenon results from managerial attachment to a losing division. Obviously, new managers will more readily discontinue a division to which they are not personally committed. 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Journal of Finance 40, 777-792. Statman, Meir, and James F. Sepe. (1989). "Project Termination Announcements and the Market Value of the Firm". Financial Management Winter 1989, 74-81. Tang, Ming-Je. (1988). "An Economic Perspective on Escalating Commitment". Strategic Management Journal 9, 79-92. 247 Appendix A The Final Sample of 131 Termination Events 248 K X X X X K X X X X X X X K K K X X X X X X X X K X X X X K X X K K X X X X K K X K K X K X X K K X K K K K X K X X X K K K K K X X * x x x T h i s i s t h e f i n a l s a m p l e o f 131 t e r m i n a t i o n e v e n t s x x x x K X K K K K K X X X X X K X X X X X K X X K X K X X X X X X X K K X X X X X K X X K X X X X K X K K X X K X K X X K X K X K K X K X C U S I P • YR HO DA 0 0 5 0 4 1 1 0 8 1 11 2 3 0 1 2 0 4 1 1 0 8 2 11 2 4 0 1 4 4 7 6 1 0 8 5 10 2 5 0 1 4 4 7 6 1 0 8 6 2 24 0 1 5 4 2 6 1 0 8 7 7 9 0 2 6 8 7 9 1 0 7 2 7 2 1 0 2 9 4 2 9 1 0 8 0 3 7 0 3 2 0 8 7 1 0 7 5 5 1 0 3 9 3 7 5 1 0 7 2 2 14 0 4 2 7 3 5 1 0 76 6 16 0 4 3 3 7 5 1 0 70 11 3 0 5 3 2 1 3 1 0 7 3 4 2 7 0 6 7 8 0 6 1 0 8 2 9 2 9 0 7 1 7 0 7 1 0 81 11 19 0 7 7 8 5 1 1 0 76 1 21 0 8 3 7 3 9 1 0 77 3 1 1 1 5 2 2 3 1 0 8 2 11 17 1 2 3 1 6 9 1 0 71 12 16 1 2 5 0 0 5 1 0 7 8 6 19 1 4 8 4 2 9 1 0 8 4 6 12 1 6 1 1 7 7 1 0 81 6 4 1 6 1 1 7 7 1 0 8 6 4 21 1 6 1 2 4 1 1 0 7 2 10 2 0 1 6 3 2 6 7 1 0 7 8 1 16 1 7 0 5 2 0 1 0 8 0 7 2 5 2 0 0 2 7 3 1 0 86 4 4 2 0 4 5 2 5 1 0 71 12 16 2 0 7 1 9 2 1 0 76 6 16 2 0 B 4 5 3 1 0 70 10 26 2 1 2 3 6 3 1 0 84 9 2 8 2 2 4 3 9 9 1 0 8 3 12 2 8 2 2 8 0 9 3 1 0 77 1 6 2 4 5 0 9 1 1 0 78 12 19 2 4 7 5 3 2 1 0 7 2 2 8 2 5 0 5 9 5 1 0 8 2 6 2 5 2 5 4 1 1 1 1 0 77 9 2 3 2 5 5 2 6 4 1 0 7 2 5 2 2 5 5 2 6 4 1 0 81 9 I B 2 6 1 4 7 1 1 0 84 12 4 2 6 8 1 6 2 1 0 8 5 10 24 2 8 6 1 4 5 1 0 8 2 3 2 2 9 4 0 9 8 1 0 80 1 11 2 9 4 7 3 2 1 0 73 3 14 3 0 3 7 1 1 1 0 8 6 12 11 3 1 5 7 1 1 1 0 76 11 18 3 6 1 4 2 8 1 0 77 7 2 5 3 6 2 3 6 0 1 0 7 8 9 1 3 7 0 1 1 8 1 0 74 12 1 2 3 7 1 5 3 2 1 0 70 8 7 3 7 4 4 7 8 1 0 7 8 1 4 3 8 2 3 8 8 1 0 84 12 7 3 9 8 0 2 8 1 0 8 5 8 16 4 0 2 4 9 6 1 0 81 11 11 4 0 2 7 3 3 1 0 8 5 1 18 4 0 5 8 9 1 1 0 8 5 8 1 5 4 1 1 6 3 1 1 0 79 2 14 4 2 2 6 8 6 2 0 8 2 10 21 4 2 2 7 0 4 1 0 78 11 1 4 4 1 8 1 5 1 0 74 1 9 249 45747210 83 11 1 45747210 83 12 26 45747210 85 4 20 45852910 83 6 15 45955010 77 8 1 46072310 83 12 28 46261410 72 9 5 47717810 71 4 5 48258410 86 1 17 49262010 78 2 13 49262010 82 12 14 50175810 70 10 27 50221010 77 9 16 51369610 80 6 19 51369610 83 9 16 53982110 81 12 8 55113710 73 1 12 55167510 76 7 15 55284510 74 12 17 55420510 77 12 23 56167150 80 6 13 59478010 78 12 28 62915610 82 9 13 63087110 72 4 18 63876010 75 12 23 63890110 84 9 25 66744610 62 10 6 68066520 72 11 17 69005210 75 12 11 72447910 83 10 11 72811710 83 9 19 72811710 86 5 2 72818510 72 1 18 74310710 72 12 5 74579110 79 3 22 74625210 70 2 13 74740210 62 4 21 74836910 61 2 11 76035420 70 12 10 76312110 71 7 12 76648110 64 2 27 77513310 76 1 9 78120710 71 11 4 78224220 75 3 21 78354910 75 2 IB 78377110 70 6 11 79389710 81 7 11 80912310 73 2 23 81064010 81 12 4 82654610 71 5 17 82686210 72 8 21 85178310 81 2 17 85470110 75 12 24 85928110 72 1 20 86211110 64 2 9 86671310 81 11 2 87538610 82 3 31 88311810 70 9 28 89401510 80 5 9 91972010 80 4 10 91972010 80 4 15 92220410 79 1 26 92220410 85 4 22 92549610 77 6 29 92829810 77 4 20 92904110 61 10 21 250 92904110 82 2 9 96668010 74 5 17 97416510 80 8 29 98088110 82 9 27 98934910 77 9 19 98991710 84 12 3 251 Appendix B The Final Sample of 388 Sell-Off Events 252 K K X X X X K X X X X X X X K X X X K X X K K X X X X X K X X X X X X K X X X X K X X K K X X K K K K K X K X K X X K X X X X K K X X This i s the final sample of 388 sail-off svents **** K K X X K X X X X X K K K X K X X K X K K X X X X X X K X X X X X X X X K X X X X X X X X X K K X X K K X X K X X X K K X K X K X K K resulting in a total of 656 announcements «xxx X X K X X X X K X X K X X X X X X X X K K X K X X X K X X K K K K X X X K K K K X X K X X X K X K X K X K X X X X X X X X X X The codes in the data bass below have the following interpretation: TYP : Type of sell-off announcement » 1 for i n i t i a l intent of sale 2 for negotiating sale 3 for sold 4 for sale cancelled S6N : Sign of total income from discontinued operations • 1 for positive blsnk for negative 0 : Operating income from discontinued operations • 1 for positive 2 for negative 0 for zero blank i f unknown D : Disposal income from discontinued operations • 1 for positive 2 for negative 0 for zero blank i f unknown CUSIP • VR HO DA TYP S6N 0 1 00176510 79 8 6 1 1 00176510 79 8 9 2 1 00228010 72 1 21 2 00228010 72 2 7 2 00228010 72 3 17 4 00228010 74 4 11 2 1 00228010 74 5 17 3 1 00228010 78 5 10 1 1 11 00228010 78 7 17 2 1 11 00228010 78 11 28 3 1 11 00462610 85 4 4 1 22 00505530 81 9 29 3 00505530 84 9 11 1 00505530 85 3 19 3 00628410 83 3 24 1 1 11 00635110 82 11 26 1 1 00768010 74 9 23 2 12 00768010 74 10 9 3 12 00768010 79 3 1 3 1 01 00818510 77 11 21 2 1 00818510 78 1 5 4 1 00816510 78 3 8 2 1 00818510 78 4 21 2 1 00818510 78 6 30 2 1 00818510 78 9 19 3 1 00826110 86 11 20 1 1 11 00826110 87 1 2 2 1 11 01306810 85 7 3 3 01378810 85 2 26 1 01378810 85 5 3 3 253 01447610 83 01717510 83 01717510 83 01717510 83 01717510 84 01737210 75 01737210 76 01737210 76 01737210 85 02145410 87 02459110 81 02657310 87 02733920 82 02733920 82 02733920 82 02946510 77 02960910 74 02960910 75 03203710 84 03505310 83 03505310 85 03741110 78 03821310 80 03821310 80 03821310 80 04208310 80 04223110 77 04314710 82 04648610 87 04648610 87 04926730 78 04926730 78 04926730 87 05380710 81 05380710 81 05590010 72 06081510 87 06081510 87 06914910 72 06914910 73 06972510 74 08172110 82 08172110 82 0B172110 82 08441910 81 08441910 81 08441910 85 09179710 83 09179710 83 09517320 77 09985510 71 09985510 71 10550240 78 10550240 78 11522310 85 11704310 80 11704310 80 11742110 82 11883510 70 11883510 70 11883510 70 12008510 81 12008510 81 12169710 82 12189710 82 12189710 82 8 26 1 9 27 1 12 19 2 12 23 2 1 12 3 11 11 1 4 7 2 7 12 3 12 23 3 4 22 1 7 10 2 2 13 5 6 29 1 7 23 2 8 18 3 2 2 2 7 8 1 8 26 3 12 26 1 11 3 3 3 13 1 11 7 2 2 12 1 4 24 4 10 29 2 9 9 3 9 1 3 12 23 1 4 17 1 7 13 2 4 25 2 6 1 3 12 9 1 6 23 1 7 22 2 9 26 3 5 12 3 10 12 3 11 14 1 1 15 3 10 21 3 7 22 1 8 3 2 11 5 3 3 24 1 10 2 3 9 9 3 3 3 2 4 4 3 4 26 2 11 5 1 12 1 2 12 28 2 12 29 3 7 31 3 4 28 2 10 31 3 11 24 1 4 27 1 5 12 2 8 3 4 7 17 1 7 30 3 3 22 1 4 26 2 5 4 3 1 1 1 1 11 11 11 22 11 1 11 1 11 1 11 1 11 1 11 22 22 22 1 11 1 11 22 1 11 1 11 2 2 02 22 1 1 1 22 22 02 1 1 12 1 1 22 1 1 1 254 12237510 78 11 2 4 1 11 12237510 79 7 24 2 1 11 12237510 79 12 21 3 1 11 12484510 82 2 1 1 22 12488410 73 2 1 2 12488410 73 3 19 2 12488410 78 6 13 1 1 01 12488410 78 6 20 3 1 01 12488410 78 6 21 4 1 01 12488410 78 9 5 3 1 01 12500510 80 12 11 1 21 12500510 81 10 1 1 21 12500510 81 10 2 4 21 12500510 82 3 3 1 21 12561520 81 1 19 1 12650110 84 9 24 1 21 12705510 80 6 2 2 1 11 12705510 85 10 17 1 22 12738810 76 1 14 2 22 12738810 82 6 16 3 1 12769510 70 3 25 1 1 12769510 70 4 7 2 1 12769510 70 4 15 4 1 12769510 70 5 18 1 1 12769510 70 7 17 2 1 12769510 70 8 3 3 1 13106910 80 11 18 2 1 11 13435710 77 12 19 3 1 11 13705110 77 12 19 3 1 13781610 71 3 11 3 14057310 75 8 14 2 14146610 82 8 24 3 22 14842910 86 1 15 1 15130310 74 9 IB 3 22 15130310 81 4 10 3 1 11 16117710 87 8 4 1 1 16117710 87 10 19 3 1 16359610 78 9 28 2 1 16359610 86 10 30 1 1 16372710 75 9 30 3 1 16776310 85 2 5 1 1 16776310 85 2 6 2 1 16776310 85 2 13 2 1 16776310 85 2 20 2 1 16776310 85 2 21 3 1 17026810 77 10 10 3 1 01 17052010 81 9 24 1 1 17052010 84 1 9 1 17081910 86 4 15 3 17217210 80 3 13 2 1 11 17217210 80 5 16 3 1 11 18139610 86 6 12 1 1 18148610 79 6 28 1 1 11 18148610 79 11 1 3 1 11 18589610 87 8 17 3 19257610 82 7 8 3 19827910 76 6 4 1 1 01 19827910 76 8 3 3 1 01 19827910 77 9 6 3 1 01 20161510 87 3 23 1 20341710 84 7 23 1 20341710 84 11 29 3 20341710 86 8 26 3 20479530 85 12 27 3 1 11 20479530 86 10 30 3 1 11 20970510 84 2 1 1 11 255 20970510 84 4 17 3 11 21036R10 82 1 26 1 21036R10 82 5 17 3 21617410 78 6 7 3 1 21617410 81 10 7 1 1 21866110 74 2 13 2 21866110 74 2 19 3 21866110 77 9 6 1 22 218661X0 77 11 22 3 22 21909310 73 3 14 2 1 22374110 74 6 18 2 1 22374110 75 1 13 3 1 22417410 83 6 27 1 226745?R 70 5 5 3 22674510 80 4 18 2 1 22674510 80 5 22 S 1 22674510 80 5 30 3 1 22711110 86 12 29 3 22 22712910 72 4 17 1 1 11 22821910 64 11 20 1 1 11 22821910 85 1 7 3 1 11 22989010 61 1 28 1 1 22989010 81 3 19 3 1 22989010 86 1 2 3 1 22989010 87 11 5 3 1 21 23102110 75 7 15 3 22 23571710 63 8 18 1 1 01 23975310 86 10 1 1 1 11 23975310 86 11 28 2 1 11 24363120 82 10 5 3 24711410 84 8 2 3 1 11 2478B310 79 1 19 3 1 11 24788310 79 5 24 3 1 11 24984410 71 4 9 3 24984410 73 2 5 2 1 21 25243510 85 1 3 3 21 25526410 76 4 23 1 22 25526410 76 11 19 2 22 25526410 76 12 23 3 22 26147110 83 7 1 3 26147110 86 10 17 1 26147110 86 12 22 2 26147110 87 1 23 2 26147110 87 12 21 1 26414710 81 9 9 1 1 11 26414710 81 11 3 2 1 11 26414710 81 12 2 3 1 11 26414710 87 9 22 1 22 26414710 87 12 4 2 22 26803910 72 11 6 2 27033010 B5 8 29 1 21 27033010 85 10 29 2 21 28134710 83 4 27 1 22 28134710 83 6 10 3 22 28244310 71 7 15 2 28244310 71 7 28 3 28336210 76 6 28 1 28336210 76 11 9 2 28336210 76 12 16 3 28336210 78 8 7 1 28458710 71 12 23 3 29380510 87 2 25 1 1 11 29409810 80 2 7 2 29409810 80 3 25 3 29665910 79 2 16 2 1 30608410 71 9 8 3 256 30608410 73 5 7 2 1 11 30608410 73 5 15 3 1 11 30717110 69 6 6 1 1 30717110 69 6 16 2 1 31313510 79 2 13 3 31313510 85 10 8 1 1 51385510 73 1 22 3 31385510 73 1 24 3 31742110 74 9 13 2 31742110 74 10 7 2 31742110 75 11 6 3 1 31963310 87 6 2 1 1 11 33836010 83 2 11 1 33890910 87 3 5 3 33937610 80 6 6 1 33937610 80 7 31 1 34346510 83 4 14 3 22 34386110 87 7 28 1 1 21 34386110 87 8 26 2 1 21 34482010 72 10 26 2 34482010 72 11 3 2 34487210 71 1 8 3 34583810 74 3 29 1 36102810 81 9 8 3 36144810 85 8 15 1 36161410 85 4 5 1 1 11 36244210 69 5 2 2 36244210 69 6 13 4 36442410 84 7 26 1 02 36442410 84 9 5 3 02 36476010 80 1 14 1 22 36476010 80 3 18 3 22 36935210 86 3 27 1 1 11 37006410 69 6 25 2 37006410 69 7 25 1 37006410 69 9 12 2 37006410 69 10 29 2 37006410 70 2 26 3 37062210 87 3 6 1 1 37062210 87 4 27 3 1 37153210 83 7 12 1 1 37153210 86 6 16 3 1 37244710 81 8 31 1 37244710 82 1 5 4 37244710 82 7 16 3 37244710 86 9 29 3 22 37371210 86 4 7 1 22 38137010 81 10 28 1 38274810 87 3 25 3 22 38937010 70 7 20 3 1 38985630 80 3 11 2 22 38985630 83 9 1 3 22 39056810 74 3 22 1 1 39802810 83 2 16 1 1 39802810 83 3 25 3 1 39802810 83 6 13 1 1 39802810 83 6 20 2 1 39802810 83 6 30 2 1 39802810 83 9 23 2 1 39802810 83 12 20 3 1 40249610 85 5 9 1 1 11 40249610 85 7 22 3 1 11 40530710 75 5 2 1 22 40530710 75 5 13 2 22 40530710 75 7 2 3 22 40536310 76 8 17 3 1 257 41052210 86 9 12 41766810 82 9 2 41766810 82 : 11 2 42268620 82 4 21 42268620 82 8 3 42300210 81 8 27 42300210 81 11 3 42343410 74 6 3 42839910 84 10 16 42961210 75 7 23 42981210 75 8 29 42981210 83 6 27 43307610 85 11 13 43575630 64 4 2 43575830 84 5 7 44041610 83 4 15 44050610 71 3 51 44050610 72 9 29 44181510 66 12 26 44305110 81 9 3 44305110 81 10 9 46378410 74 8 30 44929010 80 3 12 44929010 83 4 19 45254010 86 12 19 45666810 84 5 11 45666810 84 6 5 45764110 69 10 9 45779430 70 10 30 45793310 86 10 1 45835110 85 10 3 45835110 86 1 9 45877620 84 3 26 45881310 86 8 18 45910110 84 12 26 46059610 74 5 20 46261410 77 10 14 46261410 77 12 6 46261410 80 5 8 46334910 77 1 24 46334910 84 4 2 46334910 86 10 31 46334910 86 11 4 48205810 83 11 16 48245210 87 6 10 48602610 77 2 23 48602610 86 4 8 48602610 86 11 17 48687210 70 12 18 49308010 83 7 27 49447410 81 9 21 49447410 82 8 31 49447410 82 12 3 49849410 72 8 2 50060210 86 6 30 50062010 73 8 27 50185810 81 7 16 50185810 81 8 10 50243910 71 8 17 50243910 71 8 31 50243910 79 12 14 50243910 82 5 18 50243910 82 7 14 50247010 64 9 24 52189010 86 11 14 52169010 86 12 30 1 22 1 02 2 22 1 3 1 22 3 22 2 22 3 1 01 2 1 21 3 1 21 1 22 1 22 1 1 3 1 1 3 1 3 1 2 1 1 1 21 3 1 21 1 22 2 1 22 3 22 2 21 3 21 3 2 1 1 1 3 1 1 3 1 22 3 1 3 22 2 1 21 3 1 21 1 22 1 3 1 1 1 2 1 1 1 21 1 1 11 2 22 1 3 3 1 1 1 1 21 2 1 21 3 1 21 3 1 3 21 1 22 3 22 2 3 1 1 22 2 22 1 12 2 2 258 52189010 87 1 2 3 52728810 75 11 6 3 52728810 86 9 16 1 1 52728810 86 12 2 3 1 53048910 70 12 17 3 53245710 87 8 6 2 1 53625710 78 5 31 1 53625710 84 7 31 1 1 11 536257!0 84 12 11 2 1 11 53625710 85 9 20 3 1 11 54042410 77 6 3 1 1 11 54042410 83 3 14 3 1 54042410 85 4 9 1 1 54411610 79 6 6 3 54411610 61 12 2 3 54966210 77 7 15 3 55061910 64 7 3 3 1 11 55113710 62 6 24 3 12 55261810 67 5 12 1 55290110 65 11 5 1 1 11 55290110 85 11 29 3 1 11 55371310 70 2 4 2 55420510 73 9 5 3 1 55420710 79 10 5 3 55430710 72 6 13 2 55430710 72 8 2 2 55430710 72 9 19 3 56509710 84 7 5 3 1 21 56613910 81 11 6 3 02 57235010 80 4 14 1 57235010 80 4 30 3 57239310 71 11 8 2 57537920 82 7 26 1 57537920 82 7 29 2 57537920 62 6 27 3 57541810 69 12 23 2 57541810 69 12 31 2 57541810 80 1 17 3 1 01 57641210 72 12 13 2 1 57708110 73 5 2 2 57777110 64 7 IB 1 1 11 57777110 84 11 28 2 1 11 57777110 64 12 27 3 1 11 58062810 64 9 18 1 58123810 85 11 12 1 58513610 63 5 25 1 58964220 71 11 15 2 1 59150310 80 12 9 1 1 21 59150310 81 1 27 3 1 21 59169010 82 4 7 1 1 11 59169010 82 10 25 3 1 11 59169010 82 11 30 3 1 11 60107310 82 1 6 1 1 61942610 82 2 23 1 1 11 61942610 82 3 18 2 1 11 61942610 82 5 3 2 1 11 61942610 82 6 10 3 1 11 62012710 87 8 11 1 21 62985310 78 9 5 1 22 62985310 78 11 10 2 22 62985310 79 2 5 3 22 63085410 78 9 11 2 63085410 78 10 25 3 63581910 78 2 6 3 63581910 79 4 27 1 1 63581910 79 5 30 2 1 259 63581910 79 7 9 3 1 63631610 79 12 31 1 1 63631610 81 1 9 3 1 63631610 81 2 6 4 1 63631610 81 3 13 3 1 63631610 85 6 20 3 63690510 86 4 21 1 11 63690510 86 6 6 2 11 63690510 86 6 18 3 11 63713010 79 9 21 1 22 63713010 87 6 11 1 1 11 63809710 73 4 12 2 63890110 81 5 15 1 63890110 81 7 27 2 63890110 81 9 15 3 65163910 85 4 3 1 1 11 65163910 85 5 31 3 1 11 65163910 85 9 23 3 1 11 65406110 63 5 10 1 1 21 65406110 86 7 10 3 1 11 65602530 76 12 6 1 22 65602530 76 12 24 2 22 65602530 77 4 12 3 22 65655910 73 9 22 2 65655910 86 1 7 2 66752810 81 11 9 1 1 11 66752810 82 1 15 3 1 11 67025010 71 7 14 2 67052210 86 1 2 3 67634610 85 7 19 1 67740110 85 7 3 1 11 67740110 85 10 1 3 11 68066520 85 1 17 1 1 11 68066520 65 7 26 3 1 11 68250510 B3 8 12 1 12 68250510 83 12 6 2 12 68590510 86 3 6 1 68628510 80 3 19 3 68628510 81 4 21 2 1 68628510 81 6 22 3 1 68667910 72 9 22 2 68667910 72 10 5 3 69010510 81 7 29 1 22 69010510 81 9 29 2 22 69144910 78 12 27 2 69144910 80 4 10 1 1 69144910 80 5 21 4 1 69144910 80 5 28 1 1 69144910 80 7 9 2 1 69144910 80 8 25 3 1 69362410 87 1 23 1 1 21 69362410 87 3 IB 2 1 21 69362410 87 4 28 2 1 21 70334720 63 8 11 1 22 70456210 80 7 9 1 70456210 80 12 17 2 70456210 80 12 22 3 70644610 73 5 23 2 70935210 86 9 9 1 22 71344810 65 5 21 2 1 71536110 74 6 25 2 22 71800960 81 2 19 1 1 71800960 81 5 27 3 1 71832010 75 8 15 1 22 71859210 87 7 3 1 1 71879910 87 5 4 3 1 260 72364510 84 6 25 1 1 72364510 84 8 23 2 1 72364510 84 8 24 2 1 72811710 84 2 17 1 1 01 72811710 84 2 29 2 1 01 72811710 84 3 13 3 1 01 73016210 84 12 28 1 1 01 73620210 84 12 12 1 22 73620210 85 1 2 3 22 74100410 78 3 28 3 74100410 79 8 3 3 74310710 79 7 5 3 1 11 74956210 80 1 15 2 1 749562)0 80 11 3 3 1 75127710 86 7 11 1 1 01 75510310 77 8 26 1 1 11 75510310 77 10 3 3 1 11 75510310 82 6 29 3 75510310 83 7 25 2 1 11 75510310 84 9 14 1 75510310 84 11 2 2 75510310 84 11 29 3 75528110 84 12 21 3 75623110 70 9 21 2 75764010 73 7 6 1 22 75865010 74 3 28 2 1 11 75865010 74 4 8 4 1 11 75865010 74 5 9 2 1 11 75865010 74 10 23 3 1 11 75946610 75 11 19 1 75946610 79 7 17 2 1 75946610 79 7 31 2 1 75946610 79 8 9 2 1 75946610 80 1 2 3 1 76312110 71 7 20 2 76710010 83 9 16 1 1 76710010 84 1 6 3 1 76775410 87 3 31 1 1 02 77101010 78 6 13 2 1 21 77101010 79 7 6 2 1 11 77101010 82 1 15 1 1 01 77379410 74 12 11 3 12 77542210 75 12 30 1 22 78176810 77 4 5 2 78176810 77 5 12 3 78377110 77 3 30 2 22 78377110 77 4 27 3 22 78377110 87 8 24 3 1 21 78501110 74 1 3 1 1 78644910 80 3 7 2 1 78662910 81 10 6 3 1 79389710 82 1 12 1 1 01 79409910 82 2 24 1 22 79840710 82 9 2 1 79840710 82 10 27 3 80068110 71 9 10 2 80366710 73 6 19 2 1 11 80366710 73 7 15 3 1 11 80460010 79 3 28 1 22 80685710 86 10 27 2 80685710 87 3 13 2 80685710 87 3 17 4 80685710 87 6 4 2 80685710 87 9 1 2 B0685710 87 10 9 3 80851910 84 12 19 1 261 81064010 75 6 26 1 81064010 76 3 10 2 61064010 76 4 19 3 81185010 80 4 8 1 1 81185010 80 4 9 2 1 81185010 80 4 14 2 1 81185010 80 4 17 2 1 81185010 80 4 28 2 1 81185010 80 9 15 3 1 81237010 77 8 31 2 22 81732010 87 1 5 3 1 11 81760610 81 10 19 1 1 81760610 61 12 9 3 1 81760610 82 9 29 1 1 62661910 83 6 30 1 82675010 75 5 23 1 82675010 75 6 24 2 82675010 75 12 18 3 82867510 69 9 19 2 82867510 69 10 22 4 82930210 86 5 13 1 1 83117510 62 9 13 3 1 01 83166510 75 9 24 1 22 83186510 75 9 25 1 22 83211010 87 7 24 1 1 22 64760910 79 3 30 2 12 84760910 79 5 25 3 12 85224510 81 11 13 1 1 85224510 81 12 31 3 1 85928110 70 9 28 2 85926110 70 10 13 3 86157210 74 9 19 1 22 66183910 79 11 23 3 22 86365910 70 11 9 1 86365910 82 3 1 1 22 66621220 72 5 19 2 86664510 81 7 31 1 86664510 81 8 18 3 86664510 86 11 21 2 1 11 86803510 84 3 14 1 1 11 86803510 84 8 20 3 1 11 87114010 83 5 27 1 87114010 83 10 4 3 87156510 84 1 4 3 1 87246410 86 1 21 1 1 11 87468710 77 5 27 2 1 87468710 77 8 15 3 1 67468710 77 9 7 3 1 87568410 80 5 21 1 22 87655330 81 10 12 3 22 87651210 76 9 2 3 1 88160910 77 10 26 3 88642310 87 6 25 1 1 11 88642310 87 9 30 3 1 11 88673510 82 6 24 3 88826610 83 8 15 1 88826610 83 9 2 3 86883710 79 10 4 2 89027810 80 9 11 1 1 11 89027810 80 11 17 2 1 11 89027810 80 12 18 2 1 11 89027810 81 1 5 3 1 11 89130510 86 2 24 1 02 89345110 72 8 22 2 89348510 81 5 22 1 1 89675540 82 3 9 3 262 89675540 82 3 10 3 89675540 87 12 15 1 1 90148610 76 8 24 3 90148610 82 2 26 1 90148610 82 3 29 2 90266010 77 9 2 1 22 90266010 77 11 2 3 22 90307010 79 3 21 3 90320010 74 7 2 2 90320010 76 3 5 3 90607210 83 7 6 3 1 01 92227210 85 11 5 2 92227210 85 12 24 2 92872010 73 4 23 2 93067610 76 3 22 2 1 11 93235510 75 12 31 2 93235510 76 3 2 5 93405110 78 9 19 3 1 11 93405110 78 12 18 3 1 11 94866210 77 6 30 3 94866210 79 8 27 2 22 95980710 74 8 28 1 97188910 80 8 25 1 1 11 98190410 73 6 6 2 1 98259410 85 7 3 3 98305110 73 1 5 1 98305110 73 2 1 3 98305110 78 12 15 2 22 98305110 79 1 3 3 22 98305110 82 11 26 3 12 98477710 86 11 4 1 98477710 87 3 23 1 263 Appendix C The Initial Sample of 2,034 Firms 264 • • • • • FULL SAMPLE OF 2034 FIRMS SELECTED OFF THE COMPUSTAT TAPE • • • • » Each l ine contains the following Information: (1) F isca l year In which a given f i r * had a "s igni f icant" discontinuation (2) Firm's name (3) Firm's 6 -d lg l t CUSIP number (4) Ratio of (5)/(6) — must exceed a 0.10 (or 10X) threshold (In absolute value) (5) Income from discontinued operations (COMPUSTAT data I tern 66) (6) Firm's operating Income for that r isca l year (7) Firm's total assets (a measure of size) (8) Firm's Industry category (9) Calendar months Included In that f i s c a l year (useful for event search purposes) The following firms were not on the CRSP tape: (73 firms) 1970 BALFOUR MACLAINE CORP 058459 -1.056 -0.244 0.231 33.668 GROCERIES ft RELATED 3 / 70 TO 2 / 71 1970 COBURN CORP OF AMERICA 191054 0.119 0 .320 2.681 59.054 PERSONAL CREDIT INST • 3 / 70 TO 2 / 71 1970 ROYAL CASTLE SYSTEMS INC 780155 -0.112 -0 .179 1.597 19.558 RETAIL-EATING PLACES • 7 / 69 TO 12 / 70 1971 BALFOUR HACLAINE CORP 058459 3.400 -0 .221 -0.065 21.693 GROCERIES ft RELATED 3 / 71 TO 2 / 72 1971 COBURN CORP OF AMERICA 191054 50179.992 -5 .018 0.000 43.230 PERSONAL CREDIT INST • 3 / 71 TO 2 / 72 1972 PENN MERCHANDISING CORP 707549 -0.639 -1.818 2.846 57.653 RETAIL-GROCERY STORE • 9 / 71 TO 8 / 72 1973 WTC INC 929340 -0.509 -1 .898 3.728 25.810 FREIGHT FORWARDING • YEAR 1973 1974 BALFOUR MACLAINE CORP 058459 -167.683 -6.023 0.036 93.071 GROCERIES ft RELATED YEAR 1974 1974 HYATT CORP 448564 -0.348 -4 .530 13.032 184.295 HOTEL-MOTELS • 2 / 74 TO 1 / 75 1974 PENN MERCHANDISING CORP 707549 -0.665 -1 .957 2.941 47.033 RETAIL-GROCERY STORE • 9 / 73 TO 8 / 74 1974 VALLEY FORGE CORP 919640 0.574 -6 .251 -10.886 76.177 ABRAS 1VE,ASBESTOS,M1 1 / 73 TO 12 / 74 1974 WIDENER PLACE FUND INC 967589 -0.208 -1 .049 5.032 45.706 RETAIL-APPAREL ft ACC • 2 / 74 TO 1 / 75 1975 AMC INVESTORS INC 001670 -0.401 -1 .425 3.550 42.078 APPAREL ft OTHER FINI • YEAR 1975 1975 BALFOUR MACLAINE CORP 058459 -0.454 -0 .490 1.080 101.691 GROCERIES ft RELATED YEAR 1975 1975 HYATT CORP 448564 -0.192 -2 .061 10.709 208.814 HOTEL-MOTELS • 2 / 75 TO 1 / 76 1975 LIN BROADCAST 1NG 532763 -0.352 -4 .911 13.968 87.964 TELEVISION BROADCAST YEAR 1975 1975 VALLEY FORGE CORP 919640 -3.372 2 .327 -0.690 60.047 ABR AS 1 VE, ASBESTOS ,M 1 TRUCK 1NG-LOCALftLONG YEAR 1975 1975 WOODS INVESTMENT CO 980124 1.250 6 .574 5.260 46.532 • YEAR 1975 1976 OVERSEAS NATIONAL AIRWAYS 690343 0.208 -2 .127 -10.217 63.970 AIR TRANSPORTAT 1ON-C • YEAR 1976 1976 TRC COS INC 872625 -0.335 -0 .080 0.239 1.575 ENGR, ARCHITECT, SUR 7 / 75 TO 6 / 76 1976 VALLEY FORGE CORP 919640 0.142 0 .260 1.837 51.753 ABRAS 1VE,ASBESTOS,M1 YEAR 1976 1977 HOWE RICHARDSON INC 443009 -4.021 -1, .335 0.332 5.222 OFFICE,COMPUTING,ACC YEAR 1977 1977 OVERSEAS NATIONAL AIRWAYS 690343 -5.344 -2 .640 0.494 97.433 AIR TRANSPORTATION-C • YEAR 1977 1977 TGC INC-OLD 872415 -0.456 -1, .525 3.346 80.783 TOYS ft AMUSEMENT SPO • 8 / 76 TO 7 / 77 1977 VADER GROUP INC 918732 -0.869 -0 .352 0.405 2.450 MISC NONDURABLE GOOD YEAR 1977 1978 BETZ LABORATORIES INC 087779 0.147 4 .904 33.256 112.998 MISC CHEMICAL PRODUC YEAR 1978 1979 MALLINCKROOT INC 561229 0.126 9 . 136 72.354 333.001 MISC CHEMICAL PRODUC • YEAR 1979 1979 VADER CROUP INC 918732 -0.905 -0.239 0.264 2.290 MISC NONDURABLE GOOD YEAR 1979 1979 WTC INC 929340 0.185 -0, .273 -1.475 34.322 FREIGHT FORWARDING • YEAR 1979 1980 BOWATER INDS PLC -ADR 102187 -0.219 -71.000 323.587 2296.600 LUMBER AND CONSTR MA YEAR 1980 1980 LATSHAW ENTERPRISES INC 518399 -0.954 -0. .965 1.011 18.358 INDUSTRIAL CONTROLS 11 / 79 TO 10 / 80 1980 WTC INC 929340 -2.450 -2, .259 0.922 22.307 FREIGHT FORWARDING • YEAR 1980 1981 LATSHAW ENTERPRISES INC 518399 0.117 0.073 0.622 18.058 INDUSTRIAL CONTROLS 11 / 80 TO 10 / 81 1981 PENN TRAFFIC CO 707832 -0.101 -1 .620 16.072 97.450 GROCERY STORES 2 / 81 TO 1 / 82 1981 SPARTECH CORP 847220 -0.147 -1. .776 12.114 103.874 MISC PLASTICS PRODUC 11 / 80 TO 10 / 81 1982 DATAMETRICS CORP 238085 11.164 -1, .228 -0.110 1.978 COMPUTER PERIPHERALS 11 / 81 TO 10 / 82 1982 SPARTECH CORP 847220 0.132 0. .325 2.460 64.347 MISC PLASTICS PRODUC 11 / 81 TO 10 / 82 1982 VALLEY FORGE CORP 919640 -0.556 -0. .195 0.351 12.188 ABRASIVE,ASBESTOS,Ml TELEPHONE COMM (WIRE YEAR 1982 1983 COM SYSTEMS INC 199773 -12.086 -4, .774 0.395 12.610 1 / 83 TO 3 / 84 1983 LATSHAW ENTERPRISES INC 518399 -0.145 -0. .138 0.954 14.644 INDUSTRIAL CONTROLS 11 / 82 TO 10 / 83 1983 MARLTON TECHNOLOGIES 571263 1.510 -7. .647 -5.063 72.728 TELE ft TELEGRAPH APP YEAR 1983 1983 SPARTECH CORP 847220 -10.270 -10. .496 1.022 17.176 MISC PLASTICS PRODUC 11 / 82 TO 10 / 83 1984 COM SYSTEMS INC 199773 -0.111 0. .512 -4.619 15.654 TELEPHONE COMM (WIRE 1 / 84 TO 3 / 85 1981 DIASONICS INC 252836 0.436 -11. .904 -27.304 151.909 X-RAY,ELECTROMED1CAL YEAR 1984 1981 INTEGRA A HOTEL ft REST 457948 0.353 2. .376 6.733 322.701 EATING PLACES YEAR 1984 198U LATSHAW ENTERPRISES INC 518399 0.389 0. .352 0.904 15.790 INDUSTRIAL CONTROLS 11 / 83 TO 10 / 84 198ft MARLTON TECHNOLOGIES 571263 0 . 1 1 3 0 . 2 2 3 1 . 9 7 0 6 8 . 9 3 1 TELE ft TELEGRAPH APP YEAR 1 9 8 0 198ft RESOURCE RECOVERY TECH 760930 91.969 -2.658 -0 .028 11.261 APPAREL,PIECE GOS,NO 3 / 8 3 TO 12 / 8ft 198ft SPARTECH CORP 8H7220 0.636 0.962 1.513 17.736 MISC PLASTICS PROOUC 11 / 83 TO 10 / 8ft 198ft VADER GROUP INC 918732 -3.181 -1.038 0.326 2.370 MISC NONDURABLE GOOD YEAR 198ft 198ft VALLEY FORGE CORP 919610 0. 189 0.156 2.110 13.688 ABR AS 1VE,ASBES TOS,M1 MOTOR VEHICLES ft CAR YEAR 1981 1985 COLLINS INDUSTRIES INC 19ft858 -0.151 -1.237 2.711 5ft.118 11 / 8ft TO 10 / 8 5 1985 GRAHAM FIELD HEALTH PD9 38D632 3.683 - 5 .152 -1.399 52.010 PROFESSIONAL EQ ft SU YEAR 1985 1985 IGI INC ftft9575 -0.179 -0.733 1.531 19.160 BIOLOGICAL PRODUCTS YEAR 1985 1985 LATSHAW ENTERPRISES INC 518399 0.106 0. 170 1.605 16.H39 INDUSTRIAL CON1ROLS 11 / 81 TO 10 / 8 9 1985 TENERA -LP 880331 0.191 -0.938 -1.831 29.087 ENGR, ARCHITECT, SUR MISC NONDURABLE GOOD 7 / 81 TO 6 / 8 5 1985 VADER GROUP INC 918732 -0.97ft -0.531 0.515 21.112 13 / 81 TO 9 / 85 1986 BALFOUR HACLAINE CORP 058H59 0.282 7.771 27.580 217.19ft GROCERIES ft RELATED YEAR 1986 1986 BAXTER INTERNATIONAL IHC 871813 0.169 321.000 681.000 7068.000 PHARMACEUTICAL PREPA YEAR 1986 1986 BUFFTON CORP 119885 -0.101 -0.123 1.193 39.821 MISC PLASTICS PRODUC 18 / 85 TO 9 / 8 6 1986 EKCO GROUP INC 282636 12.181 -5.755 -0.161 118.950 METAL FORGINGS AND YEAR 1986 1986 GRAHAM FIELD HEALTH PDS 38H632 -0.262 -0.761 2.915 38.869 PROFESSIONAL EQ ft SU YEAR 1986 1986 LIN BROADCASTING 532763 0.326 23.858 73.201 538.766 TELEVISION BROADCAST YEAR 1986 1986 TENERA -LP 880331 -0.326 -2.291 7.032 33.935 ENGR, ARCHITECT, SUR MISC NONDURABLE GOOD 7 / 8 5 TO 12 / 8 6 1986 VADER GROUP INC 918732 -0.358 -1.551 1.316 2ft.623 10 / 6 5 TO 9 / 8 6 1987 BIOPHARMACEUTICS INC 0906U6 1.089 -1.295 -1.189 7.611 PHARMACEUTICAL PREPA 19 / 86 TO 9 / 8 7 1987 CROSS ft TRECKER CORP 227130 0.759 -1.385 -5.780 381.031 MACHINE TOOLS, METAL TELEVISION BROADCAST 10 / 86 TO 9 / 87 1987 LIN BROADCASTING 532763 0.311 31.987 102.005 536.182 YEAR 1987 1987 MCCLATCHY NEWSPAPERS-CL A 579189 0.207 11.150 68.202 323.7ft0 NEWSPAPER:PUBG, PUBG YEAR 1987 1987 QUANTUM CHEMICAL CORP 7H7633 0.207 108.000 521.500 2581.200 PLASTICS,RESINS,ELAS YEAR 1987 1987 TRANSCISCO INDS -CL 893531 1.119 3.260 2.298 57.378 MISC REPAIR SERVICES YEAR 1987 1987 UAL CORP 902519 0.135 339.311 780.231 8226.266 AIR TRANSPORTATION^ YEAR 1987 1987 VALLEY FORGE CORP 919610 0.139 0.616 ft.639 27.797 ABR AS 1 VE, ASBESTOS, M1 YEAR 19B7 Companies not found In the Wall Street Journal Index aearch: (211 f i res) 1968 ALLIED ARTISTS INDUSTRIES 018859 -10.533 0.632 -0.060 10.66ft MOTOR HOMES • 1" / 67 TO 9 / 68 1969 CORDON INTL 218531 -2.188 -1. .288 1.960 30.569 SPECIAL INDUSTRY MAC • YEAR 1969 1969 REDM INDUSTRIES INC 719185 -0.156 -0. .231 1.182 7.5ft7 ELECTRONIC COMPONENT • YEAR 1969 1969 SEAPORT CORP 812205 -0.537 -0. .811 1.516 23.521 AUTO PARTS ft SUPPLIE YEAR 1969 1970 ACTON CORP 005055 2.020 -1 . 502 -2.229 31.08ft CABLE TELEVISION OPE YEAR 1970 1970 AEGIS CORP 007603 -0.715 -2. 317 3.211 35.806 SHIP-BOAT BUILOINGftR • YEAR 1970 1970 BARBARA LYNN STORES INC 067077 -6.011 -0. .731 0.121 11.122 RETAIL-APPAREL ft ACC • YEAR 1970 1970 CLARK CONSOLIDATED INDS 180688 -0.211 -0. .059 0.215 7.626 ELEC APPARATUS ft EQU 2 / 70 TO 1 / 71 1970 COSCO INC 221116 -0.105 -0. ,156 1.339 37.572 HOUSEHOLD FURNITURE • YEAR 1970 1970 ELCOR CORP 281113 1.309 -1 . 017 -0.236 60.351 PAVING AND ROOFING 7 / 69 TO 6 / 70 1970 FIRST HARTFORD CORP 320188 -0.898 -0. ,121 0.169 18.572 TEXTILE MILL PRODUCT • 12 / 69 TO 11 / 70 1970 GREINER ENGINEERING INC 397627 -0.315 - 1 . 308 1.151 21.318 ENGR, ARCHITECT, SUR AIRCRAFT ENGINE,ENGI YEAR 1970 1970 HE ICO CORP 122805 13.660 -0. 312 -0.025 1.512 11 / 69 TO 1« / 70 1970 INTERMARK INC 158776 -0.676 -1 . 129 1.670 31.860 FURNITURE,HOME FURNI ft / 70 TO 3 / 71 1970 INTL BANKNOTE 159101 -1.977 -6. 980 3.530 68.009 COMMERCIAL PRINTING YEAR 1970 1970 IROQUOIS BRANDS LTD 163319 -1.292 -2. 218 1.710 18.733 PHARMACEUTICAL PREPA YEAR 1970 1970 RE CAPITAL CORP 751901 -0.385 -0. 911 2.368 11.903 FINANCE-SERVICES YEAR 1970 1970 REDM INDUSTRIES INC 719185 -0.171 -0. 151 0.900 7.136 ELECTRONIC COMPONENT • YEAR 1970 1970 SERVICEMASTER -LP 817615 -0.390 -0. 671 1.729 9.138 MGMT, CONSULTING ft YEAR 1970 1970 THORTEC INTERNATIONAL INC 885155 -0.317 -0. 368 1.060 11.080 ENGR, ARCHITECT, SUR ELECTRIC LIGHTING-WI 11 / 69 TO 10 / 70 1970 UN 1 MAX CORP 901790 -0.117 -0. 712 1.815 86.915 • YEAR 1970 1971 AEGIS CORP 007603 -1.600 -1 . 586 2.866 26.353 SHIP-BOAT BUILOINGftR • YEAR 1971 1971 ANGLO ENERGY INC 035053 62.111 -25. 913 -0.117 16.887 DRILLING OIL ANO GAS 10 / 70 TO 9 / 71 1971 BASIX CORP 070121 -0.233 -0. 855 3.677 36.597 COMMERCIAL PRINTING YEAR 1971 1971 BELL INDUSTRIES INC 078107 -0.573 -0. 989 1.727 28.350 ELECTRONIC PARTS ft E 7 / 70 TO 6 / 71 1971 BICKFORD CORP 088710 -0.281 -0. 255 0.909 21.309 RETAIL-EATING PLACES • YEAR 1971 1971 DEVON GROUP 251800 -0.116 -0. 100 3.116 38.732 WHSL-NONDURABLE GOOD • ft / 71 TO 3 / 72 1971 ELCOR CORP 281113 10.521 -2. 516 -0.212 11.509 PAVING AND ROOFING 7 / 70 TO 6 / 71 1971 GELMAN SCIENCES INC 368511 -0.339 -0. 118 0.318 6.339 ENGR, LAB AND RESEAR 8 / 70 TO 7 / 71 1971 GENERAL RESOURCES CORP-DEL 370698 -11.636 -0 . 512 0.011 6.122 WHSL-LUMBER ft CONSTR • 11 / 70 TO 10 / 71 1971 HOWELL INDUSTRIES INC 113073 -0.158 -0 . 117 0.739 6.122 METAL FORGINGS AND 8 / 70 TO 7 / 71 1971 INTL FOODSERVICE CORP 159528 -0.163 -0 . 779 1.781 13.129 WHSL-GROCER1ES ft REL • YEAR 1971 1971 LEVITT INDUSTRIES INC 527129 -0.657 -2 . 105 3.201 15.068 RETAIL-VARIETY STORE • 5 / 71 TO ft / 72 1971 MEDALLION GROUP INC 581025 -0.133 -0. 665 1.536 25.118 SOAP ft OTHER DETERGE • YEAR 1971 to 1971 MICKELBERRY CORP 591780 7. .873 -0.315 1971 SCHENUIT INVESTMENTS INC 886517 -0, . 160 -0.180 1971 SCHRAOER (ABE) CORP 808060 -0.101 -0.196 1971 SEAPORT CORP 812205 -1 .125 -0.396 1971 THORTEC INTERNATIONAL INC 885155 -0 .215 -0.111 1971 ZERO CORP-OEL 989181 -0.672 -0.853 1972 ACTON CORP 005055 1.696 1.671 1972 BICKFORO CORP 088710 1 .023 -2.076 1972 CALIFORNIA LIFE CORP 130376 0 . 110 0.101 1972 GALVESTON HOUSTON 361121 -0 .315 -0.056 1972 HALCO PRODUCTS CORP-NV 105363 -11 .898 -0.583 1972 LYNNWEAR CORP-CL A 551675 -0 . 100 -0.260 1972 NATIONAL EDUCATION CORP 635771 -0 .160 -0.116 1972 PNEUMO CORP 730196 -0 .260 -1.619 1972 ROWLAND INC 779661 -0.122 -0.185 1972 SCHAEFER (F.ftM.) CORP 806228 -0 .157 -5.387 1972 SCHENUIT INVESTMENTS INC 806517 -0.635 -1.920 1972 STANWOOD CORP 851867 -1. .393 -1.297 1972 TRITON ENERGY CORP 896750 0 .116 0.218 1972 VERIT INDUSTRIES 923131 -0 .332 -0.588 1972 WABASH INC 929501 -0 .185 -0.369 1973 ALPINE GROUP INC 020825 -0 .612 -0.158 1973 BASIX CORP 070121 -1 .008 -3.111 1973 CHILTON CORP 169277 -0 .205 -0.139 1973 DEVON GROUP 251800 -3 .181 -12.310 1973 EECO INC 268120 0 .213 0.167 1973 ELECTROSOUND GROUP INC 286115 1 .691 -1.753 1973 GALVESTON HOUSTON 361121 -3 .611 -0.798 1973 GLASROCK MEDICAL SERVICES 377118 -0.882 -0.892 1973 LEVITT INDUSTRIES INC 527129 -0 . 101 -0.312 1973 MARCADE GROUP INC 566139 -107.989 -51.212 1973 NATIONAL EDUCATION CORP 635771 -8 .133 -3.677 1973 PENTRON CORP 709686 -0.820 -0.292 1973 RLC CORP 719901 -0 . 109 -3.112 1973 SANTA ANITA REALTY ENTER 801209 -0 .107 -1.559 1973 STANWOOD CORP 851867 -1.059 -5.708 1973 THREE D DEPARTMENT -CL 885539 1 .282 -0.361 1973 TOROTEL INC 891305 -0.173 -0.017 1973 UNC INC 903070 -1 .155 -3.172 1973 UN I MAX CORP 901790 -0 .581 -2.135 1971 ALLIED ARTISTS INDUSTRIES 018859 0 .235 0.135 1971 ANGELES CORP 031621 18 . 178 -12.960 197U BICKFORD CORP 088710 -1 .012 -0.388 1971 COMPUTER TASK GROUP INC 205177 -0 .286 -0.078 1971 DESIGNCRAFT INDUSTRIES 250568 0 .105 -0.812 197M ELECTROSOUND GROUP INC 286115 1 .018 -5.291 1971 GLASROCK MEDICAL SERVICES 377118 0 .158 0.171 1971 INTL FOODSERVICE CORP 159528 -2 .365 -5.619 1971 MARCADE GROUP INC 566139 -1, .070 -0.811 1971 PENTRON CORP 709686 -1 .901 -1.158 1971 RAD ICE CORP 750339 -0. .181 -0.137 1971 REDLAW INC 757633 8 .716 1.618 1971 THOR ENERGY RESOURCES INC 885118 -1 .192 -2.020 1971 YARDNEY CORP 985012 -0 . 122 -0.156 1975 ALPINE GROUP INC 020825 -0 .690 0.118 1975 AMERICAN CAPITAL CORP 021898 1, .311 -0.101 1975 ANDAL CORP 033352 -0 .528 -11.213 1975 ANGELES CORP 031621 -0 .185 0.216 1975 ARMATRON INTERNATIONAL INC 012167 -1, .151 -1.106 1975 ARTRA GROUP INC 013117 0 .271 0.738 1975 ARX INC 001909 -0 .211 -0.058 1975 BMC INDUSTRIES INC-MINN 055607 -0 .115 -0.715 1975 CARDIFF EQUITIES CORP 111166 -0 .139 -1.333 1975 CMX CORP 126030 -13 .522 -0.906 1975 ECC INTERNATIONAL INC 268255 -1 .069 -0.265 1975 ELECTROSOUND GROUP INC 286115 3.013 3. 122 -0.010 5.956 COMMERCIAL PRINTING YEAR 1971 1.127 19.681 INVESTORS-NEC • 10 / 70 TO 9 / 71 1.911 6.159 APPAREL ft OTHER FINI • 8 / 70 TO 7 / 71 0.096 19.202 AUTO PARTS ft SUPPLIE YEAR 1971 1.680 12.890 ENGR, ARCHITECT, SUR 11 / 70 TO 10 / 71 1.269 21.856 METAL FORGINGS AND 1 / 71 TO 3 / 72 0.985 30.262 CABLE TELEVISION OPE YEAR 1972 -0.516 13.579 RETAIL-EATING PLACES • YEAR 1972 0.722 15.958 FINANCE-SERVICES • 7 / 71 TO 6 / 72 0.178 2.600 CONSTR,MIN1NG,MATL H YEAR 1972 0.019 3.710 MEAT PRODUCTS • 11 / 71 TO 10 / 72 2.588 17.890 APPAREL ft OTHER FINI • 12 / 71 TO 11 / 72 0.912 21.263 EDUCATIONAL SERVICES YEAR 1972 6.235 110.090 RETAIL-GROCERY STORE • 12 / 71 TO 11 / 72 0.138 6.613 MISC CHEMICAL PRODUC • 1 / 72 TO 3 / 73 11.788 198.568 MALT BEVERAGES • YEAR 1972 3.026 15.261 INVESTORS-NEC • 10 / 71 TO 9 / 72 0.931 77.510 KNITTING MILLS 8 / 71 TO 7 / 72 1.191 23.839 CRUOE PETROLEUM ft NA 6 / 72 TO 5 / 73 1.772 12.617 ELEC APPLIANCE,TV,RA 7 / 71 TO 6 / 72 1.999 13.815 ELECTRICAL MACHYftEQU • YEAR 1972 0.258 1.919 COSTUME JEWLRY.BUTTO 1 / 73 TO 4 / 71 3.116 32.175 COMMERCIAL PRINTING YEAR 1973 2.110 16.858 CREDIT REPORTING AGE • 1 / 73 TO 3 / 71 3.536 27.128 WHSL-NONDURABLE GOOD • 1 / 73 TO 3 / 71 2.190 10.918 COMPUTER EQUIPMENT, YEAR 1973 -1.035 28.316 PHONO RECORDS,MAGNET 1 / 73 TO 5 / 71 0.219 6.381 CONSTR,MINING,MATL H YEAR 1973 1.011 12.979 SERV-EQUIP RENTAL ft • 1 / 73 TO 3 / 71 3.297 17.360 RETAIL-VARIETY STORE • 5 / 73 TO 1 / 71 0.502 83.708 APPAREL ft OTHER FINI 1 / 73 TO 1 / 71 0.136 13.616 EDUCATIONAL SERVICES YEAR 1973 0.356 10.386 MOTOR VEHICLE PART,A 7 / 72 TO 6 / 73 31.321 226.721 AUTO RENT ft LEASE,NO 18 / 72 TO 9 / 73 11.507 131.680 RACING,INCL TRACK OP 11 / 72 TO 10 / 73 5.392 71.799 KNITTING MILLS 8 / 72 TO 7 / 73 -0.281 7.351 FURNITURE,HOME FURNI 8 / 72 TO 7 / 73 0.271 2.316 ELECTR COIL.TRANSFRM 1 / 73 TO 3 / 71 2.717 121.261 AIRCRAFT ENGINE,ENGI 1 / 73 TO 3 / 71 3.677 19.799 ELECTRIC LIGHTING-WI • YEAR 1973 0.575 20.312 MOTOR HOMES • 10 / 73 TO 9 / 71 -0.269 23.810 REAL ESTATE 1 / 73 TO 12 / 71 0.096 7.081 RETAIL-EA1ING PLACES • YEAR 1971 0.273 1.191 CMP PROGRAM ft SOFTWA 1 / 73 TO 12 / 71 -2.078 21.879 JEWELRY, PRECIOUS ME 3 / 71 TO 2 / 75 -5.018 13.896 PHONO RECORDS,MAGNET 6 / 71 TO 5 / 75 1.083 13.175 SERV-EQUIP RENTAL ft • 1 / 71 TO 3 / 75 2.389 77.611 WHSL-GROCERIES ft REL • YEAR 1971 0.758 11.923 APPAREL fe OTHER FINI 2 / 71 TO 1 / 75 0.609 7.727 MOTOR VEHICLE PART,A 7 / 73 TO 6 / 71 0.283 62.280 SUBDIVID,DEVELOP,EX 1 / 73 TO 6 / 71 0.185 9.510 METAL FORGINGS fe STA • 13 / 71 TO 2 / 75 1.695 11.561 ENGR, ARCHITECT, SUR 2 / 71 TO 1 / 75 1.282 9.512 ELECTRICAL MACHYftEQU • 1 / 73 TO 10 / 71 -0.171 1.186 COSTUME JEWLRY.BUTTO 5 / 75 TO 1 / 76 -0.093 52.137 SUBDIVID DEVELOP EX • 9 / 71 TO 8 / 75 26.908 102.179 METALS SERVICE CENTE YEAR 1975 -1.165 17.593 REAL ESTATE YEAR 1975 1.222 12.218 MISC ELEC MACHY.EQ.S 18 / 71 TO 9 / 75 2.698 61.377 COSTUME JEWLRY.BUTTO YEAR 1975 0.211 2.657 MISC FABRICATED META 7 / 71 TO 6 / 75 6.500 16.981 OPHTHALMIC GOODS YEAR 1975 3.035 57.630 LUMBER ft WOOD PRODUC • 2 / 75 TO 1 / 76 0.067 1.352 PHOTOGRAPHIC EQUIP ft YEAR 1975 0.218 1.215 TRAINING EQUIP ft SIM 7 / 71 TO 6 / 75 1.026 10.221 PHONO RECORDS,MAGNET 6 / 75 TO 5 / 76 1975 GLASROCK MEDICAL SERVICES 1975 HELM RESOURCES INC 1975 HUFFY CORP 1975 MARATHON OFFICE SUPPLY INC 1975 MORGAN FOODS INC 1975 NATIONAL EDUCATION CORP 1975 NELLY DON INC 1975 NEW IDRIA INC 1975 RE CAPITAL CORP 1975 SCHAEFER (F.AM.) CORP 1975 SMITH (A.O.) CORP -CL A 1976 ALPINE GROUP INC 1976 ANDAL CORP 1976 ANGELES CORP 1976 BRIGADIER INDUSTRIES CORP-1976 CLAIRE'S STORES INC 1976 GEMCO NATIONAL INC 1976 GLASROCK MEDICAL SERVICES 1976 HELM RESOURCES INC 1976 JOHNSTON IND-DEL 1976 MATRIX CORP-N J 1976 MCO HOLDINGS INC 1976 MED1CORE INC 1976 MORGAN FOODS INC 1976 REPUBLIC GYPSUM CO 1976 SANTA ANITA REALTY ENTER 1976 STANHOME INC 1976 THOR ENERGY RESOURCES INC 1977 ALPINE GROUP INC 1977 BISCAYNE HOLDINGS -CL A 1977 GLASROCK MEDICAL SERVICES 1977 HELM RESOURCES INC 1977 JOHNSTON IND-DEL 1977 JWP INC 1977 KEYSTONE CAMERA PRODUCTS 1977 MATEC CORP 1977 MED I CORE INC 1977 SANMARK-STARDUST INC 1977 THOR ENERGY RESOURCES INC 1977 TRAFALGAR INDUSTRIES INC 1977 UN IMAX CORP 1978 ALPINE GROUP INC 1978 ANDAL CORP 1978 ARMATRON INTERNATIONAL INC 1978 HELM RESOURCES INC 19T8 KEYSTONE CAMERA PRODUCTS 1978 MATRIX CORP-N J 1978 RE CAPITAL CORP 1979 ALLIED SIGNAL INC 1979 ALPINE CROUP INC 1979 BISCAYNE HOLOINGS -CL A 1979 CMX CORP 1979 FRANKLIN RESOURCES INC 1979 HELM RESOURCES INC 1979 KEYSTONE CAMERA PRODUCTS 1979 MORGAN FOODS INC 1979 RE CAPITAL CORP 1979 THOR ENERGY RESOURCES INC 1980 ALPINE GROUP INC 1980 BISCAYNE HOLOINGS -CL A 1980 GRAY DRUG STORES 1980 HAL INC 1980 HELM RESOURCES INC 1980 KEYSTONE CAMERA PROOUCTS 1980 MARATHON OFFICE SUPPLY INC 1980 MARCADE GROUP INC J77118 0 .361 0.198 423425 -4 .216 -1.092 414356 -0 .951 -5.287 565840 -0 .609 -0.207 616900 -8 .458 -7.578 635771 -0 . 104 -0.134 610303 1 .261 -0.324 615631 -0 .465 -1.246 75l»90U -0 .279 -0.943 806228 0 .360 2.359 831865 -0 .739 -12.887 020825 0 .166 -0.541 033352 -6 .352 -21.330 034624 23 .833 0.286 109017 2 .215 -0.288 179584 -2 . 181 -3.119 368636 -0 .309 -0.538 377118 1 .299 0.301 423125 -0 .228 -0.068 179368 -9 .758 -8.099 576829 0 .108 0.066 552901 -1 , .591 -58.957 584931 0 .318 0.107 616900 -0 .404 -0.038 760473 2.774 -0.180 801209 -0 .728 -8.049 851425 -0 . 102 -1.810 885148 -0 .193 0.770 020825 0 .156 -0.066 091360 -0 .476 -1.756 377118 -0. .234 -0.197 423425 2, . 102 -0.288 479368 -1 , .336 -1.157 466265 -0 .368 -2.265 493397 -14 .729 -16.438 576667 0. .557 0.402 584931 -0. .119 -0.165 801050 0 .353 -0.246 885148 -1, .172 -1.922 892711 -2.858 -3.870 904790 -0. . 144 -1.342 020825 7. . 187 -1.193 033352 0.624 2.866 042167 -6, .478 -12.429 423425 14. .837 0.638 493397 -0. .115 -0.421 576829 -0. .725 -0.732 754904 0. 227 0.418 019512 -0. .179 -164.816 020825 -3.588 4.026 091360 -0. 428 -4.900 126030 -0. 140 -0.263 354613 0. 162 0.056 423425 -0. 170 0.024 493397 -0. .569 -2.364 616900 5.088 -0.519 754904 0. 295 0.510 885148 -37. 577 0.977 020825 -1 . 779 0.514 091360 -1 . 814 11.738 389280 0. 177 0.762 404073 -0. 563 -2.781 423425 -0. 281 -0.064 493397 0. 100 0.385 565840 -0. 297 -0.333 566139 -0. 202 -3.908 0.549 11.970 0.259 17.816 5.558 51.915 0.340 3.328 0.896 9.789 1.285 14.282 -0.257 7.270 2.677 14.454 3.385 10.276 6.560 165.261 17.435 313.088 -3.251 4.531 3.358 215.155 0.012 15.572 -0.130 2.636 1.430 7.937 1.743 13.338 0.234 12.385 0.298 14.898 0.830 21.082 0.610 5.175 37.050 314.441 0.337 3.765 0.094 5.233 -0.173 10.386 11.057 67.470 17.822 98.037 -3.988 29.115 -0.424 3.850 9.987 56.912 0.843 13.373 -0.137 15.050 0.866 9.439 6. 157 60.380 1.116 47.566 0.722 9.665 1.391 5.229 -0.696 7.594 1.640 21.672 1.354 51.087 9.326 55.190 -0.166 1.840 4.594 155.617 1.921 19.061 0.043 3.867 3.650 45.718 1.009 8.112 1.844 14.765 920.703 4209.621 -1.122 5.589 11.441 77.526 1.882 5.359 0.345 2.330 -0.141 2.554 4.152 47.921 -0.102 2.993 1.730 15.912 -0.026 14.421 -0.289 10.939 -6.471 82.514 4.306 107.059 4.940 98.029 0.228 4.764 3.848 41.059 1.120 6.501 19.338 112.214 SERV-EQUIP RENTAL ft CHEMICALS ft ALLIED MOTORCYCLES,BICYCLES PAPER ft PAPER PRODUC EATING PLACES EDUCATIONAL SERVICES APPAREL ft OTHER FINI OFFICE FURNITURE FINANCE-SERVICES MALT BEVERAGES MOTOR VEHICLE PART,A COSTUME JEWLRY.BUTTO METALS SERVICE CENTE REAL ESTATE WOOD BUILDINGS-MOBIL APPAREL AND ACCESSOR APPAREL,PIECE CDS,NO SERV-EQUIP RENTAL ft CHEMICALS ft ALLIED BRD WOVN FABRC MAN-M PHOTOGRAPHIC EQUIP ft SUBDIVIO,DEVELOP,EX ELECTRONIC COMPONENT EATING PLACES CONCRETE, GYPSUM AND RACING,INCL TRACK OP SOAP.DETERGENT,TOILE ENGR, ARCHITECT, SUR COSTUME JEWLRY.BUTTO ORTHO,PROSTH,SURG AP SERV-EQUIP RENTAL ft CHEMICALS ft ALLIED BRD WOVN FABRC MAN-M ELECTRICAL WORK PHOTOGRAPHIC EQUIP ft ELECTRONIC COMPONENT ELECTRONIC COMPONENT APPAREL ft OTHER FINI ENGR, ARCHITECT, SUR BITUMINOUS COAL ft LI ELECTRIC LIGHTING-WI COSTUME JEWLRY.BUTTO METALS SERVICE CENTE MISC ELEC MACHY,EQ,S CHEMICALS ft ALLIED PHOTOGRAPHIC EQUIP ft PHOTOGRAPHIC EQUIP ft FINANCE-SERVICES AIRCRAFT ENGINE,ENGI COSTUME JEWLRY.BUTTO ORTHO,PROSTH,SURG AP PHOTOGRAPHIC EQUIP ft SVCS ALLIED WITH EXC CHEMICALS ft ALLIED PHOTOGRAPHIC EQUIP ft EATING PLACES FINANCE-SERVICES ENGR, ARCHITECT, SUR COSTUME JEWLRY.BUTTO ORTHO,PROSTH,SURG AP RETAIL-DRUGftPROPRIET AIR TRANSPORTATIONS CHEMICALS ft ALLIED PHOTOGRAPHIC EQUIP ft PAPER ft PAPER PROOUC APPAREL ft OTHER FINI • «»/ 75 TO 3 / 76 YEAR 1975 7 / 74 TO 6 / 75 7 / 74 TO 6 / 75 3 / 75 TO 2 / 76 YEAR 1975 • 11 / 74 TO 10 / 75 • 7 / 74 TO 6 / 75 YEAR 1975 • YEAR 1975 YEAR 1975 5 / 76 TO 4 / 77 YEAR 1976 YEAR 1976 • 11 / 75 TO 10 / 76 9 / 76 TO 1 / 77 YEAR 1976 • 1 / 76 TO 3 / 77 YEAR 1976 YEAR 1976 9 / 75 TO 8 / 76 YEAR 1976 YEAR 1976 3 / 76 TO 2 / 77 7 / 75 TO 6 / 76 7 / 75 TO 6 / 76 YEAR 1976 2 / 76 TO 1 / 77 5 / 77 TO 4 / 78 YEAR 1977 • 1 / 77 TO 3 / 78 YEAR 1977 YEAR 1977 YEAR 1977 YEAR 1977 YEAR 1977 YEAR 1977 7 / 76 TO 6 / 77 2 / 77 TO 1 / 78 • 5 / 77 TO 4 / 78 • YEAR 1977 5 / 78 TO 4 / 79 YEAR 1978 10 / 77 TO 9 / 78 YEAR 1978 YEAR 1978 9 / 77 TO 8 / 78 YEAR 1978 YEAR 1979 5 / 79 TO 4 / 80 YEAR 1979 YEAR 1979 18 / 78 TO 9 / 79 YEAR 1979 YEAR 1979 3 / 79 TO 2 / 80 YEAR 1979 2 / 79 TO 1 / 80 5 / 80 TO 4 / 81 YEAR 1980 • 5 / 80 TO 4 / 81 YEAR 1980 YEAR 1980 YEAR 1980 7 / 79 TO 6 / 80 2 / 80 TO 1 / 81 1980 MORGAN FOODS INC 616900 -1.371 -0.151 0.329 3.679 EATING PLACES VEA£ 8 0 TO 2 / 8 1 1980 MUNSINGWEAR INC 626320 -2.011 - 3.201 1.593 61.656 APPAREL ft OTHER FINI 1980 1980 RE CAPITAL CORP 751901 0.151 0.236 1.568 16.186 F1 NANCE-SERVICES YEAR 1980 1980 THOR ENERGY RESOURCES INC 885118 -3.812 -0.568 0.119 10.191 ENGR. ARCHITECT, SUR 2 / 80 TO 1 / 8 1 1981 MARK IV INDUSTRIES INC 570387 -0.392 -0.917 2.312 10.611 INDUSTRIAL MEASUREME 3 / 81 TO 2 / 8 2 1981 MARSHALL FOODS INC 572350 2.278 -1.080 -0.171 5.103 WHSL-GROCERIES ft REL • «• / 6 1 TO 3 / 82 1981 MOORE MEDICAL CORP 615799 -0.568 -3.827 6.733 25.017 DRUGS AND PROPRIETAR YEAR 1981 1981 RE CAPITAL CORP 751901 0.121 0. 181 1.192 17.718 FINANCE-SERVICFS YEAR 1981 1981 U l GROUP INC 902710 -0.198 1.586 •8.003 115.120 AGRICULTURE PRODUCT 1 • 3 / 81 TO 2 / 6 2 1982 AMBRIT INC 023363 -0.738 -0.568 0.770 11.079 SUGAR ft CONFECTIONER 2 / 6 2 TO 1 / 8 3 1982 BISCAYNE HOLDINGS -CL A 091360 -1.615 1.208 -0.718 18.595 ORTHO.PROSTH.SURG AP PHOTOGRAPHIC EQUIP ft YEAR 1982 1982 KEYSTONE CAMERA PRODUCTS 193397 -0.118 -0.116 0.783 67.211 YEAR 1982 1982 PENTRON CORP 709686 0.658 -0.315 -0.521 9.179 MOTOR VEHICLE PART,A 7 / 6 1 TO 6 / 8 2 1982 R.B ft W CORP 719252 -2.525 -5.070 2.008 75.322 BOLT,NUT,SCREW,RIVET 2 / 6 1 TO 12 / 82 1982 RE CAPITAL CORP 751901 0.112 0.372 0.811 19.321 FINANCE-SERVICES YEAR 1982 1983 ALLIED SIGNAL INC 019512 -0.219 -391.000 1573.000 7617.000 AIRCRAFT ENGINE,ENGI YEAR 1983 1983 BISCAYNE HOLDINGS -CL A 091360 -1.057 -1.263 1.195 5.361 ORTHO.PROSTH.SURG AP TEMPORARY HELP SUPPL YEAR 1983 1983 COSMOPOLITAN CARE CORP 221337 -0.126 -0.212 1.911 8.826 2 / 8 3 TO 1 / 8 1 1983 CUSTOMED IX CORP 232038 -0.873 -0.853 0.977 12.110 DENTAL EQUIPMENT ft 7 / 8 2 TO 6 / 83 1983 ECOLAB INC 278865 -0.521 -13.006 82.137 375.669 SOAP,DETERGENT,TOILE SERV-MGMT CONSULTING 7 / 8 2 TO 6 / 83 1983 FIRST CAPITAL HOLDINGS CORP 319117 -10.053 2.855 -0.281 3.225 • YEAR 198) 1983 MAXPHARMA INC 577726 -0.961 -0.763 0.791 56.658 INVESTORS, NEC YEAR 1983 1983 NATL PATENT DEVELPHNT 637130 -0.129 -1.669 12.901 123.711 EDUCATIONAL SERVICES YEAR 1983 1983 R.B ft W CORP 719252 0.120 0.819 6.810 83.015 BOLT,NUT,SCREW,RIVET YEAR 1983 1983 RE CAPITAL CORP 751901 0 .115 0.021 0.208 23.328 FINANCE-SERVICES YEAR 1983 1983 TW SERVICES INC 873118 -0.327 -67.876 207.886 1173.017 EATING PLACES YEAR 1983 1981 AMERICAN BARRICK RESOURCE CP 0215 IE -2.583 -9.370 3.628 165.785 GOLD AND SILVER ORES 1 / 83 TO 12 / 8 1 1981 CSS INDS INC 125906 -6.786 -0.570 0.081 30.105 MAIL ORDER HOUSES 2 / 8 1 TO 1 / 8 5 1981 CUSTOMED IX CORP 232038 -0.313 0. 171 -0.199 13.760 DENTAL EQUIPMENT ft 7 / 83 TO 6 / 81 1981 MAXPHARMA INC 577726 1.995 -0.810 -0.106 52.055 INVESTORS, NEC YEAR 1981 1981 PHLCORP 718799 20.510 127.811 6.233 513.585 BUSINESS SERVICES, YEAR 1981 1981 SAN JUAN RACING ASSN 798107 -0.133 -0.676 5.073 61.681 RACING,INCL TRACK OP 5 / 81 TO 1 / 8 5 1985 AMERICAN BARRICK RESOURCE CP 02151E -1.815 -18.870 10.396 117.881 GOLD AND SILVER ORES YEAR 1985 1985 BISCAYNE HOLOINGS -CL A 091360 -0.151 -0.391 0.861 1.610 ORTHO.PROSTH.SURG AP DENTAL EQUIPMENT ft YEAR 1985 1985 CUSTOMEDIX CORP 232038 -0.812 -0.329 0.105 31.939 7 / 8 1 TO 6 / 8 5 1985 ENERGY SERVICES COMPANY INC 292719 -0.153 -3.711 8.192 61.767 OR ILLING OIL AND GAS YEAR 1985 1985 HAMPTON HEALTHCARE INC 109181 -0.369 0.381 -1.032 12.512 EATING PLACES 10 / 8 1 TO 9 / 6 5 1985 MAXPHARMA INC 577726 0.521 -1.210 -2.367 36.932 INVESTORS, NEC YEAR 1985 1985 MED 1CORE INC 581931 -1.028 0.729 -0.181 19.131 ELECTRONIC COMPONENT YEAR 1985 1985 MORGAN FOODS INC 616900 -0.295 -0.153 1.533 7.517 EATING PLACES 3 / 85 TO 2 / 86 1985 RE CAPITAL CORP 751901 2.318 -0.688 -0.293 22.233 FINANCE-SERVICES YEAR 1985 1985 TW SERVICES INC 873118 0.160 112.711 215.065 1329.316 EATING PLACES YEAR 1985 1986 CUSTOMEDIX CORP 232038 29.138 -9.936 -0.311 11.227 DENTAL EQUIPMENT ft 7 / 85 TO 6 / 86 1986 1986 MAXPHARMA INC 577726 701227 - 980 -1.109 0.000 16.187 INVESTORS, NEC COMMERCIAL PRINTING YEAR 1986 1986 PAXAR CORP -0.178 -0.700 3.935 23.505 YEAR F o r t h e F o l l o w i n g , n o d i s c o n t i n u a t i o n a n n o u n c e m e n t s w e r e f o u n d I n t h e W a l l S t r e e t J o u r n a l I n d e x : ( 6 7 8 f i r s t s ) 1968 DEL LABORATORIES INC 215091 -0 .113 -0.377 2.630 25.032 PERFUME,COSMETIC,TO1 13 / 6 7 TO 12 / 6 8 1969 CANOGA INDS 137816 5 .107 -1.160 -0. .270 7.817 AIRCRAFT PARTS ft AUX • 11 / 6 8 TO 10 / 69 1969 OEL LABORATORIES INC 215091 -0 . 177 -0.166 2, .626 23.169 PERFUME,COSMETIC,TOI YEAR 1969 1969 ROYAL CROWN COS INC 780210 0 .107 1.292 12, .117 11.699 BOTTLED-CANNEO SOFT • YEAR 1969 1969 SIGMA INSTRUMENTS 826588 0, .222 -0.032 -0. .111 12.778 ELECTRONIC COMPONENT • YEAR 1969 1969 STRUTHERS WELLS CORP 863659 -1 .987 -0.298 0. .150 30.111 FABRICATED PLATE WOR 12 / 68 TO 11 / 69 1970 AMERICAN MFC CO 027357 -0, . 107 -0.212 2, .265 35.066 TEXTILE MILL PRODUCT • YEAR 1970 1970 AVC CORP 002280 -1 .006 -3.189 3. .168 62.968 BOLTS-NUTS-SCREWS-R1 • YEAR 1970 1970 AYOIN CORP 051681 0. .218 -0.211 -0. .850 17.752 RADIO, TV COMM EQ, A YEAR 1970 1970 BERTEA CORP 085815 -0.262 -0.635 2. .123 16.215 AIRCRAFT PARTS ft AUX • YEAR 1970 1970 BRODY (B.) SEATING CO 112061 -0.663 -0.277 0. .118 5.295 HOUSEHOLD FURNITURE • 9 / 6 9 TO 6 / 7 0 1970 BURGESS INDS 121232 -3, .017 -1.901 0. .631 11.265 WHSL-MACHINERY ft EQU • 16 / 69 TO 9 t 70 1970 CALLAHAN MINING CORP 131069 -0 .201 -0.367 1.798 11.838 GOLD AND SILVER ORES YEAR 1970 1970 CANOGA INDS 137816 -0 . 138 -0.097 0. .703 7.099 AIRCRAFT PARTS ft AUX • 11 / 69 TO 10 / 70 1970 CELLU-CRAFT INC 151159 -1. .562 -2.289 1. ,165 21.137 MISC PLASTIC PRODUCT • 13 / 70 TO 2 / 71 1970 CERTIFIED CORP 156897 -0 . 136 -0.160 1. 175 10.366 MISC MANUFACTURING 1 • 7 / 69 TO 6 / 70 to 1970 CONGOLEUM CORP 207192 -0.246 -1.700 1978 CURTISS-WRICHT CORP 231561 -0.430 -1.832 1970 DEL LABORATORIES INC 2U5091 -0.116 -0.431 1970 DORR-OLIVER INC 258363 -1.134 -3.583 1970 ENERGY RESOURCES CORP 292713 -0.112 -0.085 1970 GENERAL HOUSEWARES 370073 -1.054 -4.610 1970 GENERAL INTERIORS CORP 370154 -0.959 2.023 1970 GENERAL STEEL INDS 370856 1.465 -0.504 1970 GREAT AMERICAN INDUSTRIES 389856 -0.295 -0.436 1970 HARVEY GROUP •t 17668 -1.192 -0.647 1970 HOUGHTON MIFFLIN CO 441560 -0.114 -0.987 1970 HOUSTON OIL ft MINERALS CORP 442281 -1.109 -1.010 1970 HOWELL INDUSTRIES INC 443073 -12.295 -0.750 1970 KINARK CORP 494474 -0.621 -1.388 1970 KLEER-VU INDUSTRIES INC 498494 0.911 0.163 1970 LOGISTICS INDUSTRIES CORP 541415 -0.196 -0.406 1970 LYNCH CORP 551137 -0.259 0.096 1970 MAGIC MARKER CORP 559142 1.509 -0.163 1970 MCKESSON CORP 581556 -0.131 -7.500 1970 METEX CORP 591503 -0.633 -0.112 1970 ORMAND INDUSTRIES 686679 -0.155 -0.229 1970 RAYMOND INTL INC-DELAWARE 751721 1.939 -2.726 1970 SCIENCE MANAGEMENT CORP 808638 -0.314 -0.867 1970 SOLITRON DEVICES INC 831256 0.219 -1.878 1970 SORG PAPER CO 835852 0.656 -0.086 1970 STANRAY CORP 854701 -0.138 -0.345 1970 STELLAR INDUSTRIES INC-DEL 858552 -1.096 -0.610 1970 TECHNICAL TAPE INC 878504 -0.681 -0.175 1970 TECHNICOLOR INC 878521 -0.151 -0.515 1970 TEJON RANCH CO 879080 0.105 0.071 1970 TITAN CORP 888266 -0.524 -3.027 1970 TYCO LABORATORIES INC 902120 -0.138 -0.331 1970 WILLCOX ft GIBBS INC 969207 -0.177 -0.501 1971 ALTAMIL CORP 021375 0.363 1.280 1971 AMERICAN MFG CO 027357 0.115 0. 116 1971 AMERICAN PRECISION INDS 029069 -0.218 -0.116 1971 APPLIED DATA RESEARCH INC 038159 0.170 -0.033 1971 ARCATA CORP 039375 -0.266 -1.312 1971 AYD IN CORP 054681 -10.474 -1.755 1971 BARTELL MEDIA CORP 069149 -0.238 -0.517 1971 BOHACK CORP 097309 -0.109 -0.521 1971 BOLT BERANEK ft NEWMAN INC 097689 -0.220 -0.139 1971 BOWMAR INSTRUMENT CORP 103025 -0.174 -0.235 1971 BROWN ft SHARPE MFG CO 115223 -0.149 -0.655 1971 BURGESS INDS 121232 -1.069 0.356 1971 CALLAHAN MINING CORP 131069 0.128 0.132 1971 CASTLE TON INDS INC 148573 0.300 0.277 1971 CELLU-CRAFT INC 151159 0.438 -0.512 1971 CHRISTIANA COMPANIES 170819 -16.303 -2.178 1971 CRITON CORP 226745 4.841 -1.119 1971 CURTISS-WRIGHT CORP 231561 -0.253 -3.056 1971 DATA DESIGN LABORATORIES 237649 -6.679 -0.511 1971 OORR-OLIVER INC 258363 -0.526 -2.500 1971 DYNAMICS CORP OF AMERICA 268039 -1.350 -5.211 1971 ELECTROGRAPHIC CORP 285335 -0.391 -0.917 1971 GENERAL EMPLOY ENTERPRISES 369730 1.211 -0.272 1971 GENERAL HOUSEWARES 370073 -0.101 -0.615 1971 GENERAL INTERIORS CORP 370154 8.133 0.211 1971 HARVEY GROUP 417668 0.161 -0.081 1971 HELENE CURTIS INDS 423236 0.266 -0.119 1971 KANSAS CITY SOUTHERN INDS 485170 -0.181 -11.328 1971 MACKE CO 554528 -0.101 -1.162 1971 NATIONAL ALFALFA DEHYDRATING 632448 0.177 0.286 1971 ORMAND INDUSTRIES 686679 0.226 0.315 1971 PANTASOTE INC 698635 -0.371 -0.470 1971 PLY-GEM INDUSTRIES 729416 -0.120 -0.152 19.112 135.682 MISC PLASTIC PRODUCT • YEAR 1970 11.240 284 . 126 MISC PRIMARY METAL YEAR 1970 3.718 22 .483 PERFUME,COSMET1C,TO1 YEAR 1970 3.160 69.850 GENERAL INDUSTRIAL • YEAR 1970 0.762 6.252 CRUDE PETROLEUM ft NA • 7 / 69 TO 6 / 7 0 4.372 33 .720 METAL FORCINGS AND YEAR 1970 -2.109 23.057 HOUSEHOLD FURNITURE • 11 / 69 TO 10 / 7 0 -0.344 101 .431 IRON ft STEEL FOUNDRt • YEAR 1970 1.479 22 .533 FABRICATED RUBBER PR • YEAR 1970 0.543 18.987 RADIO AND TELEVISION 2 / 70 TO 1 / 71 8.641 54 .383 BOOKS: PUBG, PUBG ft YEAR 1970 0.911 6 .839 CRUDE PETROLEUM ft NA • YEAR 1970 0.061 7.997 METAL FORCINGS AND 8 / 69 TO 7 / 7 0 2.224 19 .224 COAT 1NG,ENGRAV1NG,AL YEAR 1970 0.179 4.637 BLANKBOOKS,B1NDRS.BO YEAR 1970 2.076 13 .752 PAPERBOARO CONTAINER • YEAR 1970 -0.370 26.097 SPECIAL INDUSTRY MAC YEAR 1970 -0.108 3.050 PENS-PENCIL ft OTH OF • 2 / 70 TO 1 / 7 1 57.324 655 .313 DRUGS AND PROPR1ETAR 1 / 70 TO 3 / 71 0.177 3.542 RADIO, TV COMM EQ, A YEAR 1970 1.479 11.195 METAL CANS YEAR 1970 -1.406 83 .901 CONSTRUCTION-NOT BLD • YEAR 1970 2.518 11 .006 MGMT, CONSULTING ft YEAR 1970 -8.580 62 . 160 SEM1 CONDUCTOR.RELATE 3 / 70 TO 2 / 7 1 -0.131 23 .332 PAPER ft ALLIED PRODU • YEAR 1970 2.507 44 .715 RAILROAD EQUIPMENT • YEAR 1970 0.584 13.751 MOTOR VEHICLE PARTS- • 5 / 70 TO 4 / 7 1 0.697 15 .882 CONVRT.PAPRBRO PD.EX YEAR 1970 3.614 69.590 SERV-MOTION PICTURE • 13 / 69 TO 6 / 7 0 0.677 12, .309 AGRICULTURE PRODUCT 1 YEAR 1970 5.780 65 .605 CMP PROGRAM ft SOFTWA YEAR 1970 2.404 42, .815 GENERAL INDUSTRIAL 6 / 70 TO 5 / 7 1 2.825 31, .100 ELEC APPARATUS ft EQU YEAR 1970 3.523 26. .303 TRUCK ft BUS BODIES • 9 / 7 0 TO 8 / 71 1.273 72. .808 TEXTILE MILL PRODUCT • YEAR 1971 0.532 7. ,112 ELECTR COIL.TRANSFRM YEAR 1971 -0.194 8, .790 SERV-CMP PROGRAM ft • YEAR 1971 16.188 214, .121 COMMERCIAL PRINTING • 7 / 70 TO 6 / 7 1 0.454 11, .517 RADIO, TV COMM EQ, A YEAR 1971 2.169 33, .131 PERIODICALS:PUBLISHI • YEAR 1971 4.805 69 .710 RETAIL-GROCERY STORE • 2 / 71 TO 1 / 7 2 2.000 12. .110 OFFICE AUTOMATION SY 7 / 70 TO 6 / 71 1.352 11. .660 ELEC MEAS ft TEST INS 18 / 70 TO 9 / 71 4.387 77. .239 METALWORKING MACHINE YEAR 1971 -0.333 13, .606 WHSL-MACHINERY ft EQU • 10 / 70 TO 9 / 7 1 1.034 14, .517 GOLD AND SILVER ORES YEAR 1971 0.923 29 .157 SERV-RACING INCL TRA • YEAR 1971 -1.238 16. .728 MISC PLASTIC PRODUCT • 3 / 71 TO 2 / 7 2 0.152 45. .180 SUBDIVID.DEVELOP.EX 7 / 70 TO 6 / 71 -0.231 23. .907 AIRCRAFT PARTS ft AUX • 5 / 71 TO 4 / 7 2 12.074 258. .893 MISC PRIMARY METAL YEAR 1971 0.081 3. .854 ELECTRONIC COMPONENT. 7 / 70 TO 6 / 71 4.751 71.830 GENERAL INDUSTRIAL • YEAR 1971 3.881 79 .938 ELEC,ELECTR MACH,EQ, YEAR 1971 2.326 13. .553 SERVICE INDUS FOR PR • YEAR 1971 -0.224 2. .166 PERSONNEL SUPPLY SER 10 / 70 TO 9 / 71 5.925 31. .999 METAL FORCINGS AND YEAR 1971 0.030 18. .848 HOUSEHOLD FURNITURE • 11 / 70 TO 10 / 7 1 -0.504 20. .438 RADIO AND TELEVISION 2 / 71 TO 1 / 7 2 -0.447 25. .665 PERFUME,COSMETIC.TOI 3 / 71 TO 2 / 72 23.538 282.853 RAILROADS,L1NE-HAUL YEAR 1971 11.538 75. .434 RETAIL-AUTO MDSNG MA • 10 / 70 TO 9 / 71 1.614 20. . 146 FOOD-PREP FEEDS FOR • 5 / 71 TO 4 / 72 1.396 14. .514 METAL CANS YEAR 1971 1.268 46. .060 MISC PLASTICS PRODUC YEAR 1971 1.262 13.085 MILLWORK,VENEER,PLYW YEAR 1971 1 9 7 1 REED TOOL CO 750260 -0.226 -1.653 1971 RUDDICK CORP 781258 0.129 1.333 1971 SCIENCE MANAGEMENT CORP 808638 0.119 0. 121 1971 SOLID STATE SCIENTIFIC 831207 -0.785 0.372 1971 STANDARD ALLIANCE INDUSTRIES 853037 -1.135 -1.500 1971 TECH-SYM CORP 878308 0.110 -0.093 1971 UNITED BRANDS 909660 0.132 7.268 1971 WILLCOX ft GIBBS INC 969207 -0.377 -0.937 1971 WYOMISSING CORP 983511 -1.931 -0.381 1971 ZENITH LABORATORIES INC 989365 0.718 -1.097 1972 AMREP CORP 032159 -0.319 -0.988 1972 BELDING HEM1NWAY 077191 -0.110 -0.987 1972 BERGEN BRUNSWIG CORP -CL A 083739 -18.180 -0.162 1972 BETHLEHEM CORP 087257 -1.587 -0.311 1972 CALLAHAN MINING CORP 131069 0.102 0.160 1972 COMPUTER SCIENCES CORP 205363 5.668 8.100 1972 CONTINENTAL MATERIALS CORP 211615 0.162 0.330 1972 DYNCORP INC 268162 -0.266 -1.213 1972 FLAGG INDUSTRIES 338360 -0.181 -0.119 1972 FOREST LABORATORIES -CL A 315838 -0.661 -0.152 1972 GENERAL HOST CORP 370061 -0.213 -1.327 1972 GENERAL RESOURCES CORP-DEL 370698 2.726 -0.199 1972 GEN 1 SCO TECHNOLOGY 372298 -0.105 -0.056 1972 CLEN-CERY CORP 377568 -0.217 -1.076 1972 GREAT AMERICAN INDUSTRIES 389856 -0.311 -0.592 1972 HARVEY GROUP 117668 -0.105 -0.113 1972 HEUBLEIN INC 128182 -0.213 -15.250 1972 INTERMEDCO INC 158799 -0.103 -0.192 1972 KINARK CORP 191171 -0.291 -0.518 1972 MDC CORP-PA 552677 0.621 0.083 1972 MEGO INTERNATIONAL 585163 1.512 -0.161 1972 PACIFIC SCIENTIFIC CO 691806 -0.115 -0.099 1972 PIER 1 IMPORTS INC 720280 -0.101 -0.900 1972 REDM INDUSTRIES INC 719185 1.328 -0.896 1972 SCOA INDUSTRIES INC 809123 -0.218 -3.369 1972 SEAPORT CORP 812205 -1.716 0.121 1972 STANDARD-PACIFIC -LP 853753 -0.131 -0.219 1972 STELLAR INDUSTRIES INC-DEL 858552 19.619 -0.727 1972 SUPRONICS CORP 868617 -1.253 -0.228 1972 TECH-SYM CORP 878308 5.575 -1.076 1972 TENNEY ENGINEERING INC 880625 2.620 -0.566 1972 WESTERN ORB IS CO 959078 -2.051 -0.378 1973 ACME PRECISION PRODUCTS INC 001770 0.809 0.151 1973 AEROOEX INC 007752 0.501 0.197 1973 AMERICAN PRECISION INDS 029069 -0.259 -0.361 1973 ASSOCIATED FOOD STORES INC 015609 1.753 -2.081 1973 BEVERLY ENTERPRISES 087851 -0.155 -1.391 1973 COLECO INDS 193378 -0.391 -3.136 1973 CONTINENTAL MATERIALS CORP 211615 -0.135 -0.372 1973 EAGLE CLOTHES INC 269161 0.293 -0.881 1973 ENSTAR CORP-DEL 293582 -0.173 -0.676 1973 FIRST HARTFORD CORP 320188 -0.202 -0.170 1973 HALCO PRODUCTS CORP-NY 105363 -1.000 -0.181 1973 HARCOURT BRACE JOVANOVICH 111631 -0.102 -2.525 1973 INOLEX CORP 157618 0.119 0.137 1973 K V PHARMACEUTICAL CO 182710 -0.188 -0.275 1973 KILLEARN PROPERTIES INC 191125 1.211 -2.919 1973 KING OPTICAL CORP 195576 -3.386 1.618 1973 MARK PRODUCTS INC 570108 -0.123 -0.080 1973 MEGO INTERNATIONAL 585163 -0.398 -0.310 1973 MERIDIAN INDUSTRIES INC 589612 -2.861 -1.195 1973 MOULDINGS INC 620178 -0.511 0.763 1973 NATIONAL ALFALFA DEHYDRATING 632118 -1.332 -6.161 1973 NATL PATENT DEVELPMNT 637130 0.585 -1.055 1973 PLAZA GROUP INC 728185 0.115 0.015 1973 POLORON PRODUCTS INC 731588 0.103 -1.807 7.315 92.181 OIL FIELD MACHINERY • YEAR 1971 10.332 61.120 GROCERY STORES 10 / 7 0 TO 9 / 7 1 1.020 9.015 MGMT, CONSULTING ft YEAR 1971 -0.171 2.331 SEMICONDUCTORS ftREL • YEAR 1971 1.015 27.300 METAL FORGINGS ft STA • YEAR 1971 -0.227 13.759 SE ARCH, N A V1 GATE, GU1D YEAR 1971 51.996 1069.227 MEAT PACKING PLANTS YEAR 1S71 2.185 32.157 ELEC APPARATUS ft EQU YEAH ' >71 0.197 11.717 TEXTILE MILL PRODUCT • YEAR 1971 -1.528 8.687 PHARMACEUTICAL PREPA YEAR 1971 3.091 137.967 SUBDIVID,DEVELOP,EX 5 / 72 TO / 7 3 9.001 65.252 TEXTILE MILL PRODUCT YEAR 1972 0.025 87.010 DRUGS AND PROPRIETAR 9 / 71 TO 8 / 7 2 0.196 10.193 FABRICATED PLATE WOR YEAR 1972 1.563 16.391 GOLD AND SILVER ORES YEAR 1972 1.129 107.596 CMP PROGRAM ft SOFTWA 4 / 72 TO 3 / 7 3 2.035 11.797 AIR COND.HEATING,REF YEAR 1972 1.566 38.551 MGMT, CONSULTING fe YEAR 1972 2.176 26.563 SERV-NURS1NGfePERSON • 5 / 72 TO 1 / 7 3 0.230 11.617 PHARMACEUTICAL PREPA 4 / 72 TO 3 / 73 20.297 213.371 BLOG MATL,HARDWR,GAR YEAR 1972 -0.073 6.089 WHSL-LUMBER ft CONSTR • 11 / 71 TO 1 0 / 7 2 0.531 3.359 COMPUTER OISK ft TAPE 18 / 71 TO 9 / 72 1.351 27.939 STRUCTURAL CLAY PROD • YEAR 1972 1.906 18.727 FABRICATED RUBBER PR • YEAR 1972 1.075 21.556 RADIO AND TELEVISION 2 / 72 TO 1 / 7 3 71.605 153.571 DISTILLED RECTIF BLE • 7 / 71 TO 6 / 72 1.872 19.216 WHSL-MACH1NERY ft EQU • 12 / 71 TO 11 / 72 1.760 19.626 COATING,ENGRAVING,AL YEAR 1972 0. 133 22.331 F1 NANCE-SERVICES • 3 / 72 TO 2 / 7 3 -0.299 11.257 TOYS ft AMUSEMENT SPO • 6 / 72 TO 5 / 73 0.862 8.099 AIRCRAFT PARTS, AUX YEAR 1972 8.627 15.879 RETAIL-STORES E C • 4 / 72 TO 3 / 7 3 -0.207 1.586 ELECTRONIC COMPONENT • YEAR 1972 15.159 123.313 RETAIL-VARIETY STORE • 2 / 72 TO 1 / 7 3 -0.071 11.920 AUTO PARTS ft SUPPLIE YEAR 1972 1.667 56.327 SUBDIVI0,DEVELOP,EX YEAR 1972 -0.037 9.686 MOTOR VEHICLE PARTS- • 5 / 72 TO 4 / 7 3 0.182 2.519 PERFUMES COSMETICS T • 9 / 71 TO 0 / 72 -0.193 15.765 SEARCH,NAV1 GATE,GU1D YEAR 1972 -0.216 2.663 GENERAL INDUSTRIAL YEAR 1972 0.181 27.119 WOOD BUILOINGS-MOBIL • 7 / 71 TO 6 / 7 2 0.561 5.085 METALWORKING MACHINE 10 / 72 TO 9 / 73 0.992 16.651 AIRCRAFT PARTS ft AUX • YEAR 1973 1.101 9.050 ELECTR COIL.TRANSFRM YEAR 1973 -1.189 18.223 WHSL-GROCERIES ft REL • 8 / 72 TO 7 / 7 3 9.661 89.216 SKILLED NURSING CARE YEAR 1973 8.781 71.010 DOLLS YEAR 1973 2.753 16.382 AIR COND,HEATING,REF YEAR 1973 -3.009 52.127 APPAREL,PIECE CDS,NO 8 / 72 TO 7 / 7 3 3.900 168.232 CRUDE PETROLEUM ft NA • YEAR 1973 2.322 12.663 TEXTILE MILL PRODUCT • 12 / 73 TO 1 / 7 4 0.181 2.972 MEAT PRODUCTS • 11 / 7 2 TO 10 / 73 21.635 127.931 BOOKS: PUBG, PUBG ft YEAR 1973 1.150 30.816 ORUGS • YEAR 1973 1.165 8.120 PHARMACEUTICAL PREPA 4 / 7 3 TO 3 / 7 4 -2.371 10.013 SUBDIV10,DEVELOP,EX 1 / 7 3 TO 4 / 74 -1.361 17.687 OPTICAL INSTRUMENTS • YEAR 1973 0.653 3.928 ENGR LAB ft RESEARCH • 9 / 72 TO a / 7 3 0.851 11.293 TOYS ft AMUSEMENT SPO • 6 / 73 TO 2 / 74 1.571 16.851 MOTOR VEHICLE PARTS- • 4 / 73 TO 3 / 74 -1.111 5.559 LUMBER ft WOOD PRODUC • 5 / 73 TO 4 / 74 1.626 25.580 FOOD-PREP FEEDS FOR • 5 / 73 TO 4 / 74 -1.803 30.913 EDUCATIONAL SERVICES YEAR 1973 0.392 1.781 SERV-ADVERT1S1NG AGE • YEAR 1973 -1.186 39.293 WOOD BUILDINGS-MOBIL * 12 / 72 TO 11 / 73 197J RED* INDUSTRIES INC 719185 -0 .108 -0.010 1973 RESTAURANT ASSOC INDS -CL 761252 -0. .705 -1.820 1973 STORM DRILLING ft MARINE INC 862173 -0.962 -13.005 1973 TENNEY ENGINEERING INC 880625 0, .116 0.025 1973 TRANS-LUX CORP 893217 0.295 0.950 1973 VERIT INDUSTRIES 923131 -0, .137 -0.258 1973 VIATECH INC 925528 6. .677 -0.661 1973 VIRCO MANUFACTURING 927651 -0, .328 -0.772 197U AAR CORP 000361 -0. .368 -1.761 1974 ADAMS-MILL IS CORP 006281 -1. .061 -6.770 1974 ALLERGAN PHARMACEUTICALS INC 018192 -0. .112 -1.621 197H ALPHA INDS 020753 -0, . 126 -0.061 1974 AMERICAN SHIP BUILDING CO 029609 -0, . 161 -0.992 1974 ASK IN SERVICE CORP 0115177 -5.001 -1.201 1974 ASSOCIATED FOOD STORES INC 015609 -157. .111 -1.117 1974 AVX CORP 0021140 -0. .311 -1.079 1974 BREEZE CORP 106763 -1. .221 -1.566 1974 CHEMICAL EXPRESS 163727 -0, .197 -0.889 1974 COMPAC CORP 201257 -6, .925 -1.118 1974 CONGOLEUM CORP 207192 -0, .178 -1.380 1974 COOK INTERNATIONAL INC 216171 -0, .125 -7.056 1974 COSCO INC 221116 -1 .338 -1.128 1974 CROMPTON CO INC 227129 0. . 181 0.310 1971 ENSTAR CORP-DEL 293582 -0, .111 -2.969 1974 FIBREBOARD CORP 315711 -0.282 -9.235 1974 GENERAL RESOURCES CORP-DEL 370698 0, .397 -0.219 1974 INOLEX CORP 157618 0. . 101 0.118 1974 INTEGRATED RESOURCES INC 158121 -0 .280 -1.720 1974 INTL PROTEINS 160200 -0 .551 -0.876 1974 IRT CORP 150052 -8, . 180 -0.109 1974 L'AIGLON APPAREL INC 501758 -1. .719 -0.101 197H MACANDREWS ft FORBES GP INC 551207 -0. .105 -0.120 1974 MAMMOTH MART INC 561569 1. .811 -1.381 1974 OXFORD FIRST CORP 691119 -9, .555 -9.169 1974 PACIFIC HOLDING CORP 691102 -2, .197 -3.116 1974 PANOEL-BRADFORD INC 698333 -0. .828 -0.506 197U PAT FASHIONS INDUSTRIES 702860 0. .515 -0.133 1974 PATO CONS GOLD DREDGING LTD 703251 -10. .731 8.027 19711 PIONEER SYSTEMS INC 723886 -0. .203 -0.160 197l» POLORON PRODUCTS INC 731588 -0. .916 -0.575 1974 ROYAL AMER INDS INC 780053 0. .100 1.317 197U SIMPLEX INDUSTRIES INC 828828 -6. .102 -0.781 1971 SYSTRON-DONNER CORP 872056 -0. .208 -1.112 1971 UNION CORP 906072 -0. . 101 -1.285 1971 VERIT INDUSTRIES 923131 -0. .221 -0.182 1975 ALTAMIL CORP 021375 -0. .117 -0.578 1975 AMERICAN TECHNICAL IND 030111 -0. .238 -0.161 1975 APPLIED OATA RESEARCH INC 038159 -0. .120 -0.132 1975 BREEZE CORP 106763 -3. 659 -0.900 1975 COLE NATIONAL CORP 193288 -0. . I l l -1.286 1975 CORENCO CORP 218687 -0. .717 -1.621 1975 DEVON GROUP 251800 -0. 318 -1.185 1975 GLADDING CORP 376121 -0. 719 -1.688 1975 GROLIER INC 398781 -1 . 638 -21.190 1975 INTER-REGIONAL FINANCIAL GP 158351 -0. 307 -2.298 1975 IRT CORP 150052 125. 750 -0.377 1975 KATY INDUSTRIES 186026 -0. 102 -2.068 1975 LAMSON ft SESSIONS CO 513696 -0. 139 -1.181 1975 LUOLOW CORP 519662 -0. 681 -3.718 1975 MARION LABORATORIES 569713 -0. 129 -3.617 1975 MCINTOSH CORP 581182 -0. 257 -2.138 1975 MEDALLION GROUP INC 581025 -1 . 553 -1.791 1975 MYLAN LABORATORIES 628530 -0. 131 -0.085 1975 NARCO SCIENTIFIC INC 630851 0. 117 0.659 1975 OXFORD FIRST CORP 691119 -5.116 -5.297 1975 PACIFIC HOLDING CORP 691102 -0.213 -1.187 0.372 1.209 2.583 32.828 13.518 96.753 0.216 2.803 3.225 19.516 1.890 9.973 -0.099 5.296 2.352 22.761 1.785 13.353 6.361 11.078 3.931 29.080 0.508 5.775 6.011 81.275 0.210 7.571 0.009 11.631 3.168 17.638 0.371 10.351 1.516 33.171 0.599 16.581 7.717 236.831 56.601 611.167 0.260 12.188 1.815 83.566 21.021 196.952 32.770 213.319 -0.551 19.581 1.160 35.071 6.152 71.071 1.591 39.505 0.050 6.707 0.231 5.226 1.116 28.860 -2.117 57.807 0.991 72.772 1.118 33.011 0.611 23.190 -0.211 17.792 -0.718 29.550 2.265 37.697 0.608 28.168 3.291 89.131 0.122 21.321 5.313 11.308 12.370 92.815 0.812 5.161 1.955 20.969 0.676 13.581 1.101 7.367 0.216 9.297 9.103 51.739 2.262 25.065 3.721 15.112 6.521 57.112 12.910 309.700 7.179 95.115 -0.003 3.277 20.239 115.258 8.196 75.109 5.500 122.823 28.026 67.127 8.305 29.611 1. 153 35.270 0.197 9.731 5.618 10.592 0.978 61.060 1.891 33.958 ELECTRONIC COMPONENT EATING PLACES SERV-COMPUTER ft OATA GENERAL INDUSTRIAL MISC MANUFACTURNG IN ELEC APPLIANCE,TV,RA MISC PLASTICS PRODUC PUBLIC BLDG ft REL FU MACHINERY AND EQUIPM KNITTING MILLS DRUGS SEMI CONDUCTOR.RELATE SHIP ft BOAT BLDG ft R RETAIL-APPAREL ft ACC WHSL-GROCERIES ft REL ELECTRONIC COMP, ACC HARDWARE-N E C TRUCK ING-LOCALftLONO MISC CHEMICAL PRODUC MISC PLASTIC PRODUCT SERV-BUSINESS SERVIC HOUSEHOLD FURNITURE TEXTILE MILL PRODUCT CRUDE PETROLEUM ft NA PAPERBOARO CONTAINER WHSL-LUMBER ft CONSTR DRUGS SECURITY BROKERS ft D FATS AND OILS X-RAY,ELECTROMEDICAL APPAREL ft OTHER FINI CANDY ft OTHER CONFEC RETAIL-DEPARTMENT ST PERSONAL CREDIT INST FABRICATED METAL PRD MISC PLASTIC PRODUCT WHSL-NONDURABLE GOOD GOLD ft SILVER ORES MISC FABRICATED TEXT WOOO BUILDINGS-MOBIL SUBDIVID DEVELOP EX PAPER ft ALLIED PRODU MEASURING ft CONTROLL PREFAB METAL BLDGS ft ELEC APPLIANCE,TV,RA TRUCK ft BUS BODIES MISC MANUFACTURING I SERV-CMP PROGRAM ft HARDWARE-N E C RETAIL-STORES E C FATS ft OILS WHSL-NONDURABLE GOOD RADIO-TV TRANSMTTNG BOOKS: PUBG, PUBG ft SECURITY BROKERS ft 0 X-RAY.ELECTROMEDICAL SPECIAL INDUSTRY MAC ELECTRIC LIGHTING,Wl CONVERT PAPER-PAPERB PHARMACEUTICAL PREPA FABRICATED METAL PRD SOAP ft OTHER DETERGE PHARMACEUTICAL PREPA SURG ft MED INSTRUMEN PERSONAL CREDIT INST FABRICATED METAL PRD • YEAR 1973 YEAR 1973 • 11 / 72 TO 10 / 7J YEAR 1973 YEAR 1973 7 / 72 TO 6 / 73 YEAR 1173 2 / 73 TO 1 / 74 6 / 71 TO 5 / 75 YEAR 1971 • YEAR 1971 1 / 71 TO 3 / 75 18 / 73 TO 9 / 71 • 2 / 71 TO 1 / 75 • 8 / 73 TO 7 / 71 YEAR 1971 • YEAR 1971 • YEAR 1971 • 10 / 73 TO 9 / 74 • YEAR 1971 • 6 / 71 TO 5 / 75 • YEAR 1971 • 18 / 73 TO 9 / 74 • YEAR 1971 • YEAR 1971 • 11 / 73 TO 10 / 74 • YEAR 1971 10 / 73 TO 12 / 74 YEAR 1971 1 / 71 TO 3 / 75 • 7 / 73 TO 6 / 74 • 5 / 71 TO 1 / 75 • 2 / 71 TO 1 / 75 YEAR 1971 • YEAR 1971 • 10 / 73 TO 9 / 74 • 12 / 73 TO 11 / 74 • YEAR 1971 12 / 73 TO 11 / 74 • 12 / 73 TO 11 / 74 • 10 / 73 TO 9 / 74 • YEAR 1971 • 8 / 73 TO 7 / 74 7 / 73 TO 6 / 74 7 / 73 TO 6 / 74 • 9 / 71 TO 8 / 75 • 1 / 75 TO 3 / 76 • YEAR 1975 • YEAR 1975 • 11 / 71 TO 10 1 75 • YEAR 1975 • 1 / 75 TO 3 / 76 • 10 / 71 TO 9 / 75 YEAR 1975 YEAR 1975 1 / 75 TO 3 / 76 YEAR 1975 YEAR 1975 • YEAR 1975 7 / 74 TO 6 / 75 • 7 / 74 TO 6 / 75 • YEAR 1975 1 / 75 TO 3 / 76 • 12 / 74 TO 11 / 75 YEAR 1975 • YEAR 1975 1975 PEMCOR INC 706446 -0.103 -0.627 1975 POST CORP 737421 -0.570 -2.576 1975 SERVOTRONICS INC 817732 0.507 -1.756 1975 SIMPLEX INDUSTRIES INC 828828 -1.023 -0.699 1975 STANWOOD CORP B51867 -0.189 -0.781 1975 TREADWAY COS INC 891516 -0.573 -1.210 1975 TUFTCO CORP 899011 -0.154 -0.235 1975 UNITED PIECE DYE WORKS 911332 -1.625 -1.734 1975 UNIVERSAL CONTAINER CORP 913153 -1.166 -3.031 1975 VEEDER INDUSTRIES INC 922125 -0.194 -2.628 1975 VERIT INDUSTRIES 923134 -0.167 -0.132 1975 VOPLEX CORP 929032 -0.823 -1.179 1975 WARNER COMMUNICATIONS INC 931136 -0.434 -11.000 1975 WE 1 MAN CO INC 918662 -0.402 -0.541 1975 WOLF (HOWARD 8) INC 977725 -18.984 -1.177 1976 ALLIED PRODUCTS 019111 0.151 0.956 1976 ASK IN SERVICE CORP 015177 -3.147 -1.202 1976 BARNES ENGINEERING CO 067797 -3.651 -0.785 1976 BETHLEHEM CORP 087257 -0.138 0.133 1976 BLOUNT INC -CL A 095173 -0.117 -1.828 1976 CERTIFIED CORP 156897 -2.537 -0.312 1976 COMPUTER INSTRUMENTS CORP 205165 -0.771 0.226 1976 CONTINENTAL MATERIALS CORP 211615 -0.326 -0.586 1976 ELECTRONIC ASSOCIATES INC 285551 -0.154 0.541 1976 FARAH INC 307387 0.254 -1.621 1976 FIRST HARTFORD CORP 320188 -0.826 -1.193 1976 GENERAL EMPLOY ENTERPRISES 369730 -1.924 -0.302 1976 GIT INDUSTRIES INC 361722 -0.168 -0.761 1976 HAJOCA CORP-ME 105307 -0.751 -3.219 1976 HOWELL CORP 113051 -0.108 -1.561 1976 HUDSON GENERAL CORP 113781 -0.473 -2.434 1976 INOLEX CORP 157618 0.234 0.228 1976 INSTRUMENT SYSTEMS CORP 157791 -1.706 -7.868 1976 INTERMARK INC 158776 -0.232 -0.442 1976 INTL MINING CORP 160020 -0.666 -1.020 1976 IRT CORP 150052 0.212 0. 101 1976 NELLY DON INC 610303 -20.428 -1.859 1976 OXFORD FIRST CORP 691119 -0.894 -1.539 1976 OXFORD INDUSTRIES INC 691197 0.480 6.725 1976 POPE ft TALBOT INC 732827 -0.149 -2.669 1976 RAYCHEM CORP 751603 0.123 3.415 1976 REDMAN INDUSTRIES INC 757610 14.058 7.226 1976 SERVOTRONICS INC 817732 -0.758 -0.467 1976 SIKES CORP -CL A 826750 -0.829 -2.414 1976 SUMMIT ORGANIZATION INC 866212 0.350 1.685 1976 SUPRON ENERGY CORP 868638 0.282 5.747 1976 UNION CORP 906072 -0.119 -1.166 1976 UNITED PIECE DYE WORKS 911332 -7.962 -1.656 1977 ALLIED ARTISTS INDUSTRIES 018859 -0.321 -0.742 1977 ALTEX OIL CORP 021456 1.714 0.024 1977 AMFAC INC 031111 -0.183 -17.600 1977 AMREP CORP 032159 -0.344 -1.072 1977 BANISTER CONT LTD 060339 -0.250 0.877 1977 BERKEY INC 081419 -2.326 -24.783 1977 BOLT BERANEK ft NEWMAN INC 097689 1.269 0.590 1977 CHICAGO MILWAUKEE CORP 167763 -73.865 -389.857 1977 CINEMA 5 LTD 172435 0.169 -0.120 1977 COMPUDYNE CORP 204795 0.173 0.654 1977 CROWN INDUSTRIES 228381 -0.168 -0.462 1977 DAMON CORP 235717 -0.435 -2.916 1977 DAMSON OIL 235766 0.240 1.444 1977 ENERGY RESOURCES CORP 292713 0.548 1.048 1977 GIT INDUSTRIES INC 361722 0. 143 1.664 1977 HMW INDUSTRIES INC 404215 -1.712 -7.797 1977 INOLEX CORP 157618 -5.143 0.216 1977 KEARNEY NATIONAL INC 486872 -0.648 -1.127 6.072 35.237 WHSL-ELECTRONIC PART • 1 / 75 TO 3 / 76 4, .521 21.714 NEWSPAPERS:PUBL1SH1N • YEAR 1975 -3 .464 11.791 CUTLERY,HAND TOOLS,0 YEAR 1975 0 .683 16.630 PAPER ft ALLIED PROOU • YEAR 1975 4 . 136 60.912 KNITTING MILLS 8 / 74 TO 7 / 75 2, .112 15.472 SERV-MISC AMUSEMENT • 9 / 74 TO 8 / 75 1. .523 15.058 SPECIAL INDUSTRY MAC « YEAR 1975 1, .067 20.407 KNITTING MILLS • YEAR 1975 2. .601 24.250 METAL CANS ft SHIPPIN • 12 / 74 TO 11 / 75 13. .518 66.144 MEASURING ft CONTROLL • YEAR 1975 0. .790 5.237 ELEC APPLIANCE,TV,RA MISC PLASTICS PRODUC 7 / 74 TO 6 / 75 1, .433 10.343 YEAR 1975 94. .363 804.209 MOTION PICTURE PROOT YEAR 1975 1. .346 19.883 SPORTING ft RECREATN YEAR 1975 0.062 5.631 APPAREL ft OTHER FINI 6 / 75 TO 5 / 76 6 .335 165.889 FARM MACHINERY AND E YEAR 1976 0. .382 4.970 RETAIL-APPAREL ft ACC • 2 / 76 TO 1 / 77 0 .215 5.736 RADIO-TV COMM EQUIP • 7 / 75 TO 6 / 76 -0 .961 9.925 FABRICATED PLATE WOR YEAR 1976 15 .645 159.018 GEN BLDG CONTRACTORS 3 / 76 TO 2 / 77 0 . 123 10.900 MISC MANUFACTURING 1 • 7 / 75 TO 6 / 76 -0 .293 2.080 ELECTRONIC COMPONENT • YEAR 1976 1 .800 16.559 AIR COND,HEATING,REF COMPUTERS-MA 1NFRAME YEAR 1976 -3 .536 21.112 YEAR 1976 •18 . 192 80.306 MEN,YTH,BOYS FRNSH,W 11 / 75 TO 10 / 76 1 .445 19.447 TEXTILE MILL PRODUCT • 2 / 76 TO 4 / 77 0 .157 1.732 PERSONNEL SUPPLY SER 18 / 75 TO 9 / 76 4. .538 77.479 RUBBER ft MISC PLAST 1 • 1 / 75 TO 12 / 76 4. .288 71.618 WHSL-HARDWR PLUM HEA • 7 / 75 TO 12 / 76 14.396 55.020 PETROLEUM,EX BULK ST YEAR 1976 5 . 142 41.871 FIXED FACILITY,SVC-A 7 / 75 TO 6 / 76 0 .974 27.466 ORUGS • YEAR 1976 4 .612 140.075 MISC FURNITURE AND F 10 / 75 TO 9 / 76 1 .904 25.327 FURNITURE,HOME FURNI 1 / 76 TO 3 / 77 1 .531 89.380 WATER TRANSPORTATION • YEAR 1976 0.477 2.900 X-RAY,ELECTROMEDICAL 1 / 76 TO 3 / 77 0 .091 5.431 APPAREL ft OTHER FINI • 11 / 75 TO 11 / 76 1. .721 60.487 PERSONAL CREDIT INST YEAR 1976 14 .021 102.596 APPAREL ft OTHER FINI 6 / 76 TO 5 / 77 17 .893 89.541 SAWMILLS, PLANING Ml ELECTRIC LIGHTING,Wl YEAR 1976 27.839 164.233 7 / 75 TO 6 / 76 0. .514 50.801 M08ILE HOMES 1 / 76 TO 3 / 77 0 .616 6.375 CUTLERY,HAND TOOLS,G YEAR 1976 2 .913 18.953 STRUCTURAL CLAY PROD 3 / 76 TO 2 / 77 4.808 64.205 APPAREL ft OTHER FINI • 7 / 75 TO 6 / 76 20. .383 89.990 CRUDE PETROLEUM ft NA • YEAR 1976 9. .821 89.137 PREFAB METAL BLDGS ft 7 / 75 TO 6 / 76 0. .208 15.316 KNITTING MILLS • YEAR 1976 2. .310 29.209 MOTOR HOMES • 1 / 77 TO 3 / 78 0.014 1.685 OIL ft CAS FIELD SERV • 10 / 76 TO 9 / 77 96. .428 801.217 DRUGS AND PROPRIETAR YEAR 1977 3. .117 91.835 SUBDIVID,DEVELOP,EX CONSTRUCTION-NOT BLD 5 / 77 TO 4 / 78 -3.503 67.368 1 / 77 TO 3 / 78 10. .654 106.716 MGMT, CONSULTING ft YEAR 1977 0. .465 13.110 OFFICE AUTOMATION SY 7 / 76 TO 6 / 77 5. .278 38.881 REAL ESTATE DEALERS YEAR 1977 -0, .712 8.061 SERV-MOTION PICTURE • 10 / 76 TO 9 / 77 3. .789 25.696 SEARCH,NAV1 GATE,GU10 10 / 76 TO 9 / 77 2. .752 13.157 LUMBER ft WOOD PRODUC • 10 / 76 TO 9 / 77 6. .711 105.731 MEDICAL LABORATORIES 9 / 76 TO 8 / 77 6. .015 11.512 CRUDE PETROLEUM ft NA YEAR 1977 1. .911 11.818 CRUDE PETROLEUM ft NA • 7 / 76 TO 6 / 77 11. .629 68.181 RUBBER ft MISC PLASTI • YEAR 1977 4. .554 36.621 SILVERWARE-PLATEWARE • 2 / 77 TO 1 / 78 -0.042 27.216 ORUGS • YEAR 1977 1. .740 15.308 ELEC,ELECTR MACH.EQ, YEAR 1977 1977 LEAR PETROLEUM CORP 521890 0.107 0 .556 1977 LLOYD'S ELECTRONICS 539131 -0. .476 -1 , .752 1977 LOWENSTEIN (M.) CORP 517779 0. .156 1, .010 1977 NELLY DON INC 610303 -11. .558 -1 , .787 1977 NORTEK INC 656559 -0. ,610 -2 .500 1977 OXFORD FIRST CORP 691119 -0. .358 -0.509 1977 PATO CONS GOLD DREDGING LTD 703251 -0. .305 0 .113 1977 REOLAW INC 757633 -1 . . 182 0 .376 1977 REEVES TELECOM CORP 758650 0. .348 0 .032 1977 RUSCO INDUSTRIES INC 781768 0. . 188 0 .657 1977 SCHOOL PICTURES INC 807859 -0. .196 -0 .738 1977 SERVOTRONICS INC 817732 0. ,460 0 .278 1977 SPENCER FOODS INC 817889 -1.011 -1.091 1977 STONER1DGE RESOURCES INC 861839 2.163 -1 .320 1978 ADAMS RESOURCES It ENERGY INC 006351 0. .175 1 .111 1978 ATCO INDS 016787 -1.516 -0 .620 1978 CENCO INC 151303 0. .107 1 .995 1978 FIRST HARTFORD CORP 320488 -0.661 -3 .135 1978 GEOTHERMAL RES INTL INC 373676 1.698 -0 .275 1978 GIT INDUSTRIES INC 361722 -0. .271 -2 .371 1978 GOLOFIELD CORP 381370 -1 . .166 -1 .766 1978 INTL FOODSERVICE CORP 159528 0 .996 -1 .212 1978 KEARNEY NATIONAL INC 186872 -0, . 100 -0 .115 1978 MARSHALL FOODS INC 572350 -1.961 0 .355 1978 MAUL TECHNOLOGY CORP 577377 -0. .438 -0 .912 1978 NCR CORP 626862 0 .220 121 .273 1978 POLORON PRODUCTS INC 731588 -1.827 -2 .123 1978 RUSCO INDUSTRIES INC 781768 0. ,291 1 .131 1978 SAV-A-STOP INC 801600 -0, .115 -1 .006 1978 STERLING ELECTRONICS 859281 -2, .311 -2.311 1978 TRAFALGAR INDUSTRIES INC 892711 0. .161 -0 .238 1979 ADAMS RESOURCES ft ENERGY INC 006351 0, .137 1 .781 1979 ADAMS-MILL IS CORP 006281 -0. .308 -2 .011 1979 AMERICAN SEATING CO 029165 1. .853 -0 .101 1979 ARTRA GROUP INC 043117 0. .210 2 .012 1979 ASK IN SERVICE CORP 015177 0. .301 -0 .010 1979 CALIFORNIA LIFE CORP 130376 37919. ,988 -3 .795 1979 CENCO INC 151303 0, .113 2 .126 1979 CHOCK FULL 0 NUTS CORP 170268 0. .217 1 .200 1979 CORDURA CORP 218661 -0. .508 -1 .800 1979 DRUG FAIR INC 262188 -0. .187 -1 .077 1979 EAGLE CLOTHES INC 269461 0. .511 -3 .510 1979 FLORIDA CAPITAL CORP 310567 -0. .381 -0.662 1979 GIT INDUSTRIES INC 361722 -0. .167 -1 , .000 1979 HAJOCA CORP-ME 105307 -0. .168 -1 .318 1979 HEALTH-CHEM CORP 422171 -0. .107 -0 .762 1979 JONATHAN LOGAN INC 179898 -1 , .862 -11 .951 1979 KEARNEY NATIONAL INC 186872 -0. .583 -3 .533 1979 MCO HOLDINGS INC 552901 0. .910 23 .991 1979 MICKELBERRY CORP 591780 0. .878 1.810 1979 RUSCO INDUSTRIES INC 781768 -1 , ,511 -2, .285 1979 STANCE CO 851112 -0. ,132 -0, .510 1979 TANOYCRAFTS INC 875386 2. .357 5. .990 1979 TRAFALGAR INDUSTRIES INC 892711 0. .603 -1.860 1979 TRIANGLE CORP 895853 -0. .356 -1, .789 1979 VIATECH INC 925528 -0. .332 -0 .103 1988 AFFILIATED HOSPITAL PROS 008230 -0. .113 -0.669 1980 ATCO INDS 016787 0. . 137 0.072 1980 BARCLAY INDUSTRIES 067371 8. .332 -3 .208 1980 BARNWELL INDUSTRIES 068221 -0. ,835 -2, .523 1980 BUILOEX INC 120085 - 1 , ,056 -7.018 1980 CALIFORNIA LIFE CORP 130376 -2120. .000 -0 .212 1980 CAVITRON CORP 119615 -0. . 137 -0 .665 1980 CHOCK FULL 0 NUTS CORP 170268 0. , 147 0 .811 1980 EECO INC 268420 0. .138 2 .928 1980 GENERAL HOST CORP 370064 -0. .516 -18 . 142 5.220 31.268 NATURAL OAS TRANSMIS 3.679 16.052 RAD 10-TV RECEIVING 6.653 326.576 TEXTILE MILL PRODUCT 0.013 3.501 APPAREL ft OTHER FINI 1.096 61.119 SHEET METAL WORK 1.121 60.384 PERSONAL CREDIT INST -0.370 36.520 GOLD ft SILVER ORES -0.318 19.347 METAL FORGINGS ft STA 0.092 7.588 RADIO-TV BROADCASTER 3.193 10.212 MTL DOORS,FRAMES,MOL 3.768 23.027 PHOTOFINISHING LABOR 0.601 1.712 CUTLERY,HAND TOOLS,G 1.076 51.698 MEAT PRODUCTS -0.536 101.981 CAN,PRESERVE FRUIT.V 6.523 70.972 PETROLEUM,EX BULK ST 0.101 6.355 ROLLING ft DRAW NONFE 18.658 179.111 SERV-NURSINGftPERSON 5.175 11.830 TEXTILE MILL PRODUCT -0.162 17.190 STEAM SUPPLY 8.773 37.062 RUBBER ft MISC PLASTI 1.511 11.892 WATER,SEWER,PIPE LIN -1.217 73.973 WHSL-GROCERIES ft REL 1.150 16.171 ELEC.ELECTR MACH.EQ, -0.181 24.098 WHSL-GROCERIES ft REL 2.081 42.208 SPECIAL INDUSTRY MAC 564.180 2596.160 ELECTRONIC COMPUTING 0.502 29.149 WOOD BUILDINGS-MOBIL 3.885 39.622 MTL DOORS,FRAMES,MOL 8.772 78.121 WHSL-ORUGS ft PROPRIE 1.000 19.678 ELECTRONIC PARTS ft E -1.175 26.896 BITUMINOUS COAL ft LI 12.996 87.166 PETROLEUM,EX BULK ST 6.531 10.752 KNITTING MILLS -0.218 66.916 OFFICE FURNITURE 8.376 71.167 COSTUME JEWLRY.BUTTO -0.133 1.117 RETAIL-APPAREL ft ACC 0.000 77.058 FINANCE-SERVICES 16.956 186.537 SERV-NURSINGftPERSON 1.852 11.156 MISC FOOD PREPS, KIN 3.515 21.693 PRINTING PUBLISHING 5.760 65.931 RETAIL-DRUGftPROPRIET -6.871 13.656 APPAREL,PIECE COS,NO 1.726 8.535 SPECIAL INDUSTRY MAC 5.979 39.757 RUBBER ft MISC PLASTI 8.029 73.336 WHSL-HARDWR PLUM HEA 7.096 11.716 BRD WOVN FABRC MAN-M 21.110 262.681 APPAREL ft OTHER FINI 6.060 15.902 ELEC.ELECTR MACH.EQ, 26.376 283.853 SUBDIVID,DEVELOP,EX 2.062 29.131 COMMERCIAL PRINTING 1.509 39.010 MTL DOORS,FRAMES,MOL 1.081 30.061 FOOO PREPARATIONS 2.511 13.071 HOBBY, TOY, ANO GAME -3.081 23.857 BITUMINOUS COAL ft LI 5.021 27.170 CUTLERY,HAND TOOLS,G 0.310 3.156 MISC PLASTICS PRODUC 1.669 29.912 FABRICATED RUBBER PR 0.525 5.157 ROLLING ft DRAW NONFE -0.385 7.162 LUMBER ft WOOD PRODUC 3.022 27.396 CRUDE PETROLEUM ft NA 6.613 51.937 HARDWARE-N E C 0.000 70.210 FINANCE-SERVICES 1.816 21.635 DENTAL EQUIP ft SUPPl 5.733 37.927 MISC FOOO PREPS, KIN 6.678 32.787 COMPUTER EQUIPMENT, 35.131 271.911 BLDG MATL.HARDWR,GAR I B / 76 TO 9 / 77 • 4 / 77 TO 3 / 78 • YEAR 1977 « 12 / 76 TO 11 / 77 YEAR 1977 YEAR 1977 • YEAR 1977 • YEAR •977 • YEAR 1977 • 2 / 77 TO 1 / 78 7 / 76 TO 6 / 77 YEAR 1977 • 11 / 76 TO 10 / 77 9 / 76 TO 6 / 77 4 / 78 TO 3 / 79 • 5 / 76 TO 4 / 79 • 5 / 78 TO 4 / 79 • 5 / 78 TO 4 / 79 YEAR 1978 • YEAR 1978 YEAR 1978 • YEAR 1978 YEAR 1978 • 4 / 78 TO 3 / 79 • YEAR 1978 YEAR 1978 • 12 / 77 TO 11 / 78 • 2 / 78 TO 1 / 79 • 9 / 77 TO 8 / 78 4 / 78 TO 3 / 79 • 5 / 76 TO 4 / 79 4 / 78 TO 12 / 79 YEAR 1979 • YEAR 1979 YEAR 1979 • 2 / 79 TO 1 / 80 • YEAR 1979 • 5 / 79 TO 4 / 80 8 / 78 TO 7 / 79 • YEAR 1979 • 7 / 79 TO 1 / 80 8 / 78 TO 7 / 79 • YEAR 1979 • YEAR 1979 • YEAR 1979 1 / 78 TO 12 / 79 • YEAR 1979 YEAR 1979 YEAR 1979 YEAR 1979 • 2 / 79 TO 1 / 80 • YEAR 1979 7 / 78 TO 6 / 79 • 5 / 79 TO 4 / 80 YEAR 1979 YEAR 1979 • YEAR 1980 • YEAR 1980 • 9 / 79 TO 7 / 80 18 / 79 TO 9 / 80 • 18 / 79 TO 9 / 80 • YEAR 1980 • 18 / 79 TO 9 / 80 8 / 79 TO 7 / 80 YEAR 1980 YEAR 1980 to 1980 GOL0FIEL0 CORP 381370 -6.279 -0.510 I960 ICH PHARMACEUTICALS 1NC-DEL Utt9290 -0.963 -3.000 1980 INSTRUMENT SYSTEMS CORP 157791 -1.330 -15.791 1980 INTERSTATE BAKERIES CORP 160723 -1.321 -30.105 1980 KINC OPTICAL CORP 195576 1.557 -0.515 1980 PACE PETROLEUM LTD 695533 -0.113 -1.186 1980 PRESIDENTIAL RLTY NEW -CL 711001 -1.020 -2.151 1980 SCHEIB (EARL) INC 806398 -0.382 -1.082 1980 SIMMONDS PRECISION PROOS INC 828675 -0.382 -7.986 1960 SSP INDUSTRIES 781719 0.351 0. 136 1980 STEVCOKNIT INC 860156 -0.171 -3.118 1980 UNIVERSITY PATENTS INC 911802 -3.773 2.521 1980 VIATECH INC 925528 0.335 0.156 1980 WEAN INC-PA 917015 -0.312 -2.516 1981 AMBRIT INC 023363 -1.571 -1.917 1981 AMERICAN SCIENCE ENGINEERING 029129 -1.213 0. 108 1981 ANDAL CORP 033352 -0.355 -1.523 1981 ANGELES CORP 031621 -1.511 -7.830 1981 ANTA CORP 036628 -0.151 -3.113 1981 ATCO INDS 016787 -2.665 -0.589 1981 AVX CORP 002110 -0.103 0.071 1981 BISCAYNE HOLDINGS -CL A 091360 -1.906 13.997 1981 CCX INC 125005 0.303 3.370 1981 CHRISTIANA COMPANIES 170819 -0.786 -1.167 1981 CLABIR CORP 178872 -0.112 -1.578 1981 CLAIRE'S STORES INC 179581 -0.703 -2.051 1981 DENTSPLY INTERNATIONAL INC 219028 -0.325 -10.151 1981 FABERCE INC 302808 -0.370 -5.116 1981 FIDATA CORP 315728 -0.312 -10.129 1981 FLAGG INDUSTRIES 338360 -0.275 -0.990 1981 INSTRUMENT SYSTEMS CORP 157791 -1.515 -6.205 1981 INTERSTATE BAKERIES CORP 160723 -0.198 -5.702 1981 IROQUOIS BRANDS LTD 163319 -0.189 -2.625 1981 MASLANO ( C H . ) ft SONS 571803 -0.288 -2.028 1981 MICKELBERRY CORP 591780 -0.111 -0.105 1981 NATIONAL ENTERPRISES INC 635819 -0.173 0.891 1981 NEW MEXICO a ARIZONA LAND 617072 -1.031 -3.600 1981 NICOLET INSTRUMENT 651061 -0.226 -3.300 1981 REPUBLIC GYPSUM CO 760173 -0.265 -1.151 1981 ROB INTECH INC 771010 0.218 1.021 1981 SANTA ANITA REALTY ENTER 801209 -1119.996 -0.112 1981 SSP INDUSTRIES 781719 0.993 -1.909 1981 STARRETT HOUSING CORP 855677 -1.518 -8.611 1981 SULLAIR CORP 865112 -0.121 -1.927 1981 TECHN1TROL INC 878555 -0.211 -0.897 1981 THOR ENERGY RESOURCES INC 885118 0.213 0.101 1982 ANGLO ENERGY INC 035053 0.106 3.080 1982 CCX INC 125005 -2.725 -13.123 1982 CHRISTIANA COMPANIES 170819 -0.286 1.090 1982 DAMON CORP 235717 -1.906 -9.837 1982 GALVESTON HOUSTON 361121 -0.150 -3.185 1982 GEMCO NATIONAL INC 368636 -0.191 -0.717 1982 GT1 CORP 362360 -0.201 -0.277 1982 HI-SHEAR INDUSTRIES 128399 -1.086 -8.179 1982 INSTRUMENT SYSTEMS CORP 157791 87.769 -6.191 1982 INTERSTATE BAKERIES CORP 160723 -0.717 -11.000 1982 JEWELCOR INC 177205 -0.112 -1.072 1982 KEYSTONE INTERNATIONAL 193503 -0.110 -1.811 1982 LA BARGE INC 502170 -0.120 -0.355 1982 M/A-COM INC 552618 -0.119 -10.138 1982 METEX CORP 591503 0.359 0.088 1982 PARAMOUNT PACKAGING 699313 -0.211 -0.132 1982 PIONEER SYSTEMS INC 723886 -0.102 -0.698 1982 SSP INDUSTRIES 781719 -1.275 -0.153 1982 TELECOM CORP 879276 -6.861 -25.968 1982 TRANSCON INC-CALIF 893552 -3.070 -2.180 0.086 16.130 WATER,SEWER,PIPE LIN YEAR 1980 3.115 53.289 PHARMACEUTICAL PREPA 12 / 79 T O 11 / 80 11.876 120.120 MISC FURNITURE AND F 10 / 79 TO 9 / 80 22.960 179.012 BAKERY PRODUCTS 6 / 80 TO 5 / 81 -0.350 1.713 OPTICAL INSTRUMENTS • YEAN 1980 10.371 79.218 CRUDE PETROLEUM a NA • YEAR 1980 2.102 16.997 REAL ESTATE 1NVESTME 11 / 79 TO 12 / 80 2.836 16.731 AUTO REPAIR,SERVICES 5 / r.0 TO 1 / 81 20.919 90.720 INDUSTRIAL MEASUREME • YEAR 1980 0.381 16.195 CONSTRUCTION MACHINE • 3 / 80 TO 2 / 81 7.269 31.793 KNITTING MILLS • 2 / 80 TO 1 / 61 -0.669 10.819 OPHTHALMIC GOODS 8 / 79 TO 7 / 80 0.165 3. 116 MISC PLASTICS PRODUC YEAR 1980 8.155 178.702 METALWORKING MACHINE YEAR 1980 1.220 8.188 SUGAR a CONFECTIONER 2 / 81 TO 1 / 82 -0.089 23.161 RESEARCH a DEVELOPME 1 / 81 TO 3 / 82 1.295 107.338 METALS SERVICE CENTE YEAR 1981 5.173 31.112 REAL ESTATE YEAR 1981 20.271 133.600 ROLLING ft DRAW NONFE • 7 / 80 TO 6 / 81 0.221 5.301 ROLLING ft DRAW NONFE • YEAR 1981 -0.715 119.702 ELECTRONIC COMP, ACC YEAR 1981 -2.853 27.516 ORTHO.PROSTH.SURG AP YEAR 1981 11.118 96.362 MISC FABRICATED META 7 / 80 TO 6 / 81 1.185 72.525 SUBDIVID,DEVELOP,EX 7 / 80 TO 6 / 81 11.111 73.555 INVESTORS, NEC 2 / 81 TO 1 / 82 2.921 9.591 APPAREL ANO ACCESSOR 2 / 81 TO 1 / 82 32.151 168.075 DENTAL EQUIP ft SUPPL • YEAR 1981 11.610 195.007 PERFUMES COSMETICS T • YEAR 1981 32.171 590.850 INVESTORS, NEC YEAR 1981 3.595 21.651 SERV-NURS1NGftPERSON • 5 / 81 TO 1 / 82 1.095 92.288 MISC FURNITURE AND F 10 / 80 TO 9 / 81 28.837 188.661 BAKERY PROOUCTS 6 / 81 TO 5 / 82 5.778 91.371 PHARMACEUTICAL PREPA YEAR 1981 7.019 59.370 FLOOR COVERING MILLS • YEAR 1981 3.562 17.770 COMMERCIAL PRINTING YEAR 1981 -5.115 88.075 PREFAB WOOD BLDGS ft YEAR 1981 3.192 23.181 LESSORS OF REAL PROP YEAR 1981 11.589 75.511 ELEC MEAS ft TEST INS 1 / 81 T O 3 / 82 1.311 16.319 CONCRETE, GYPSUM AND 7 / 80 T O 6 / 81 1.706 90.951 MISC PLASTIC PRODUCT • 7 / 80 TO 6 / 81 0.000 83.911 RACING,INCL TRACK OP YEAR 1981 -1.922 12.773 CONSTRUCTION MACHINE • 3 / 61 TO 2 / 82 5.561 115.399 SUBD1V1D.DEVELOP.EX YEAR 1981 15.932 136.550 GENERAL INDUSTRIAL • YEAR 1981 1. 187 15.188 ELECTRIC LIGHTING,Wl YEAR 1981 0.116 8.380 ENGR, ARCHITECT, SUR 2 / 81 TO 1 / 82 29.163 337.073 DRILLING OIL AND GAS 10 / 81 TO 9 / 82 1.016 59.771 MISC FABRICATED META 7 / 81 TO 6 / 82 -3.812 67.687 SUBDIVID,DEVELOP,EX 7 / 81 TO 6 / 82 5.161 95.057 MEDICAL LABORATORIES 9 / 81 TO 8 / 82 23.251 210.176 CONSTR,MINING,MATL H YEAR 1982 3.911 30.917 APPAREL,PIECE CDS,NO YEAR 1982 1.359 13.060 ELECTRONIC COMPONENT YEAR 1982 7.806 82.371 BOLT,NUT,SCREW,RIVET 6 / 82 TO 5 / 83 -0.071 69.085 MISC FURNITURE AND F 10 / 81 TO 9 / 82 18.752 187.975 BAKERY PRODUCTS 6 / 82 TO 5 / 83 9.561 100.159 JEWELRY.WATCHES,D1 AM 2 / 82 TO 1 / 83 31.611 110.121 VALVE,PIPE FITTINGS, YEAR 1982 2.955 71.936 ALARM ft SIGNALING PR YEAR 1982 87.792 566.387 SEM1 CONDUCTOR.RELATE 10 / 81 TO 9 / 82 0.215 16.088 RADIO, TV COMM EQ, A YEAR 1982 0.511 17.319 PAPERBOARD CONTAINER • YEAR 1982 1.735 31.720 MISC FABRICATED TEXT 12 / 81 TO 11 / 82 0.120 10.611 CONSTRUCTION MACHINE • 3 / 12 TO 2 / 83 3.783 15.807 HAROWR, PLUMB, HEAT YEAR 1982 0.710 80.719 TRUCKING, EXCEPT LOC YEAR 1982 1982 TRANZONIC COS 891120 -1.031 -8.126 1982 UNIMAX CORP 901790 -0. .757 -7.351 1982 UNITED CABLE TELEVISION 909695 -0. .765 -33.008 1982 VARO INC 922272 -0. .382 -3.700 1982 WESTERN DIGITAL CORP 958102 0.291 -1.162 1982 WOOOSTREAM CORP 980521 -0. 519 -0.929 1982 WYNN'S INTERNATIONAL INC 983195 -1. .075 -9.525 1983 AMERACE CORP 023519 -0. .356 -8.818 1983 ASTREX INC 016357 -0. ,781 -1.935 1983 BADGER METER INC 056525 -0. ,297 -0.963 1983 BLESSINGS CORP 093532 0. ,165 0.837 1983 CALLAHAN MINING CORP 131069 0.129 0.810 1983 CASABLANCA INDS INC 117129 -15. ,500 0.062 1983 CHOCK FULL 0 NUTS CORP 170268 -0. .117 -0.788 1983 CHRIS-CRAFT INDS 170520 -0. .152 -2.080 1983 CHRISTIANA COMPANIES 170819 -0. . 166 0.709 1983 CLC OF AMERICA 125615 -1.038 1.171 1983 DIVERSIFIED INDUSTRIES INC 255261 -0, . 121 -0.270 1983 DUCOMMUN INC 261117 -0.601 -9.719 1983 FABERGE INC 302808 -0.235 -3.721 1983 GALVESTON HOUSTON 361121 1.111 -0.912 1983 GLEASON CORP 377339 -0. ,885 -3.612 1983 HELM RESOURCES INC 123125 -2, .036 -2.178 1983 HI-SHEAR INDUSTRIES 128399 -0 .266 -2.388 1983 LORI CORP 511118 1. .597 -1.963 1983 MOOG INC -CL A 615391 -0.271 -6.732 1983 NORTHWEST INDUSTRIES 667528 -0. . 156 -21.700 1983 ORIENT EXPRESS HOTELS 685905 -10 .715 -25.119 1983 PLANT INDUSTRIES INC 727316 -10 .801 -9.205 1983 RYMER CO 783771 -2 .831 -6.711 1983 SANTA FE SOUTHERN PACIFIC CP 802183 0, .353 106.500 1983 SFM CORP 781113 -0, .268 -0.255 1983 TANNETICS INC 875881 -0 .217 -2.668 1983 UNI DYNAMICS CORP 901671 -0 .106 -2.568 1983 WESTERN DIGITAL CORP 958102 -0 .118 -0.723 1983 WILLCOX ft GIBBS INC 969207 -0 .181 -1.218 1983 WOLVERINE WORLD WIDE 978097 -0, .170 -5.139 198U ACTION INDUSTRIES INC 005011 -0.259 -6.000 1981 ACTON CORP 005055 -5 .389 -7.019 1981 ADAMS RESOURCES ft ENERGY INC 006351 0 . I l l 1.271 1981 ALLEGHANY CORP 017175 -18 .781 217.331 1981 AMCA INTL LTD 001610 -0 .168 -6.722 1981 BERGEN BRUNSWIG CORP -CL A 083739 -0 . 101 -5.178 1981 BLESSINGS CORP 093532 0 .196 1.216 1981 CARDIFF EQUITIES CORP 111166 -0 .218 -0.638 1981 CCX INC 125005 -0 .151 -0.605 1981 CHRISTIANA COMPANIES 170819 -0 .206 0.130 1981 CORROON ft BLACK CORP 220291 -0 .638 -21.330 1981 OELTONA CORP 217883 1, .039 0.559 1981 DIANA CORP 252790 .900 13.918 1981 DIVERSIFIED INDUSTRIES INC 255261 -0 .521 -1.977 1981 FMC CORP 302191 -0, .127 -187.895 1981 GOLDEN WEST HOMES 381328 0.617 -2.519 1981 HALIFAX ENGINEERING INC 105805 -7. .312 -0.212 1981 INTL MINERALS ft CHEMICAL 159881 -0, .101 -30.300 1981 ISS INTL SERVICE SYSTEM 150310 21 .111 1.900 1981 KEARNEY NATIONAL INC 186872 -0 .178 -1.789 1981 KEYSTONE CONS INDUSTRIES INC 193122 -3. .052 0.879 1981 LAMSON ft SESSIONS CO 513696 -0. . 171 -1.312 1981 LORI CORP 511118 0. .707 -0.100 1981 LVI GROUP INC 502139 0 .272 -0.098 1981 MARCADE GROUP INC 566139 0 .255 -3.006 1981 NEW MEXICO ft ARIZONA LAND 617072 0 .262 1.037 1981 NOLEX CORP 655312 -0 .117 -0.500 1981 PEABOOY INTERNATIONAL CORP 701562 -1, .219 -9.526 1981 PIONEER SYSTEMS INC 7238B6 -0 .920 -3.738 7 . 8 8 2 3 2 . 0 8 7 CONVRT,PAPRBRD PD.EX J / 8 2 TO 2 1 8 3 9.709 52.531 ELECTRIC LIGHT1NG-WI • 9 / 8 1 TO 8 / 8 2 13.129 271.993 CABLE TELEVISION OPE 6 / 82 TO 5 / 8 3 9.697 73.689 OPTICAL INSTRUMENTS 5 / 82 TO 1 / 8 3 -5.021 13.785 COMPUTER EQUIPMENT. 7 / 81 TO 6 / 82 1.791 29.888 SPORTING ft ATHLETIC YEAR 1982 8.863 116.110 AIR COND.HEATING.KFF YEAR 1982 21.789 186.205 RUBBER ft MISC PL Ail1 • YEAR l'»83 2.168 21.536 ELECTRONIC PARTS ft E 1 / 03 TO 3 / 8 1 3.239 31.651 TOTALIZING FLUID MET YEAR 1983 5.061 38.392 MISC PLASTICS PRODUC YEAR 1983 1 . 8 9 8 55.966 GOLO ANO SILVER ORES YEAR 1983 -0.001 19.296 ELECTRIC HOUSEWARES 7 / 82 TO 6 / 8 3 6.708 17.722 MISC FOOD PREPS, KIN 8 / 82 TO 7 / 83 13.680 201.317 TELEVISION BROADCAST 9 / 82 TO 8 / 83 -1.277 52.333 SUBOIVID,DEVELOP,EX 7 / 82 TO 6 / 83 -1.131 103.818 TRUCKING, EXCEPT LOC YEAR 1983 2.177 53.939 SECURITY ft COMMODITY 11 / 82 TO 10 / BJ 16.093 231.672 AIRCRAFT PARTS, AUX YEAR 1983 15.836 188.811 PERFUMES COSMETICS T • YEAR 1983 -0.633 177.923 CONSTR,MINING,MATL H YEAR 1983 1.116 173.166 MACHINE TOOLS, METAL YEAR 1983 1.217 27.539 CHEMICALS ft ALLIED YEAR 1983 8.978 52.869 BOL T,NUT,SCREW,R1 VET COSTUME JEWLRY.BUTTO 6 / 8 3 TO 5 / 8 1 -0.127 2.133 12 / 82 TO 1 2 / 8 3 21.871 201.155 AIRCRAFT PARTS, AUX 18 / 82 TO 9 / 8 3 138.700 1811.099 KNITTING MILLS • YEAR 1983 2.375 152.171 HOTELS,MOTELS,TOUR 1S YEAR 1983 0.852 32.601 MISC PLASTIC PRODUCT • YEAR 1983 2.369 56.073 SAUSAGE,OTH PREPARED RA1LROADS,L1NE-HAUL 13 / 82 TO 1 0 / 8 3 1151.625 11387.700 YEAR 1983 0.951 12.168 MOTORS AND GENERATOR YEAR 1983 10.822 15.515 REFRIG ft SERVICE IND • 8 / 82 TO 7 / 8 3 21.272 229.110 REFRIG ft SERVICE IND • YEAR 1983 6.121 51.073 COMPUTER EQUIPMENT, 7 / 82 TO 6 / 8 3 6.777 81.618 ELEC APPARATUS ft EQU YEAR 1983 30.192 201.519 FOOTWEAR, EXCEPT RUB YEAR 1983 23.173 99.579 FURNITURE ft HOME FUR 7 / 83 TO 6 / 8 1 1.308 53.812 CABLE TELEVISION OPE YEAR 1981 8.869 29.163 PETROLEUM,EX BULK ST YEAR 1981 -11.572 835.111 TITLE INSURANCE YEAR 1981 39.896 1316.717 PREFAB METAL BLOGS ft YEAR 1981 51.380 379.291 DRUGS AND PROPRIETAR 9 / 83 TO 8 / 8 1 6.367 38.803 MISC PLASTICS PRODUC YEAR 1981 2.928 19.750 LUMBER ft WOOD PRODUC • YEAR 1981 3.918 39.585 MISC FABRICATED META 7 / 83 TO 6 / 8 1 -2.089 11.185 SUBOIVID,OEVELOP,EX 7 / 83 TO 6 / 81 38.110 392.132 INS AGENTS,BROKERS ft YEAR 1981 0.538 252.112 SUBOIVID,OEVELOP,EX YEAR 1981 0.000 61.253 INVESTORS, NEC 1 / 81 TO 3 / 8 5 3.798 68.226 SECURITY ft COMMODITY 11 / 83 TO 10 / 81 110.126 2399.986 CHEMICALS ft ALLIED YEAR 1981 -3.939 29.228 WOOD BUILDINGS-MOBIL • 6 / 8 1 TO 5 / 8 5 0.029 12.710 DETECTIVE ft PROTECT 1 1 / 81 TO 3 / 85 291.200 1965.600 AGRICULTURE CHEMICAL 7 / 83 TO 6 / 81 0.090 31.123 SVCS TO DWELLINGS, 0 YEAR 1 9 8 1 26.880 131.919 ELEC,ELECTR MACH.EQ, YEAR 1981 -0.288 119.233 BLAST FURNACESftROLLI 7 / 83 TO 6 / 8 1 7.658 81.577 ELECTRIC LIGHTING,Wl YEAR 1 9 8 1 -0.566 1.891 COSTUME JEWLRY.BUTTO YEAR 1981 -0.360 12.739 GEN BLOG CONTRACTORS YEAR 1981 -11.806 15.867 APPAREL ft OTHER FINI 2 / 8 1 TO 1 / 8 5 3.951 36.191 LESSORS OF REAL PROP YEAR 1 9 8 1 1.291 28.555 WHSL-NONDURABLE GOOO • YEAR 1981 7.627 266.168 SERV-ENG1NEER1NG ft A • 10 / 8 3 TO 9 / 8 1 1.061 33.621 MISC FABRICATED TEXT 12 / 83 TO 11 / 81 1984 PLYMOUTH RUBBER -CL A 738826 -1.057 -2.262 1984 PUBLICKER INDUSTRIES INC 711635 -11. I l l -11.317 198U SCIENCE MANAGEMENT CORP 808638 -1.287 -2.369 1984 TELESPHERE INTERNATIONAL INC 879908 -0.177 -1.901 1981 WATSCO INC -CL 912622 1.186 2.960 1985 AIRGAS INC 009363 -0.111 -0.865 1985 AMERICAN MEDICAL BLDGS INC 027120 8.981 -2.335 1985 ARTRA GROUP INC 013117 -0.672 -3.885 1985 BASIX CORP 070121 -0.155 -7.571 1985 BEARD CO 073817 -2.259 -10.318 1985 BMC INDUSTRIES INC-MINN 055607 -5.008 -72.169 1985 BRUSH WELLMAN INC 117121 -0.155 -10.025 1985 CHOCK FULL 0 NUTS CORP 170268 -0.127 -0.202 1985 COPPERWELD CORP 217687 -1.215 -11.315 1985 CRAIG CORP 221171 0.575 0.122 1985 CRYSTAL OIL CO 229385 -0.298 -11.158 1985 DALLAS CORP 231569 -0.311 -7.976 1985 DAMON CORP 235717 -1.733 0.130 1985 DUCOMMUN INC 261117 -2.393 -16.122 1985 E-SYSTEMS INC 269157 -0.135 -11.191 1985 EAC INDUSTRIES 268226 0.169 1.527 1985 ESPRIT SYSTEMS INC 296656 -1.030 -1.316 1985 FOOTHILL GROUP INC -CL A 315109 -0.237 -8.975 1985 G R 1 CORP 362232 -2.168 -6.709 1985 GEMCO NATIONAL INC 368636 -5.889 -5.553 1985 GOLDFIELD CORP 381370 1.896 -2.113 1985 HEALTH-CHEM CORP 122174 1.117 -2.280 1985 INTL RECTIFIER CORP 460254 -0.666 -7.116 1985 INTL THOROUGHBRED BREEDERS 460491 -3.779 12.652 1985 KEARNEY NATIONAL INC 486872 -1.622 -29.868 1985 KEY CO 493080 0.500 0.601 1985 KEYSTONE CAMERA PRODUCTS 193397 -0.159 -0.500 1985 KINARK CORP 494471 -0.581 -1.190 1985 LAMSON ft SESSIONS CO 513696 -0.151 -1.190 1985 LVI GROUP INC 502139 -2.110 -1.735 1985 MACNEAL-SCHWENDLER CORP 551806 -0.278 -2.336 1985 MARCADE GROUP INC 566139 0.919 -3.812 1985 MATEC CORP 576667 -8.363 -0.981 1985 MEDTRONIC INC 585055 -0 . I l l -11.025 1985 ORIENT EXPRESS HOTELS 685905 -57.760 -16.000 1985 PENNWALT CORP 709317 -0.273 -30.937 1985 PERINI CORP 713839 -3.736 -22.107 1985 PIER 1 IMPORTS INC-DEL 720279 0.211 1.867 1985 PIONEER SYSTEMS INC 723886 2.013 -5.910 1985 PLYMOUTH RUBBER -CL A 730026 -0.101 -0.155 1985 PORTEC INC 736202 -0.165 -1.788 1985 SAUL (B.F.) REAL ESTATE INV 801396 -0.155 -2.391 1985 SCIENCE MANAGEMENT CORP 808638 -0.339 0.378 1985 SLATTERY GROUP INC 831175 -0.153 8.109 1985 SMITH (A.O.) CORP -CL A 831865 0.180 13.100 1985 STEEGO CORP 858050 -0.110 -1.318 1985 TACOMA BOATBUILDING INC 873152 1.196 -35.789 1985 THORTEC INTERNATIONAL INC 885155 -1.113 -11.367 1985 TIGER INTERNATIONAL 886735 -0 .193 -15.500 1985 TITAN CORP 888266 -1.190 -9.726 1985 UNC INC 903070 0.187 2.837 1985 UNIVAR CORP 913353 0.395 6.391 1985 VALLEY INDUSTRIES 919720 0.135 0.970 1985 VERIT INDUSTRIES 923131 -0.162 -0.175 1985 WEDCO TECHNOLOGY INC 917900 -3.736 -5.671 1985 WYLE LABORATORIES 983051 -0.610 -1.710 1986 ACME-CLEVELAND CORP 001626 -0.711 -10.705 1986 ALBERTO-CULVER CO 013068 -0.137 -1.629 1986 AMERICAN MEDICAL BLDGS INC 027120 -1.213 -1.205 1986 ANDAL CORP 033352 5.228 13.151 1986 ANTHONY INDUSTRIES INC 036798 -0.225 -5.160 2. 111 29.676 0.318 31.893 1. 810 31.951 3. 982 61.800 1. 992 19.973 7. 763 13.733 -0. 260 8.160 5. 782 71.258 18.923 212.152 1. 580 56.551 11. 111 133.236 61. 171 299.019 1. 592 50.979 3. 372 311.916 0. 212 16.631 17. 111 311.691 23. 359 255.160 -0. ,075 122.705 6. 863 267.608 107. 309 178.802 3. 253 53.280 1. ,307 12.018 37. 870 390.192 2. ,718 33.677 0.913 15.957 -0. 199 8.992 -2. .011 61.889 11, ,171 161.115 -3. .318 271.816 18. .111 95.807 1. ,203 18.899 3. .151 36.818 2. ,037 10.213 7. .880 72.713 0. ,720 112.191 8. .389 21.196 -1 . .017 26.983 2. .702 21.135 99. .662 527.112 0. .277 115.055 113, .299 958.572 5.997 322.599 22. .708 106.581 -2, ,893 27.573 1, .538 21.656 10. .820 81.673 15. .118 396.050 -1 . ,116 30.091 -0 . .711 81.313 71.612 186.319 9, ,626 131.237 -8, .530 89.577 9, .911 90.890 80. .309 956.118 8. . 172 78.823 15. .207 390.305 16. .190 186.976 2, .229 60.029 1.028 7.567 1. .518 20.911 7, ,725 137.810 11. .153 192.016 33, .725 227.712 0, .286 8.630 2, .573 61.382 22. .919 123.775 FABRICATED RUBBER PO TEXTILE MILL PRODUCT MGMT, CONSULTING ft TELEPHONE COMM (WIRE AUTOMATIC REGULATNG ORTHO.PROSTH.SURG AP GEN BLDG CONTRACTORS COSTUME JEWLRY.BUTTO COMMERCIAL PRINTING CRUDE PETROLEUM It NA OPHTHALMIC GOODS PRIM SMELT,REFIN NON MISC FOOD PREPS, KIN STEEL PIPE ANO TUBES GROCERY STORES CRUDE PETROLEUM ft NA METAL DOORS,FRAMES,M MEDICAL LABORATORIES AIRCRAFT PARTS, AUX SEARCH, NAVI GATE ,GU ID CUTLERY,HAND TOOLS,G COMPUTER TERMINALS BUSINESS CREDIT INST MAIL ORDER HOUSES APPAREL,PIECE CDS,NO WATER,SEWER,PIPE LIN BRD WOVN FABRC MAN-N SEMICONDUCTOR,RELATE RACING,INCL TRACK OP ELEC.ELECTR MACH.EQ, SUBDIVIO.OEVELOP.EX PHOTOGRAPHIC EQUIP a COAT ING,ENGRAVING,AL ELECTRIC LIGHTING.WI GEN BLDG CONTRACTORS CMP PROGRAM ft SOFTWA APPAREL ft OTHER FINI ELECTRONIC COMPONENT X-RAY,ELECTROMEDICAL HOTELS.MOTELS,TOUR IS CHEMICALS ft ALLIED GEN BLDG CONTRACTORS FURNITURE,HOME FURNI MISC FABRICATED TEXT FABRICATED RUBBER PD CONSTRUCTION MACHINE REAL ESTATE INVESTME MGMT, CONSULTING ft CONSTRUCT ION-NOT BLD MOTOR VEHICLE PART,A AUTO PARTS ft SUPPLIE SHIP ft BOAT BLDG ft R ENGR, ARCHITECT, SUR AIR TRANSPOR TAT ION,C CMP PROGRAM ft SOFTWA AIRCRAFT ENGINE,ENGI CHEMICALS ft ALLIED STEEL PIPE AND TUBES ELEC APPLIANCE,TV,RA MISC PLASTICS PROOUC ELECTRONIC PARTS ft E MACHINE TOOLS, METAL PERFUME,COSMETIC,TOI GEN BLDG CONTRACTORS METALS SERVICE CENTE SPORTING ft ATHLETIC 12 / 83 TO 11 / 6 4 YEAR 1981 YEAR 1981 2 / 81 TO 1 / 85 2 / 81 TO 1 / 85 4 / 85 TO 3 / 86 YEAR 1985 YEAR 1985 YEAR 1985 YEAR 1985 YEAR 1985 YEAR 1985 8 / 81 TO 7 / 85 YEAR 1985 7 / 61 TO 6 / 85 YEAR 1985 YEAR 1985 9 / 81 TO 8 / 85 YEAR 1985 YEAR 1985 2 / 85 TO 1 / 86 6 / 85 TO 5 / 66 YEAR 1985 12 / 81 TO 11 / 65 YEAR 1985 YEAR 1985 YEAR 1985 7 / 61 TO 6 / 0 3 7 / 84 TO 6 / 85 YEAR 1965 11 / 84 TO 10 / 85 YEAR 1985 YEAR 1985 YEAR 1985 YEAR 1985 2 / 85 TO 1 / 86 2 / 85 TO 1 / 86 YEAR 1985 5 / 85 TO 4 / 86 YEAR 1985 YEAR 1985 YEAR 1985 9 / 85 TO 2 / 86 12 / 84 TO 11 / 85 12 / 84 TO 11 / 85 YEAR 1985 18 / 84 TO 9 / 85 YEAR 1985 YEAR 1985 YEAR 1985 5 / 85 TO 4 / 86 YEAR 1985 11 / 84 TO 10 / 85 YEAR 1985 YEAR 1985 YEAR 1985 3 / 85 TO 2 / 86 12 / 84 TO 11 / 65 7 / 84 TO 6 / 85 «• / 85 TO 3 / 66 2 / 65 TO 1 / 66 18 / 85 TO 9 / 66 10 / 85 TO 9 / 86 YEAR 1986 13 / 85 TO 9 / 86 YEAR 1986 1986 AUDIOTRONICS CORP 858753 2. .366 -1 . ,105 1986 BANK BUILDING ftEQUIP CORP AM 860815 -0. ,422 -1 . ,222 1986 BLESSINGS CORP 093532 0. .332 3. .631 1986 CCX INC 125005 0. .114 0. .100 1986 CHICAGO MILWAUKEE CORP 167763 2. .338 17.598 1986 CHOCK FULL 0 NUTS CORP 170268 -0. .366 -2.965 1986 CONCORD FABRICS INC 206219 -0. .290 -1. .747 1986 CORE INDUSTRIES INC 218675 -0. . 144 -2.606 1986 CRAIG CORP 2214171* -0. .405 0. ,278 1986 CRYSTAL OIL CO 229385 -0. .501 -10. .383 1986 CTS CORP 126501 0. .379 7. . 181 1986 DIVERSIFIED INDUSTRIES INC 255264 -0. .904 -1. .221 1986 ERC INTERNATIONAL INC 268830 -0. .434 -3. .809 1986 ESPRIT SYSTEMS INC 296656 0. .653 -0. .490 1986 G R 1 CORP 362232 -0. . 144 -O. .273 1986 GEMCO NATIONAL INC 368636 -3. . 104 -3. .430 1986 GEOTHERMAL RES INTL INC 373676 -0, .653 2, .296 1986 GOLDFIELD CORP 381370 0 .232 -0, .093 1986 GRAHAM CORP 384556 -0, .787 -2. .250 1986 GT1 CORP 362360 -2 .101 -4.054 1986 GULF RESOURCES ft CHEMICAL 402496 -0. .801 -6. .050 1986 HALL (FRANK B.) ft CO 1*05891 -0. .599 -26. .746 1986 HEALTH-CHEM CORP U2217U -0. .437 -0. .101 1986 HIGH VOLTAGE ENGINEERING •429812 -0 . 122 -1, .456 1986 IDEAL BASIC INDUSTRIES INC 451542 -0 .359 -9, .217 1986 INSPIRATION RESOURCE U57729 0 .592 -3, .351 1986 INTL RECTIFIER CORP 1*60251 0, .204 1, .217 1986 KETCHUM ft CO 192620 -0.851 1. .019 1986 KINARK CORP 494474 -0, .477 -1. .868 1986 KLEER-VU INDUSTRIES INC 498494 -7.817 -2, .345 1986 LA BARGE INC 502470 -26 .245 -20.970 1986 LANSON ft SESSIONS CO 513696 -2 .288 -9. .494 1986 LEAR PETROLEUM PARTNERS -LP 521892 235 .895 -80. .676 1986 MATEC CORP 576667 -0 .154 -0, .306 1986 MAXUS ENERGY CORP 577730 0.242 80. .000 1986 NATIONAL MINE SERVICE CO 636905 -1 .676 -3. .524 1986 PER INI CORP 713839 -0 .123 -2, .415 1986 PIONEER SYSTEMS INC 723886 2 .281 -3, .431 1986 POPE, EVANS ft ROBBINS INC 732852 0 .806 -1, .796 1986 RE CAPITAL CORP 754904 0, .242 -0. .809 1986 RIVER OAKS INDUSTRIES 768290 -46. .575 -21. .052 1986 ROBERTSON (H.H.) CO 770553 -0. .111 2. .233 1986 SANTA ANITA REALTY ENTER 801209 51789. .990 5. .179 1986 SERVICE RESOURCES CORP 817606 -0. . 168 -1. .972 1986 SI ERR AC IN CORP 826520 -0, .146 -0. .901 1986 SLATTERY GROUP INC 831175 -0, .216 2. .756 1986 STRUTHERS WELLS CORP 863659 18.754 -14. .759 1986 SYNALLOY CORP 871565 -3. .067 1.503 1986 TECHNOOYNE INC 878612 2. .962 -4. .737 1986 TITAN CORP 888266 -0. .306 -4. .888 1986 TR1 NOVA CORP 896678 0 .483 86. .330 1986 TYCO LABORATORIES INC 902120 -0. .150 -17. ,295 1986 UNIVERSITY PATENTS INC 914802 0. .207 -0. .805 1986 VALLEY INDUSTRIES 919720 0. .213 -1, .734 1986 WEATHERFORD INTERNATIONAL 947076 -4.845 -10. .800 1986 WEDCO TECHNOLOGY INC 947900 0. , 193 0. .899 1986 WMS INDUSTRIES INC 929297 -0, , 149 -0. .748 1987 ACTION INDUSTRIES INC 005041 -1, .219 -9. .905 1987 AFFILIATED PUBLICATIONS 008261 0. .313 39. .978 1987 ALBA-WALDENS1 AN INC 012041 -0. .701 -1. .584 1987 ALLEN GROUP 017634 6. .980 2. .429 1987 APACHE CORP 037411 -0. . 125 9. .342 1987 ARMATRON INTERNATIONAL INC 042167 -0. .899 1. .500 1987 ARROW ELECTRONICS INC 042735 -1. .309 12. .932 1987 ARTRA GROUP INC 043147 -0 .740 -6, .390 1987 ASTREX INC 046357 -0, .371 -0. . 166 -0.467 4.796 RADIO ft TV RECEIVING 7 / 6 5 TO 6 / 8 6 2.897 27.932 GEN BLDG CONTRACTORS 11 / 85 TO 10 / 86 10.927 60.517 MISC PLASTICS PRODUC YEAR 1986 0.875 41.037 MISC FABRICATED META 7 / 85 TO 6 / 86 7.528 362.062 REAL ESTATE DEALERS YEAR 1986 8.093 59.744 MISC FOOD PREPS, KIN 8 / 85 TO 7 / 86 6.022 49.541 TEXTILE MILL PRODUCT 9 / R5 TO 8 / 86 18.155 121.636 ELEC MEAS ft TEST INS 9 / P • TO 8 / 86 -0.687 17.082 GROCERY STORES 7 / 85 TO 6 / 86 20.705 101.927 CRUDE PETROLEUM ft NA YEAR 1986 18.960 207.899 ELECTRONIC COMP, ACC YEAR 1986 1.351 83.179 SECURITY fe COMMODITY 11 / 85 TO 10 / 6 6 8.771 53.095 ENGR, ARCHITECT, SUR YEAR 1986 -0.750 10.235 COMPUTER TERMINALS 6 / 86 TO 5 / 87 1.899 30.651 MAIL ORDER HOUSES 12 / 85 TO 11 / 86 1.105 14.117 APPAREL,PIECE COS,NO YEAR 1986 -3.518 253.645 STEAM SUPPLY YEAR 1986 -0.401 9.072 WATER,SEWER,PIPE LIN FABRICATED PLATE WOR YEAR 1986 2.858 40.952 YEAR 1986 1.930 10.646 ELECTRONIC COMPONENT YEAR 1986 7.557 354.508 BITUMINOUS COAL AND YEAR 1986 44.617 1255.685 INS AGENTS,BROKERS ft YEAR 1986 0.231 67.125 BRO WOVN FABRC MAN-M YEAR 1986 11.915 104.712 MEASURING, CONTROLLI YEAR 1986 25.694 330.194 CEMENT, HYDRAULIC PRIM SMELT,REFIN NON YEAR 1986 -5.660 780.260 YEAR 1986 5.969 189.423 SEM1 CONDUCTOR.RELATE 7 / 85 TO 6 / 06 -1.198 56.505 DRUGS ANO PROPRIETAR 5 / 86 TO 4 / 87 3.916 38.707 COAT INC.ENGRAVING,AL YEAR 1986 0.300 21.293 BLANKBOOKS,B1NDRS,B0 YEAR 1986 0.799 53.104 ALARM ft SIGNALING PR 7 / 65 TO 6 / 86 4.149 182.943 ELECTRIC LIGHTING.WI YEAR 1986 -0.342 57.888 INVESTORS, NEC YEAR 1986 1.987 21.933 ELECTRONIC COMPONENT YEAR 1986 330.200 3517.400 CRUDE PETROLEUM ft NA YEAR 1986 2.103 44.349 ELEC APPARATUS ft EQU 4 / 86 TO 3 / 87 19.687 325.310 GEN BLDG CONTRACTORS YEAR 1986 -1.504 21.225 MISC FABRICATED TEXT 12 / 85 TO 11 / 86 -2.229 70.090 WOMENS,MISSES,JRS OU 7 / 85 TO 6 / 86 -3.346 94.428 F1 NANCE-SERVICES YEAR 1986 0.452 58.187 LOAN BROKERS 7 / 85 TO 6 / 86 -20.158 344.363 SHEET METAL WORK YEAR 1986 0.000 164.313 RACING,INCL TRACK OP PERSONNEL SUPPLY SER YEAR 1986 11.726 119.116 YEAR 1966 6.191 36.807 AIRCRAFT PARTS, AUX YEAR 1986 -12.748 90.009 CONSTRUCTION-NOT BLD YEAR 1986 -0.787 28.147 FABRICATED PLATE WOR 12 / 85 TO 11 / 86 -0.490 26.053 MISC FABRICATED META YEAR 1986 -1.599 21.439 ORUGS AND PROPRIETAR 8 / 85 TO 7 / 6 6 15.961 83.010 CMP PROGRAM ft SOFTWA YEAR 1986 178.563 1167.222 MISC MACHINERY,EX EL GENERAL INDUSTRIAL YEAR 1986 115.682 594.195 6 / 86 TO 5 / 87 -3.882 12.873 OPHTHALMIC GOODS 8 / 85 TO 7 / 86 -8.133 39.551 STEEL PIPE AND TUBES 12 / 85 TO 11 / 86 2.229 108.414 OIL FIELD MACHINERY YEAR 1986 4.646 25.001 MISC PLASTICS PRODUC 1 / 86 TO 3 / 87 5.008 97.562 MISC MANUFACTURNG IN 18 / 85 TO 9 / 86 8.126 105.500 FURNITURE ft HOME FUR 7 / 86 TO 6 / 87 127.568 532.341 NEWSPAPER:PUBG, PUBG KNITTING MILLS YEAR 1987 2.261 34.721 YEAR 1987 0.348 305.927 MOTOR VEHICLE PART,A YEAR 1987 -74.725 504.333 CRUDE PETROLEUM ft NA YEAR 1987 -1.669 12.764 MISC ELEC MACHY.EQ.S 10 / 86 TO 9 / 87 -9.879 345.591 ELECTRONIC PARTS ft E YEAR 1987 8.633 228.737 COSTUME JEWLRY.BUTTO YEAR 1987 0.447 18.246 ELECTRONIC PARTS ft E 1 / 87 TO 3 / 88 bo 1987 AVALON CORP 053435 -0.330 -3. 303 1987 BOWMAR INSTRUMENT CORP 183025 -1.316 -1 . 629 1987 CACLE'S INC -CL A 127703 1.168 -1 . ,595 1987 CAMPBELL RESOURCES INC NEW 134422 -0.233 -1 . ,276 1987 CCX INC 125005 -6.961 1. 581 1987 COGNITRONICS CORP 192132 -0.118 -0. 275 1987 COMPUOYHE CORP 204795 1.108 4. .401 1987 DIVERSIFIED INDUSTRIES INC 255261 2.177 0. ,995 1987 DYNCORP INC 268162 0.327 6. ,305 1987 EMERSON RAO 10 291087 12.589 -4. ,729 1987 ENRON CORP 293561 -0.117 -82. .980 1987 ENTERTAINMENT MARKETING INC 293911 -0.585 -6. .859 1987 ESSEX CHEMICAL CORP 296695 -1.293 -13. .330 1987 EVEREST ft JENNINGS -CL A 299767 -0.157 -2.000 1987 FIRST CITY INDUSTRIES INC 319633 1.257 99. .974 1987 FLUOR CORP 313861 1.124 94. 710 1987 GENERAL CINEMA CORP 369352 -0.129 -17. . 100 1987 GENESCO INC 371532 0.246 4. ,124 1987 GEOTHERMAL RES INTL INC 373676 -0.160 1. .290 1987 GRAHAM CORP 381556 -0.248 -0. .450 1987 GRUMMAN CORP 100181 0.212 -26.400 1987 HALL (FRANK B.) A CO 105891 -3.858 -43 .095 1987 HEALTH-CHEM CORP 122171 -0.651 -0. .462 1987 HEALTH-MOR INC 122191 -0.160 -0. .462 1987 HINDERLITER INOS INC 133078 -0.612 -1, .588 1987 HOFMANN INDUSTRIES INC 131560 -0.538 -2, .244 1987 IDEAL BASIC INDUSTRIES INC 151512 0.114 1, .963 1987 INSPIRATION RESOURCE 157729 0.114 4, .250 1987 INTL TECHNOLOGY CORP 160165 -7.937 -109 .748 1987 IROQUOIS BRANDS LTD 163319 0.314 0. .314 1987 KEY CO 193080 -1.349 -1. .524 1987 KEYSTONE CAMERA PRODUCTS 193397 31.975 -17. .490 1987 KINARK CORP 191171 -1.192 -5 .348 1987 KLEER-VU INDUSTRIES INC 198191 3.322 -3 . 182 1987 LA BARGE INC 502470 0.406 1 .636 1987 LIFETIME CORP 531911 -0.124 -1 . 199 1987 LITTLEFIELD ADAMS It CO 537581 0.545 -0.640 1987 LUMEX INC 550245 -0.203 -1. .336 1987 MAXPHARMA INC 577726 - 980 -3.890 1987 MORRISON KNUDSEN CORP 618117 -11.907 -41 .800 1987 NATIONAL MINE SERVICE CO 636905 -0.192 -0 .642 1987 NELSON HOLDINGS INTL LTD 61037H -0.380 -12 .967 1987 NORTEK INC 656559 -0.150 -15, .200 1987 OAK INDUSTRIES INC 671100 3.444 1, .436 1987 PENRIL CORP 709352 -2.950 -9.653 1987 PIONEER SYSTEMS INC 723886 0.250 -0 .814 1987 POPE, EVANS It ROBBINS INC RANSBURG CORP 732852 0.471 -1, .868 1987 753228 -1.082 -21 . 109 1987 RE CAPITAL CORP 751901 -0.764 -2 .054 1987 RIVER OAKS INDUSTRIES 768290 19.285 2 .912 1987 SERVICE RESOURCES CORP 817606 -12.389 -25, .286 1987 SLATTERY GROUP INC 831175 0.216 0 .525 1987 SSMC INC 781687 -0.261 -12. .900 1987 STERLING ELECTRONICS 859281 0.161 0 .563 1987 STORAGE TECHNOLOGY CORP 862111 0.123 11, .207 1987 STRUTHERS WELLS CORP 863659 -1.306 -1, .511 1987 THORTEC INTERNATIONAL INC 885455 0.237 -2 .800 1987 TITAN CORP 888266 -0.280 -2 .615 1987 TOROTEL INC 891305 0.336 0 .238 1987 U HOME CORP 912061 -2.733 -29 .957 1987 UNION CORP 906072 -0.201 -2 .726 1987 UNITED MEDICAL CORP 910811 -0.142 -0 .795 1987 VALERO ENERGY CORP 919138 0.597 -14 .328 1987 VYQUEST INC 929222 28.908 -2 .833 1987 WE 1 MAN CO INC 948662 -0.130 -0 .202 1987 WHITTAKER CORP 966680 0.456 23 .926 1 0 . 0 0 5 134.710 CRUDE PETROLEUM It NA YEAR 1987 1.210 29.999 ELEC MEAS ft TEST INS 10 / 6 6 TO 9 / 8 7 -0.357 40.508 POULTRY DRESSING PLA 4 / 87 TO 3 / 8 8 5.173 118.879 GOLD AND SILVER ORES 7 / 86 TO 12 / 87 -0.227 31.915 MISC FABRICATED META 7 / 86 TO 6 / 87 1.862 11.307 OPTICAL CHARACTER,LA YEAR 1987 3.126 60.142 SEARCH,NAV1 GATE,GU10 18 / 8 6 TO 12 / 8 7 0.157 90.797 SECURITY ft COMMODITY 11 / 86 TO 10 / 6 7 19.295 239.652 MGMT, CONSUL 1ING ft YEAR 1987 -0.111 254.503 RADIO ft TV RECEIVING 4 / 87 TO 3 / 8 6 710.911 9528.809 NATURAL GAS TRANSMIS YEAR 1987 11.718 120.383 COMML MACHINES ft EQU 2 / 87 TO 1 / 8 8 10.307 223.531 INDL INORGANIC CHEMI YEAR 1987 12.719 188.935 ORTHO.PROSTH.SURG AP YEAR 1987 23.485 739.088 COSTUME JEWLRY.BUTTO YEAR 1987 66.515 2061.166 CONSTRUCTION-NOT BLD 11 / 8 6 TO 10 / 6 7 132.720 1647.418 BOTTLEO ft CANNED SOF 11 / 86 TO 10 / 6 7 16.751 258.493 SHOE STORES 2 / 87 TO 1 / 88 -8.053 387.441 STEAM SUPPLY YEAR 1987 1.8H 37.717 FABRICATED PLATE WON YEAR 1987 -109.071 2254.568 AIRCRAFT YEAR 1987 11.170 1325.080 INS AGENTS,BROKERS It YEAR 1987 0.710 62.144 BRD WOVN FABRC MAN-M YEAR 1987 2.898 35.917 HOUSEHOLD APPLIANCES YEAR 1987 2.474 29.109 PUMPS ANO PUMPING EQ 7 / 8 6 TO 6 / 8 7 4.173 29.760 STEEL PIPE AND TUBES 5 / 87 TO 4 / 8 8 13.665 322.270 CEMENT, HYDRAULIC YEAR 1987 37.208 894.699 PRIM SMELT,REFIN NON YEAR 1987 13.827 291.827 SANITARY SERVICES 4 / 87 TO 3 / 8 8 1.001 46.855 PHARMACEUTICAL PREPA YEAR 1987 1. 130 23.603 SUBDIVID,OEVELOP,EX 11 / 86 TO 10 / 8 7 -0.547 48.577 PHOTOGRAPHIC EQUIP It YEAR 1987 4.487 36.692 COAT 1 NG, ENGR AV 1 NG, AL YEAR 1987 -0.958 18.612 BLANKBOOKS,B1NDRS,80 YEAR 1987 4.025 39.472 ALARM ft SIGNALING PR 7 / 86 TO 6 / 8 7 9.697 233.820 HEALTH ft ALLIED SERV 4 / 86 TO 12 / 87 -1.174 5.033 APPAREL,PIECE CDS,NO YEAR 1987 6.578 57.931 SPORTING ft ATHLETIC YEAR 1987 0.000 10.508 INVESTORS, NEC YEAR 1987 3.511 898.458 GEN BLDG CONTRACTORS YEAR 1987 3.348 34.293 ELEC APPARATUS ft EQU 4 / 87 TO 3 / 8 8 34.142 192.702 MOTION PICTURE DISTR YEAR 1987 101.187 1127.834 SHEET METAL WORK YEAR 1987 0.417 181.323 AUTOMATIC REGULATNO YEAR 1987 3.272 33.525 COMPUTER EQUIPMENT, 8 / 86 TO 7 / 8 7 -3.261 17.406 MISC FABRICATED TEXT 12 / 6 6 TO 11 / 6 7 -3.963 60.870 WOMENS,MISSES,JRS OU 7 / 86 TO 6 / 6 7 19.515 188.833 GENERAL INDUSTRIAL 12 / 86 TO 11 / 87 2.687 133.402 FINANCE-SERVICES YEAR 1987 0.151 4.674 LOAN BROKERS 7 / 86 TO 6 / 87 2.041 27.755 PERSONNEL SUPPLY SER YEAR 1987 2.428 100.967 CONSTRUCTION-NOT BLO YEAR 1987 49.500 461.300 HOUSEHOLD APPLIANCES YEAR 1987 3.504 23.527 ELECTRONIC PARTS ft E 4 / 87 TO 3 / 8 8 90.831 786.078 COMPUTER DISK ft TAPE YEAR 1987 1.159 18.429 FABRICATED PLATE WOR 12 / 6 6 TO 11 / 8 7 -11.800 187.600 ENGR, ARCHITECT, SUR 11 / 86 TO 10 / 87 9.460 87.284 CMP PROGRAM ft SOFTWA YEAR 1987 0.709 5.722 ELECTR COIL.TRANSFRM 5 / 6 7 TO 4 / 8 6 10.962 722.667 SUBDIVID,DEVELOP,EX YEAR 1987 13.576 95.979 PREFAB METAL BLDGS ft 7 / 86 TO 6 / 8 7 5.605 40.147 MEDICAL LABORATORIES YEAR 1987 -23.995 964.698 NATURAL GAS TRANSMIS YEAR 1987 -0.098 55.754 MOTOR HOMES 12 / 86 TO 11 / 8 7 1.551 15.239 SPORTING ft RECREATN YEAR 1987 52.447 431.893 AIRCRAFT PARTS, AUX 11 / 86 TO 10 / 87 1987 WHS INDUSTRIES INC 929297 -8.386 -2.929 9.559 101.157 MISC MANUFACTURING IN 10 / 86 TO 9 / 6 7 1987 WORLDCORP INC 981901 -0.694 -13.726 19.788 113.767 AIR TRANSPORTATION^ YEAR 1987 The following Involved M u l t i p l e discontinuation announcements In the sane year: (419 firms) 1 9 6 7 FAIRCHILD CAMERA ftINSTRUMENT 303693 -0 .366 - 4 . 8 3 6 1 3 . 2 0 0 1 6 1 . 9 0 0 ELECTRONIC COMPONENT • YEAR ' 9 6 7 1968 FAIRCHILD CAMERA I^NSTRUMENT 303693 1.759 -0.832 -0.473 146.100 ELECTRONIC COMPONENT • YEAR 1 9 6 8 1970 AMETEK INC 031105 -0.230 -2.810 12.239 74.664 MOTORS AND GENERATOR YEAR 1970 1970 BUDD CO 118835 -5.834 -12.100 2.074 446.871 MOTOR VEHICLE PARTS- • YEAR 1 9 7 0 1970 CASTLETON INDS INC 148573 -0.283 -0.253 0.894 29.971 SERV-RACING INCL TRA • YEAR 1 9 7 0 1970 COWLES COMMUNICATIONS 223741 -7109.996 -0.711 0.000 75.189 RADIO-TV BROADCASTER • YEAR 1 9 7 0 1970 CURTIS NOLL CORP 231507 -0.277 -1.892 6.831 42.407 WHSL-AUTOS ft PARTS • YEAR 1970 1970 MARSHALL INDUSTRIES 572393 -1.400 -2.408 1.720 25.478 ELECTRONIC PARTS ft E 6 / 7 0 T O 5 / 7 1 1970 NATIONAL INDUSTRIES INC 636486 -0.119 -2.458 20.687 234.062 WHSL-NONDURABLE GOOD • YEAR 1 9 7 0 1970 OLIN CORP 680665 -0.112 -10.567 94.559 1114.739 CHEMICALS ft ALLIED YEAR 1970 1970 REEVES TELECOM CORP 758650 -0.548 0.308 -0.562 28.998 RADIO-TV BROADCASTER • YEAR 1970 1970 RESTAURANT ASSOC INDS -CL 761252 -0.679 -1.337 1.970 48.240 EATING PLACES YEAR 1 9 7 0 1971 COWLES COMMUNICATIONS 223741 -5329.996 -0.533 0.000 63.663 RADIO-TV BROADCASTER • YEAR 1 9 7 1 1971 FEDERAL-MOGUL CORP 313549 -0.297 -10.000 33.690 201.232 MOTOR VEHICLE PART,A YEAR 1 9 7 1 1971 GRANGER ASSOCIATES 387100 -0 .510 -0.098 0.192 4.394 RADIO-TV TRANSMTTNG e 9 / 7 0 T O 8 / 7 1 1971 K D 1 CORP 482452 -0 .232 -1.010 4.359 6 7 . 8 6 2 ELECTRONIC COMPONENT 1 / 7 0 T O 1 2 / 7 1 1971 KIMBERLY-CLARK CORP 494368 -0.385 -42.500 110.367 938.469 PAPER MILLS, EX BLDG FABRICATED METAL PRD YEAR 1 9 7 1 1971 PACIFIC HOLDING CORP 694402 -0.241 -0.907 3.770 45.168 • YEAR