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The regulation of trade-based manipulation Menun, Marie R. 1993-07-29

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THE REGULATION OF TRADE-BASED MANIPULATIONbyMARIE R. MENUNB.B.A., Simon Fraser University, 1988A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIES(Faculty of Commerce and Business Administration)THE UNIVERSITY OF BRITISH COLUMBIAWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJuly 1993© Marie R. Menun. 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of i-7,1,04,ce ^iCeettlzi,^miAce...0The University of British ColumbiaVancouver, CanadaDateDE-6 (2/88)AbstractWe examine a model in which security price manipulation can lead to theinefficient allocation of resources. The actions of a manipulator can createexcess noise in the market which may discourage some investors fromparticipating. We show how a regulator can use trading halts to mitigate thenegative impact of manipulation and induce investors back into the market.However, the benefits derived from using halts are somewhat offset byilliquidity costs imposed by the halts on some market participants. Thus, aregulator who must contend with a manipulator is faced with a trade-offbetween improving allocative efficiency and limiting costs associated withreduced liquidity. Our model demonstrates this trade-off and outlines possibleequilibria.iiTable of ContentsAbstract ^  iiTable of Contents ^  iiiList of Tables  vList of Figures ^  viAcknowledgements viiChapter 1Introduction ^  1I. Types of Manipulation ^  2II. Costs of Manipulation  4III. The Regulator  7IV. Models of Manipulation Profitability ^  10V.^Conclusion ^  18Chapter 2Model of Trade-Based Manipulation and Trading Halts ^  20I. The Model ^  20II. The Small Investors  22III. The Large Trader  22IV. The Regulator  25V. The Equilibrium Prices and the Final Payoffs ^ 25VI. The Strategies and the Objective Functions  29VII. Conclusion ^  32Chapter 3Demonstration and Discussion of Model ^  33I. An Example ^  33II. Discussion  50Chapter 4Sensitivity of the Assumptions ^  52I. The Regulator  52II. The Illiquidity Cost Imposed on the Large, Informed Trader ^ 53III. An Illiquidity Cost Imposed on the Small Investor ^ 54IV. Information Structure ^  55V. Risk Aversion of Small Investor ^  57VI. Correlation Between Large Trader Type and 7' ^ 57VII. Conclusion ^  58iiiChapter 5Policy Implications and Conclusion ^  59I. Policy Implications  59II. Future Research  60III.^Concluding Remarks  61References  63Appendix A ^  65Appendix B  67Appendix C ^  68Appendix D  69Appendix E ^  72Appendix F  74ivList of TablesTable 1 - The Final Payoffs from the Risky Project ^  29Table 2 - Final Payoffs to the Informed Trader and the Small Investor ^ 34Table 3 - Final Payoffs Given Presence of Uninformed Trader  37Table 4 - Final Payoffs Given the Regulator May Halt Trading ^ 44Table E.1 - The Small Investor's Final Payoffs Given an Illiquidity Cost ^ 73vFigure C.1 - Small Investor's Expected Utility vs. b(U) ^Figure D.1 - Small Investor's Expected Utility vs. r Figure D.2 - Large Traders' Expected Utilities vs. r ^Figure D.3 - Sum of Expected Utilities vs. 7r ^Figure E.1 - An Illiquidity Cost Imposed on the Small Investor ^List of FiguresFigure B.1 - Game Tree ^  676869707172viAcknowledgementsI acknowledge, with thanks, the assistance and encouragement of Ron Giammarino.Discussions with Jim Brander, Ruth Freedman, Burton Hollifield, Bryan Routledge andRaman Uppal were very helpful and are appreciated. Finally, I would like to acknowledgethe support of my parents.viiChapter 1IntroductionManipulation in the market for financial securities is often associated with increasednoise in security prices. Manipulative activity can distort the informativeness of a marketand lead to artificial prices. To the extent that this noise or misinformation may lead toinefficient allocation of resources, regulation that mitigates the adverse effects of amanipulator may increase economic efficiency. In this paper we will examine a model wherea regulator must contend with the possibility of a manipulator in the market. In most modelsof successful manipulation, the manipulator tries to deceive the market by disguising himselfas an informed trader. With the use of trading halts, a regulator can force the manipulatorto reveal himself before he is able to profit from his deception. Unfortunately, trading haltsare costly as they interrupt the flow of trades, reducing market liquidity. Some are forcedto hold a position for longer than they like, while others are unable to enter the market whenthey like. Thus, when determining policy for dealing with manipulation regulators mustrecognize the trade-offs that result from their actions.The remainder of this chapter proceeds as follows. In section I, we discuss thedifferent types of manipulation, while in section II, the costs of manipulation are examined.In section III, the role and objectives of the regulator are considered and the use of tradinghalts is analyzed. Finally, in section IV, current models of manipulation profitability aredescribed and the importance of asymmetric information is demonstrated. In chapter 2, wepresent our model of trade-based manipulation and trading halts. In chapter 3, a general1discussion of the model and the equilibria that can result is aided by a numerical example.Finally, in chapter 4, we discuss the model's sensitivity to our assumptions, and in chapter5, we conclude with policy implications and areas for further research.I. Types of ManipulationManipulation in a securities market is loosely defined by Fishel and Ross (1991) as"profitable trades made with 'bad' intent."' By tad intent', they mean that the trader feelshe can move the price of a security solely by his trading activity, either because he hasmonopoly power or because he is able to deceive others into believing he has valuableinformation. There are various forms of manipulation: corners and squeezes, fictitioustrades, fraudulent reporting, and trade-based manipulation. Although this paper focuses ontrade-based manipulation, it is important to distinguish this form from the others. Amanipulator corners the market by purchasing a substantial portion of an asset. Short sellers- those who sell the asset without first purchasing it - have little bargaining power when theyare subsequently forced to deal with the manipulator to close out their position. They aretherefore squeezed by the manipulator. Corners and squeezes normally occur where thereis a large amount of short selling and where the short sellers are faced with costly sanctionsif they default.' For this reason, corners and squeezes usually occur in futures markets.A famous example of a corner and squeeze involved Cargill, Inc. in May 1963. Cargillmanipulated the price of the May wheat futures contract by first purchasing about 85 % ofFishel and Ross (1991), pg. 510.2 See Friedman (1990).2the deliverable supply of wheat, and then buying a large quantity of futures contracts (i.e.buying wheat for future delivery) - totalling about 62% of the long open interest. Most ofthis was bought on the last day of the May contract. Thus, the short sellers in the futuresmarket, who sold contracts promising to deliver wheat, were faced with a squeeze on thecontract's expiry date. They could not buy futures contracts to offset their position, norcould they find deliverable wheat to meet their obligations without inevitably having to dealwith Cargill. The short sellers had to close out at $ 2.285 per bushel. After the settlementwas complete, cash wheat in the area of Chicago traded between $ 2.03 and $ 2.15. Thus,it was determined that Cargill had intended to squeeze the market, creating artificially highprices. 3 A corner and squeeze is an example of how monopoly power can be used tomanipulate a market.Manipulation can also occur through fictitious trades or by reporting falseinformation. An example of a fictitious trade is a 'wash sale' where the trader tradesbetween two accounts, creating the illusion of market activity. However, no actual changein ownership occurs. The intent is to deceive the market into believing that there is activityin a stock when there really is not, inducing others to trade on false market information.Manipulation is also said to occur when a trader takes a position in a security and then startsfalse rumours in order to move the security price in a favourable direction. These types ofmanipulation can be viewed as forms of fraud and treated as such.3 See Easterbrook (1986) and Edwards and Edwards (1984).3Trade-based manipulation, on the other hand, consists of legitimate trades whichresult in the movement of prices even though there is no new information to affect thesecurity's price. The manipulator is able to make profits either through his market poweror by convincing others in the market that he may be informed. For example, a trader maybuy a large portion of Company Z's shares. Others in the market may think that this traderknows something good about Company Z and they will then bid the share price up further.The trader then sells out his position before the others in the market realize that no goodnews is forthcoming. Thus, he is able to make a profit by misleading the other marketparticipants. As we will discuss later in section III, trade-based manipulation is difficult toverify and prosecute; thus, preventive measures such as random trading halts may be moreeffective then a threat of a lawsuit after the fact.II. Costs of ManipulationThe manipulation of security prices interferes with the normal functioning of themarket and can impose many different costs. Unfortunately, many of these costs are almostimpossible to measure. It is however useful to understand these costs in order to makejudgements concerning their magnitude or importance.Since a manipulator does not have any valuable information when he trades, he candrive the price away from its true value causing an artificial price to exist. One social costcreated by the existence of a manipulator stems from the artificial prices which manipulationproduces. Companies and investors that make investment and portfolio decisions based on4these artificial prices may allocate resources inefficiently. For example, suppose an increasein share price of a computer software company is taken as an indication of higher expectedreturns. This may cause greater investment in software than is economically warranted.Thus, manipulative activities can disrupt the allocative efficiency of a market. It is difficult,however, to measure the degree of inefficiency that artificial prices may cause. First, it isdifficult to measure the degree of artificiality because we can not know for certain the truevalue of a security at any one time. Second, it is argued by Edwards and Edwards (1984)that, given the market knows the probability and consequences of manipulation, companiesand investors who use prices in the futures market to predict future spot prices will be ableto adjust their estimates correctly and will not be led to make inefficient decisions. "[O]nlywhen there are unanticipated changes in permanent futures prices, or when the probabilityof manipulation's occurring is unknown, will the price discovery function of futures marketsbe adversely affected."' Finally, artificial price changes caused by manipulation are usuallyshort-lived. The manipulator does not stay in the market for very long as it can be costlyto maintain the large position needed to deceive the market. These considerations suggestthat artificial prices do not have a large effect on total welfare. However, in our model wewill show that in certain instances manipulative activity can lead to sub-optimal decisions andinefficiencies.Manipulation also increases the scepticism of the public as to the fairness of themarket, decreasing the incentive to participate. Some investors will be forced to reduce their4 Edwards and Edwards (1984), pg. 348.5trading or will stop trading altogether. This reduces the liquidity of the market for thosewho continue to trade, increasing the cost of investing. Furthermore, manipulation mightincrease the variance of security prices as manipulators add an extra source of noise. Thiswill make forecasts by investors more uncertain. An increase in variance also may make itriskier to invest and trade; thus, market participants will demand higher returns tocompensate them for the added risk if they are risk averse. This will then increase the costsof capital faced by firms. Our model will capture this increase in volatility and its impacton a risk averse investor's decision to invest.Finally, the existence of manipulation in the futures market can decrease thecorrelation between the futures price and the spot price, making hedging less effective. 5Futures prices must be adjusted for the extra risk attributable to manipulation. This weakensthe relation between the spot price and the futures price. 6 In other words, manipulation canadversely affect the risk-shifting role of the futures markets.All of these repercussions of manipulation make financial markets less useful tolegitimate traders who will then have less incentive to enter. The thinner and less liquidmarkets will affect the investors' required rate of return, and the firms' costs of capital willbe higher.5 In Donaldson (1993), it is shown that if the increased variance of the futures price is matched by a change inthe distribution of cash prices then the correlation between futures and spot prices will, in absolute terms, increase;however, the hedge ratio increases via a reduction in the cash position and therefore less is produced.6 See Easterbrook (1986).6III. The RegulatorThe role of the regulator in a securities market, as in other markets, is presumablyto act in the public interest. Policies should encourage the efficient allocation of resources.Furthermore, a fair marketplace is seen as necessary in promoting allocative efficiency, onthe grounds that a fair 'playing field' promotes confidence and encourages participation.In Canada, the securities industry is regulated at the provincial level. Although eachjurisdiction has its own specific concerns, there are three goals which appear prevalentamong all: "ensuring an efficient and competitive financial system; protecting depositors;and encouraging the development of financial institutions under their own particularjurisdictions."' Thus, it appears that the regulator has a complicated task of setting policywhich leads to the realization of all of these goals.In the area of securities fraud and manipulation, the regulator is concerned with theloss of confidence in the marketplace which these activities may cause. The loss ofconfidence results in less participation, and inefficiencies can occur if investors pass upvaluable projects because of the possibility of being deceived by a manipulator. Theregulator's role in this case is to limit the manipulator's effect on the market in the instanceswhere his presence could potentially lead to market failure.Given that manipulation impinges on the regulator's objective of allocativeefficiency, a regulator will want to find a way of reducing the negative effects of7 Coleman, William D., (1992), pg. 146.7manipulation. At the same time, the regulator must be conscious that too much interventioncan stifle legitimate trading that enhances allocative efficiency. The optimal regulation willbe such that the marginal social cost of intervening to prevent manipulation is equal to themarginal social benefits of preventing manipulation. Regulators have many ways ofmitigating the practice of trade-based manipulation. The B.C. Securities Act strictlyprohibits manipulation in section 41.1:41.1 No person, directly or indirectly, shall engage in or participate in atransaction or scheme relating to a trade or acquisition of a security if theperson knows or ought reasonably to know that the transaction or scheme(a)creates or results in a misleading appearance of trading activity in, or anartificial price for, any security listed on a stock exchange in the Province,(b) perpetrates a fraud on any person in the Province, or(c) perpetrates a fraud on any person anywhere in connection with thesecurities of a reporting issuer.'However, it is difficult to detect trade-based manipulative activity because it rests with theintent of the trader.' Edwards and Edwards (1984) discuss 3 conditions which appear to benecessary in successfully prosecuting manipulative activity. First, there must be proof thatthe activity resulted in artificial prices. Unfortunately, there does not appear to be a good,workable definition of what constitutes artificial prices. Second, the alleged manipulator'sactions must be shown to have caused the artificial price. In another words, themanipulator's position must be large enough to affect the market price. And third, thealleged manipulator must have intended to create the artificial price. It is not easy todetermine if a trader is manipulating an asset price or if he is speculating on special8 B.C. Securities Commission, consolidated Nov. 8, 1991, Section 41.1. Emphasis added.9 See Fischel and Ross (1991).8information or subjective views which he might have on the supply and demand of the asset.Furthermore, it could be that a trader has not intended to manipulate the market but hisactions are mistakenly interpreted by others as manipulative. Since the actions of a traderaccused of being a manipulator can be interpreted in many ways, this final condition can bethe most difficult to prove. Thus, given the difficulty of prosecuting trade-basedmanipulation, other means of regulation, such as preventive measures, are needed.Disclosure requirements are used to attempt to ensure that material facts arepublicized in a timely fashion. In addition, insiders must report their trades on a regularbasis. This leaves less room for the manipulator to deceive the market. In the futuresmarket they rely on position and daily price change limits. These reduce any effects that themanipulator might have on prices, and decrease the potential profit of short-termmanipulation by limiting the size of the trades. However, these limits can be ineffective,especially, if they are not coordinated across the various markets on which a security islisted. 10Exchanges also monitor price and volume changes, halting trade in the event ofunusual behaviour. If the trading of a share is halted the exchange will require the companyto explain the unusual behaviour. The company might then respond with previously-unreleased information or with a statement that it knows of no information that would cause10 See Kyle, Albert S., (1988).9such movement. Halts give the market time to digest any information and allow participantsto return to trading that is more orderly and informed.Although trading halts might mitigate manipulation, they also create costs for themarket. Gerety and Mulherin (1992) empirically studied trading activity around the dailyopening and closing of markets. They found that there was a symmetry between the tradingvolume at the close of day 1 and the opening of day 2. This implies that some traders donot prefer the risk of holding a position overnight when the market is closed. The resultsuggests that trading halts might impose costs on these investors as the closure of the marketcreates too much uncertainty for them. It may force some investors to hold positions longerthan desired. Furthermore, if the decision rule regarding trading halts is predictable byinvestors then it may lead to overreaction by market participants. A halting rule mighttrigger 'panic' selling as investors try to trade before the halt. This may lead to a less stabletrading environment. Optimal regulation has to consider the possible costs of using tradinghalts.IV. Models of Manipulation ProfitabilityRecently, there have been several studies on the profitability of trade-basedmanipulation. These studies approach the problem from different angles, consider differentmarkets, and reach differing conclusions. Some argue against the profitability ofmanipulation, while others use models to derive conditions under which a manipulator'sactions can be profitable. In most of the models, the manipulator tries to take advantage of10the presence of asymmetric information where one agent is unsure about another agent'sidentity or level of information. It is usually assumed that the manipulator disguises himselfas an informed trader in order to deceive the market.Fischel and Ross (1991) argue that successful trade-based manipulation is difficult,if not impossible, to achieve. First, they suggest that manipulation is self-defeating becausejust the possibility of manipulation can lead to thinner markets and increased costs associatedwith decreased liquidity. The cost of liquidity is the premium one pays in order to tradeimmediately. It is usually charged by the market maker who takes on a position withoutimmediate prospects of closing it out. For the risk she takes, she requires a reward. Thebid-ask spread reflects this cost. Because of liquidity costs, a manipulator must pay arelatively higher price to buy and a relatively lower price to sell which cuts into his profits.In order for manipulation to be profitable, the price movement caused by the manipulatormust be large enough to compensate for this cost. Thinly traded shares are more easilymanipulated because relatively small changes in supply or demand can cause pricemovement. Yet, the more thinly traded a security the higher its cost of liquidity and thelarger its bid-ask spread." Therefore, one will offset the other and profits may benegligible. Second, Fischel and Ross argue that the manipulator's trading strategy cannotbe profitable in the long run. In other words, the long run equilibrium does not includeprofitable manipulative activity. A manipulator must appear to have information whenbuying in order that others take his lead and bid the share price up further after he hasii See Fischel and Ross (1991).11bought. When he wants to collect his profits he must then convince the market that he is notinformed to prevent others from selling with him and driving the price down before he getsa chance to close his position. He must disguise himself as an informed trader when creatinghis position and then convince the market that he is uninformed when he unwinds hisposition. The authors suggest that in an anonymous market it is unlikely that a manipulatorcan achieve this goal without expending a large amount of capital. Unfortunately, thesearguments are not modelled rigorously and thus their plausibility is hard to evaluate.As if responding to the second argument of Fischel and Ross, Gastineau and Jarrow(1991) suggest that the manipulator can make profits by taking advantage of "differences inintertemporal price sensitivity attributable to noise traders following positive-feedback (trend-following) investment strategies. "12Jarrow (1992) extends this result. He defines a large trader as one whose tradesaffect prices, either because he has market power or because others believe that he might beinformed. The large trader is considered a manipulator if his trades are not based on anyinformation.' Thus, the model relies on a level of asymmetric information which allowsthe manipulator to hide his identity from the market. Jarrow focuses on market manipulationtrading strategies in a market which is frictionless and where the price process is stochasticbut functionally related to the trades of the large trader. In this setting, there are trading12 Gastineau and Jarrow (1991), pg. 40.13 Jarrow (1992) ignores the possibility of the large trader (e.g. a pension fund) trading for liquidity reasons.12strategies where profits are earned at no risk. In other words, the market manipulationtrading strategies are arbitrage opportunities. One such strategy involves the manipulatorcreating a trend. He buys more and more of the security, increasing its price and creatinga bubble. He then closes out his position before the trend collapses (i.e. he sells out at thetop). This strategy requires that the way prices change is affected by the speculator'sactions. Jarrow concludes that profitable manipulation is possible if the price processdepends on the past sequence of the large trader's holdings and not on his aggregateholdings.In another study of trade-based manipulation, Kumar and Seppi (1992) use a two-market model consisting of a spot market and a futures market. They show thatmanipulation is profitable if the futures account can be closed out by cash settlement and thespot price can be manipulated. Cash settlement in this model is important because it makesthe futures market infinitely liquid so that corners and squeezes are highly unlikely. Incomparison, the spot market is less liquid and therefore spot prices will be affected by trade.By manipulating the spot price once a futures position is taken it is believed that one canimprove the settlement price. As long as the futures position is larger than the spot position,a net profit can result.The model of Kumar and Seppi consists of the manipulator, noise traders who tradein both markets independently, an informed trader who trades in the spot market, and amarket maker who sets prices in order to break even. At time 1, the manipulator and noise13traders trade in the futures market. At time 2, the manipulator, noise traders and informedtrader trade in the spot market. At time 3, the futures contract is deliverable. At time 4,the liquidating dividend is announced and paid out. The manipulator can pool with the noisetraders in the futures market and with the informed trader in the spot market. Thus, themarket maker cannot be sure of the extent to which the manipulator is in the market. Themanipulator can then manipulate the price in the spot market as the other participants willnot know whether or not he has information. The artificial price in the spot market willallow for a more favourable settlement price in the futures market. Given that his futuresposition is larger than his spot position the manipulator will earn profits." This model alsohinges on the fact that the manipulator can disguise himself in both markets, thereby takingadvantage of asymmetric information.Allen and Gale (1992) show that a manipulator can make a profit in an asset marketas long as the other investors believe that there is a possibility that he may be informed. Themodel is three periods long with one consumption date at the end. It involves the possibilityof a large trader buying a portion of the asset at time 1 and selling it at time 2. This largetrader may be either an informed trader or a manipulator. Given that he is informed it isassumed that news will be released at a later date. A critical assumption of the model is thatbad news will be announced earlier than good news. This is modelled by assuming that ifthe news is bad it is announced at time 2, otherwise good news is announced at time 3.14 Kumar and Seppi (1992) suggest that the manipulator's profits can be restricted by price discreteness, positionlimits, and margin requirements. Furthermore, the manipulator's profits or utility are negatively related to the numberof manipulators in the market and the degree of risk aversion by the manipulator.14There are two levels of payoff possible at time 3, low (L) and high (H). If the large traderis the manipulator then no news will be revealed and the payoff will be L. If the large traderis the informed trader and bad news is announced at time 2 then the final payoff will alsobe L. Given the informed trader has entered, if no news is announced at time 2 then goodnews will be announced at time 3 and the payoff will be H. Finally, if no large trader entersthe final payoff is assumed to be L. The pooling equilibrium occurs when a large traderenters the market, and continues at time 2 if no announcement is made. Under thiscircumstance, the small investors are faced with asymmetric information as they do not knowif the large trader is informed or is a manipulator. The price increases between time 1 and2 because there is some resolution of uncertainty. If no news is announced at time 2 thenthe small investors know that if it is the informed trader, only good news will beforthcoming - bad news would have been revealed at time 2. Unfortunately, there is stillsome uncertainty because the small investors might be dealing with the manipulator in whichcase no news will be forthcoming at time 3.The small investors are willing to sell the asset even though it may be below the valueexpected by the large trader for several reasons. First, they are uncertain as to whether thelarge trader is informed or manipulating the market. Second, if the large trader is informedthere is still the possibility that his information may be wrong and that bad new will berevealed. And third, the small investors are more risk averse than the large trader. Themanipulator is able to make a profit when the small investors are sufficiently risk averse andthe probability of manipulation is sufficiently small.15The majority of these studies demonstrate the importance of the manipulatormasquerading as an informed trader. Asymmetric information is therefore a necessarycondition for profitable manipulation. Asymmetric information occurs when one agent doesnot know the quality of another agent's information or does not know the true identity of theother agent. For example, asymmetric information exists when an uninformed agent, tradingwith an informed agent, does not know the quality of the informed agent's information abouta security's payoffs. Or it may be the case that the uninformed agent does not know whohe is trading with; it may be an informed agent or another uninformed agent. Traders withdifferent information sets may value an asset differently and therefore may be willing to takedifferent sides of the market. The noise created by the difference in knowledge allows pricesto slowly reveal an informed trader's information; thus, he is able to profit from hisinformation. Grossman and Stiglitz (1980) argue that if prices did reflect all costlyinformation then informed traders would not be compensated for acquiring the informationand would therefore prefer to be uninformed. Without informed traders prices would bevery slow in moving toward their true values and markets would be less efficient inallocating resources. However, in addition to encouraging manipulation, asymmetricinformation can impose costs on other market participants.Even without manipulators, small investors may be harmed by asymmetricinformation. They are at a disadvantage against the informed trader and will tend to losemore often if they trade with the informed trader. The 'adverse selection' cost, identifiedby Kyle and others, will drive some of the uninformed out of the market making it less16liquid and more costly for the traders who must trade for liquidity reasons. Thus, theregulator is faced with a trade off. On one hand, keeping markets open facilitates theincorporation of information into prices. On the other hand, the asymmetric informationgives the informed trader an unfair advantage which makes trading or investing by theuninformed and liquidity traders more costly. Any resulting transfers of wealth from onemarket participant to another create distributive concerns. However, the existence ofasymmetric information may cause allocative losses as well.Several papers have looked at the trade off between insiders or informed traders andoutsiders. Ausubel (1990) argues against insider (informed) trading stating that insideractivity causes loss of confidence by outsiders who will reduce their investment. This lostinvestment more than offsets the insider's profits. He concludes that both parties are madebetter off if the insiders can credibly promise not to trade on their information. In contrast,Leland (1992) argues that the impact of insider trading is uncertain. He shows that allowinginsider (or informed) trading leads to higher, more informative stock prices and a higherlevel of real investment. However, the presence of insiders reduces liquidity and causeswelfare losses for outside investors and liquidity traders. The effect on total welfare willdepend on various factors present in the economy. For example, total welfare will likelyincrease if the information held by the informed trader affects production decisions as wellas the stock price. Bernhardt, Hollifield and Hughson (1992) also show that the net welfareeffect depends on the type of information held by the insider. Outsiders will tend to stayaway from securities that appear to be heavily traded by insiders causing portfolio distortion;17however, the insiders' information could be useful in making future real investment decisionsand should be reflected in the security price. The authors conclude that losses from portfoliodistortion may be offset by improved efficiency of real investment due to more informativeprices. Furthermore, the authors show that when insider trading has little impact on long-term real investment decisions it is far less beneficial to society.Of course, the net effect on welfare created by asymmetric information is only furthercomplicated when the market must also contend with a manipulator. The regulator is nowfaced with a three-way trade-off. In one corner, the informed trader may add value to societyby enhancing allocative efficiency. In another corner, the manipulator reaps profits from thepresence of asymmetric information, while reducing market efficiency. Finally, in the thirdcorner, the small, uninformed investors and the liquidity traders are harmed by the possiblepresence of both.V. ConclusionTo date there have been studies of the profitability of manipulation in the financialliterature and discussions on the difficulties of defining and regulating manipulation in thelegal literature. However, there does not appear to be any attempt to model the trade-offsfaced by a regulator who must contend with manipulation. In the following chapter, weconsider a model where the existence of trade-based manipulation can lead to a less efficientuse of resources. Due to the noise he creates, the manipulator can discourage capitalformation. Our model demonstrates how a regulator can reduce this noise through trading18halts which allow the revelation of the asset's true value before the manipulator is allowedto close his position. However, trading halts do create illiquidity costs and these must beweighed against the benefits derived from halts when a regulator sets policy.19Chapter 2Model of Trade-Based Manipulation and Trading HaltsI. The Mode115In this chapter, we model a market where there is a possibility of trade-basedmanipulation. The framework we use is similar to that of Allen and Gale (1992). There are3 categories of market participants: the small investors who are risk averse and uninformed,the large trader who is risk neutral and either informed or uninformed (i.e. the manipulator),and the regulator.There is a riskfree project with a rate of return normalized to zero, and a riskyproject. Both projects require the same investment of capital at the beginning. While theriskfree project has a certain payoff at the end, the risky project pays out an uncertainliquidating dividend, V q, where q E {H, L}, VH > VL.The model has 3 trading periods and one consumption date at the end. At time 0,the small investors decide whether to invest their endowed capital in a risky project or ariskfree project. If the small investors decide to invest in the risky project then Naturechooses the type of large trader they will face. At time 1, given the small investors doinvest in the risky project, the large trader (either informed or uninformed) decides whetheror not to buy shares of the project from the small investors. At time 2, the regulator,observing a purchase of shares at time 1, decides whether or not to halt trading in order to15 The variables defined below are also listed in Appendix A.20reveal information and perhaps to unmask the manipulator. If the regulator does not halttrading then the large trader is free to sell his shares back to the small investors at time 2.Otherwise, he must wait until time 3 to close his position. The effect of a halt is toeliminate the potential gain from a trade by the uninformed trader or manipulator.If the informed trader is chosen and the project's payoff is L then this is announcedat time 2. On the other hand, if the project's payoff is H it will not be announced until time3. When the uninformed trader is chosen the project's type is not revealed until time 3. Attime 3, the project pays a liquidating dividend. See Appendix B for a tree diagram of thegame.Given the small investors choose the risky project, the motivation for trade is asfollows. At time 1, there is risk with regards to the type of large trader that is chosen byNature and the uncertainty of the final payoffs. The small investors are willing to sell to thelarge trader in order to unload some of this risk, and the large trader is willing to buy tocollect a risk premium. At time 2, the informed trader wants to sell because he is faced withan illiquidity cost if he waits until time 3. 16 The large uninformed trader is able to hide hisidentity by mimicking the informed trader; therefore, he wants to sell at time 2 while hisidentity is still unknown. The small investor is willing to buy back at time 2 because someof the uncertainty will have been resolved. So at time 1, a risk premium drives the exchangein one direction while at time 2, a liquidity premium drives a reversal of trade.This illiquidity cost will be discussed in greater detail later.21II. The Small InvestorsThe small investors are risk averse. Because they are homogeneous we can treatthem as one investor. The representative small investor is endowed with capital at thebeginning of the game. At time 0, he must decide whether to invest this capital in a riskyproject or a riskfree project. The small investor makes his decision by comparing hisexpected utility from investing in the risky project with that of the riskfree project.III. The Large TraderAt time 0, Nature chooses the type of large trader that the small investor will faceif he decides to invest in the risky project. The large trader is risk neutral and his type isdenoted by t E T = {I, where I indicates the informed trader and U indicates theuninformed trader or the manipulator. The type, t, is chosen according to an exogenousprobability distribution on T. Let 0 denote the probability that the informed trader ischosen, and (1-0) denote the probability that the uninformed trader is chosen, where 0 E(0, 1). This distribution is common knowledge.The large trader maximizes his expected utility by selecting a strategy b(t), theprobability of issuing a buy order for a proportion B of the project at time 1. We assumethat b(t) E [0, 1] so that both mixed and pure strategies are allowed. The proportion, B,is exogenously chosen and lies between 0 and 1.' 717^ ^ This implies that short-selling is not allowed.22It is assumed that the informed trader is informed about good news regarding therisky project. Let 71 denote the conditional probability of a high state occurring given a largetrader of type t, or rt = prob(H I t). Thus, rt and 0 are related. In this model we assume:{ ri = 0.9Tt =TU = 0.5with probability 0with probability 1-0.Given that investment in the risky project occurs, the small investor does not observe whichlarge trader enters and therefore does not observe t directly. Therefore, at time 0, beforethe purchase decision of the large trader is made, he only knows that the probability of ahigh state occurring is equal to:0 TI + (1 - 0) TU .On the other hand, when the uninformed trader enters the market he does know that thereis no informed trader and that 7-` = TI' = 0.5. He is therefore more informed than the smallinvestor. However, the uninformed trader has less precision than the informed agent. Forexample, if H = 20 and L = 10 then the conditional variance of the risky project's finalpayoffs for the informed trader would be:Var[Payoff I Informed Trader] =0.9 (20 - 19)2 + 0.1 (10 - 19)2 = 9.0.On the other hand, the conditional variance of the risky project's final payoffs for theuninformed trader would be:Var[Payoff I Uninformed Trader] =230.5 (20 - 15) 2 + 0.5 (10 - 15) 2 = 25.0.The variance of the final payoffs is lower for the informed trader than for the uninformedtrader; therefore, the informed trader has more precision.We assume that the informed trader faces illiquidity costs. If he buys at time 1 thenhe will want to sell at time 2 for reasons that are exogeneous to the model. If he cannot sellat time 2, then he must bear a cost, w, for having to wait until time 3 to sell. We discussthe implications of this cost in chapter 4.As was discussed previously, given that an informed trader is chosen by Nature, ifthe project is of type L then bad news will be announced at time 2, instead of time 3. If theproject is of type H it will not be announced until time 3. Therefore, the actions of theinformed trader force some information to be revealed early. If we were to assume that theuninformed trader never buys at time 1 (i.e. b(U) = 0), and we witness a purchase by thelarge trader at time 1, then we will know that it is the informed trader, and therefore at time2 we will know the final payoff of the project. If no news is announced at time 2 it willautomatically be known that good news will be announced at time 3.However, if the uninformed trader does buy with probability b(U) > 0 then therewill be extra noise in the market. If no news is announced at time 2, there are now 2possibilities: either the large trader is informed and good news will be announced at time 324or the large trader is uninformed and the outcome of the project is still uncertain and willonly be resolved at time 3.IV. The RegulatorLike the small investor, the regulator does not know the identity of the large trader.If the large trader buys at time 1, then the regulator decides to halt trading at time 2 withprobability 7, where 7 E [0,1]. The regulator chooses 7r with her specific objectives inmind. In this model, we assume that her objective is to promote economic efficiency. Wemight conceptualize this by examining the maximization of the sum of the expected utilities.Although a trading halt results in the uninformed trader or manipulator being revealed, italso imposes a cost on the informed trader who is impatient to close his position. Theinformed trader does not like the illiquidity created by the halt. Thus, the regulator facesa trade-off between the benefits derived from revealing the manipulator and the costsimposed on the informed trader."V. The Equilibrium Prices and the Final PayoffsIf, at time 1, the small investor decides to invest in the risky project, then the largetrader must decide whether or not to buy a proportion, B, of the project. We assume thatthe price at which the large trader buys the share, P 1 , is determined from the first ordercondition of the maximization of the small investor's expected utility (i.e. an equilibriumprice is chosen). In other words:18 In chapter 4, we discuss the impact of imposing illiquidity costs on the small investor.25E[i I / (Ws ' Risky Project, Buy)17,]Pi = ^E[I I' (Ws I Risky Project, Buy)](2)where, Ws is the final payoff of small investor in state s, Vs is the liquidating dividend instate s, ands E [states given the small investor invests in the riskyproject, and the large trader buys at t=1]or from Appendix B, s E [U3...U6, Il...I4].For the informed trader, P1 is less than his expected value of the risky project. He knowsthat rt = ri = 0.9; however, the small investor does not know if the large trader isinformed or uninformed, given that it is optimal for both large traders to trade at least someof the time. Therefore, his belief about the probability of the high state occurring is lower.For the small investor,Prob (H I Trade) = 0.9 Prob (Informed I Trade) + 0.5 Prob ( Uninformed I Trade)= 0.9 0 b (I)^+ 0. 5 5^(1 -0)b(U) (1 -0)b(U) + Ob(l)^(1 - 0)b(U) + Ob(l)which is less than 0.9 given: 0 < Prob (Informed I Trade) < 1. Furthermore, becausethe small investor is risk averse, he is willing to sell for less at time 1 in order to pass onsome of the risk from the project to the large trader.26If the large trader buys at time 1 then he will want to sell at time 2. The uninformedtrader wants to sell at time 2, since the only way he can earn a profit is if the small investorstill thinks that he might be informed, while the informed agent wants to sell at time 2 inorder to avoid an illiquidity cost of w. We assume that w is large enough to persuade theinformed trader to always want to sell at time 2. In chapter 4, we discuss what occurs if thisis not the case.At time 2, the regulator must decide whether or not to halt trading in order to revealthe project type. If she halts trading then there is no market activity at time 2 and everyonemust wait until time 3 in order to liquidate their positions. Thus, there is no price at time2 if the regulator halts trading.If the regulator does not halt trading, then the large trader can close his position attime 2. If the large trader is informed and the project turns out to be of type L then it willbe revealed at time 2 and the informed trader will have to sell his shares at L. However,if no news is announced at time 2 then the small investor will still not know who he istrading with. It may be the informed trader, in which case, the payoff will be H, or it maybe the uninformed trader, in which case, the payoff will be either H or L. Thus, if noannouncement is made at time 2, then the price that the large trader will sell at, P2, willagain be determined from the first order condition of the maximization of the smallinvestors' expected utility. Thus,27(4)P2 =E{ U' (Ws IRisky Project, Buy, No Halt, No Announcement)]where Ws and Vs are defined as before, andsE [states given the small investor invests in the risky project, the large traderbuys at t = 1, the regulator does not halt trading, and there is no announcementat t=2];or from Appendix B, s E [U5, U6, laIf the uninformed trader never buys at time 1 (i.e. b(U)=0), then at time 2, P2 will equalH. In our model, P2 will be greater than P 1 because, for all strategies followed by theinformed and uninformed traders, the lack of announced tad news' at time 2 providesfavourable information.In the event that the regulator does not halt trading, the large trader, given he buysat time 1, will liquidate at time 2, and only the small investor will liquidate at time 3.However, if the regulator halts trading at time 2 then the small investor and the large traderwill have to liquidate at the project's true value at time 3.The final payoffs at time 3 for the uninformed trader, the informed trader and thesmall investor are as follows in Table 1. The states correspond exactly to those in the treediagram in Appendix B.E[ U' (Ws IRisky Project, Buy, No Halt, No Announcement)Vs ]28Table 1 - The Final Payoffs from the Risky ProjectState t=0 Probability Uninformed Informed Small InvestorUl (1-0)(1-b(U))Tu 0 0 HU2 (1-0)(1-b(U))(1-7") 0 0 LU3 (1-0)b(U)717" (H-P1)B 0 H + (P1-H)BU4 (1-0)b(U)71-(1-0 (L-P1)B 0 L + (P1-L)BU5 (1-0)b(U)(1-71-)ru (1)2-P1)13 0 H + (P1-P2)BU6 (1-O)b(U)(1-ir)(1-r') (132-P0 0 L + (P1-P2)BIl Ob(I)(1-0-1 0 (132-131)B H + (P1-P2)B12 Ob(I)(1-r)(1-7-1) 0 (L-P1)B L + (P1-L)B13 Ob(I)77-1 0 (H-P1)B - w H + (P1-H)B14 Ob(I)741-7-1) 0 (L-P1)B - w L + (P1-L)B15 0(1-b(I))T1 0 0 H16 O(1-b(I))(1-r') 0 0 LVI. The Strategies and the Objective FunctionsThe Small Investor:The small investor chooses between the two projects by comparing his expected utilityfrom both. His expected utility from investing in the risky project is:Em [Utility I Risky Project] = E ps E[U(Ws )]^(5)29where ps is the probability of state s occurring (as listed in Table 1), W s is the final payoffof the small investor in state s, and s E [U1...U6, 11_16]. His expected utility frominvesting in the riskfree project is just the utility from the certain payoff. Therefore, if thepayoff from the riskfree project at time 3 is Y then the small investor's expected utility frominvesting in the riskfree project is:EsjUtility I Riskfree Project] = Us1 [Y]Thus, the small investor will invest in the risky project if:Em [ Utility I Risky Project]^Us, [ Y]The Large Trader:The large trader maximizes his expected utility by choosing a strategy, b (t), theprobability that he issues a buy order at time 1. Since he is risk neutral his utility functiontranslates into his profit function. Thus, we get for the informed trader:El [Profit] = b (I) {(1 -7) b(P2 -Pi)B + (1 -7-1)(L - 131)13]^(8)+ 7rk ((H - 131)B - w) + (1 -71) ((L - 1 3 1) B - w)j}And for the uninformed trader:30Eu [Profit] = b( U){47-u(H-Pi)B + (1-ru)(L -Pi)B1^(9)+ (1-w) (P2 -Pi)B1The Regulator:We assume the regulator's objective is to promote allocative efficiency byencouraging investment in the optimal project. However, at the same time, she mustminimize the cost of intervening, which in this model is represented by the illiquidity cost,w.In the next chapter, we demonstrate an instance where if the uninformed trader neverenters, the small investor will want to invest in the risky project. However, if it is optimalfor the uninformed trader to enter then the small investor will not want to invest in the riskyproject. Thus, the uninformed trader's actions affect the small investor's investmentdecision. The regulator wants to intervene if she can, by her actions, encourage the smallinvestor to invest in the risky project once again. However, since the trading halts imposea cost on the informed trader the regulator must only intervene to the point where the smallinvestor is indifferent between the 2 projects. In this way, the regulator minimizes the costof trading halts, w, subject to the constraint of achieving investment in the optimal project.31The regulator's objective function might be viewed as the sum of the expected utilitiesof the 3 market participants. The regulator would then maximize this sum with respect to7. We might state this optimization problem as follows:Max,, 0 E1 [Profit] + (1 - 0)Eu [Profit] + E 1 [Utility]It is important to note that summing ordinal utilities may be inappropriate and thereforecaution must be taken when interpreting the results. However, conceptualizing the problemin this way does reveal that the function is not continuous at the point where the smallinvestor is indifferent between the 2 projects. If the small investor chooses the riskfreeproject then the large traders will have expected utilities equal to 0; however, when the smallinvestor chooses the risky project then the large traders will have expected utilities greaterthan 0.VII. ConclusionIn this chapter, we have described a model which can be used to show the effect ofmanipulation on market participants. We have expanded on previous models by includinga regulator whose objective is to mitigate any negative effects that a manipulator might haveon a market. In the next chapter, we will use the model to demonstrate the trade-offs facedby a regulator who is faced with the possibility of trade-based manipulation, and we willsolve for equilibria using a numerical example. In chapter 4, we will discuss further ourassumptions, commenting on their importance to our results.32Chapter 3Demonstration and Discussion of ModelI.^An ExampleIn order to illustrate different equilibria for the model we present a numericalexample. To begin let us assume that the exogenous variables are set such that:11=5050^L = 10B = 0.3 0 = 0.9Ti = 0.9^ru = 0.5w = 3.0134Payoff at time 3 of Riskfree Project = Y = 40.5Expected Payoff of Risky Project at time 0:= e[r'll + (1-7-1)L] + (1-0)[rull + (1-P)L]= 44.4Furthermore, we assume that:U[W] = utility function of small investors = ln(W)IY[VV] = marginal utility = 1/W(1)In order to provide a benchmark, consider first the possibility that the regulator neverhalts trading, i.e. 7 = 0. We will also assume that the uninformed trader never buys at time331 or that b(U) = 019, and that these constraints are common knowledge. Given the smallinvestor decides to invest in the risky project, the final payoffs at time 3 for the informedtrader and the small investor are presented in Table 2.Table 2 - Final Payoffs to the Informed Trader and the Small InvestorState t=0 Probability Informed^Small InvestorUl 0.05 0 50U2 0.05 0 10Il 0.81b(I) 0.3(P2-P1)^50 + 0.3(P1-P2)12 0.09b(I) 0.3(10-P1)^10 + 0.3(P1-10)15 0.81(1-b(I)) 0 5016 0.09(1-b(I)) 0 10(i) In this example, it is easy to solve for P2. If the large trader buys at time 1, then hemust be the informed trader (since we have set b(U) = 0). Given he buys at time 1, if noannouncement is made at time 2 then the small investor will know for sure that good newswill be announced at time 3 and will therefore set P2 = H = 50. If bad news is announcedat time 2 then the large trader will have to sell at L = 10.19 This corresponds to a world in which there are no manipulators. However, Nature still decides r t . The informedtrader only participates if e = r'.34P1 = 0.9 IE [50 + (P1 -50)0.3]+0.11P [10 +(P1 -10)0.3]0.91E[50+(P1 -50)0.3]50+0.1U/ [10+(P1 -10)0.3]10(ii)^To solve for P 1 we use the first order condition of the maximization of the smallinvestor's expected utility in order to find the equilibrium price. In this example,= 41.4677.(iii) Next, the informed trader, if he is chosen by Nature, will maximize his expectedprofit with respect to b(I):Maxbm El [Profit] = b(1)H(P2 -131 )B+(1-7-i)(L-P1 )B]= b(/)[0.9(50 -41.4677)0.3 +0.1(10-41.4677)0.3j, (12)= 1.3597b(I)Therefore, b* (I) = 1. Every time the informed trader is chosen by Nature, he willbuy proportion B of the asset at time 1. The expected profit of the informed trader is:E1[Profit 1 b*(I) = 1] = 1.3597.(iv) If the small investor invests in the risky project then his expected utility will be:35ES,[ UtilityRisky Project] =^0.05 U[50] + 0.05 U[10]+ 0.81 U[50 + 0.3(41.4677 - 50)]+ 0.09 U[10 + 0.3(41.4677 - 10)]^(13)= 3.7040The expected payoff of the small investor given he invests in the risky project is 43.1763,while the variance of his payoff is 122.7945.If the riskfree project pays out 40.5, the small investor's expected utility frominvesting in the riskfree project would be 3.701302. Thus, in this instance, the smallinvestor obtains a higher expected utility if he invests in the risky project, and therefore, hewill choose the risky project. Also, the informed trader's expected utility or profit goesfrom zero if no investment in the risky project is made, to 1.3597 if the risky project isundertaken. Hence, in the absence of a manipulator wealth-increasing trade takes place.(2)We will now consider the existence of the uninformed trader or manipulator;however, we will still assume that the regulator never halts trading (or w=0). The finalpayoffs become more complicated when we include the uninformed trader. They arepresented in Table 3.36Table 3 - Final Payoffs Given Presence of Uninformed TraderState t = 0 Probability Uninformed Informed Small InvestorUl 0.05(1-b(U)) 0 0 50U2 0.05(1-b(U)) 0 0 10U5 0.05b(U) 0.3(P2-P1) 0 50+0.3(P1-P2)U6 0.05b(U) 0.3(P2-P1) 0 10+0.3(P1-P2)Il 0.81b(I) 0 0.3(P2-P1) 50+0.3(P1-P2)12 0.09b(I) 0 0.3(10-P1) 10+0.3(131-10)15 0.81(1-b(I)) 0 0 5016 0.09(1-b(I)) 0 0 10(i) If the small investor decides to invest in the risky project, then the large trader willagain maximize his expected profit. In this case, the informed trader will maximize withrespect to b(I), and the uninformed trader will maximize with respect to b(U).Max b(J) El [Profit] = b(1)[7-1 (P2 - +(1-7-1)(L - Pi ).131= b (I)[0.9 (P2 -P1 )0. 3 +0.1(10-P1 )0.3}Maxb(u) Eu [Profit] = b( U)(P2 -1)1 )13b( U)(P2 -P1 )0.337=P2where:ru5 =rah =r11 =rus ui[wu5]50+r u6 ui[vu6]10+I` 1 vi [W11 ]50ru5 tE[wu5]+ru6 11/[vvu6]+r11 w[wa ](1 - 0)b ( U)Tu . 0.05 b (U)(1 - 0)b (U) + 0 b (I)T1 0.1b(U)+0.81b(/)(1 -0)b(U)(1- Tu) = 0.05b(U)(1 -0)b(U)+0b(l)T1 0.1b(U)+0.81b(/)0 b(I)T' 0.81 b (I)(1 - 0)b(U)+0b(l)T1 0.1b(U)+0.81b(/)P1 A ufru I E [Wu5]50 + (1 - 'ME P [IVu6110} + A ifr U / [W11]50 + (1 -TI)U 1 [1 V 12]10}A ufruU1 [Wu5]+ (1- Tu)U1 [Wuj} + tilfrUi[Wn] + (1 -7)1P [1V12]}AuA/ =(1 -0)b(U) . ^0.1b(U)(1 -0)b(U) + 0 b (I)^0.1b(U) + 0.9 b (I)Ob(I)^0.9 b (I)(1 -0)b(U) + 0 b (I)^0.1b(U) + 0.9 b (I)and Ws is the final payoff of the small investor in state s. r, is the conditional probabilitythat state s occurs given the large trader buys at time 1, the regulator does not halt tradingat time 2, and no announcement is made at time 2. A is the conditional probability that thelarge trader t buys at time 1, given a large trader buys at time 1.In this example we must solve for b(U), b(I), PI and P2 simultaneously. We get:38b*(U) = 1,b*(I) = 1,P1 = 34.5889,P2 = 39.9553.Both the uninformed and the informed trader will always want to buy at time 1 whenthey are chosen by Nature. The prices are lower than if the uninformed trader neverentered because the small investor cannot distinguish between the two large traders. In part(1) above, if the large trader bought at time 1 then the small investor knew immediately thatthe informed trader was chosen and that r = TI = 0.9. Furthermore, if the large trader didnot buy at time 1, then the small investor knew that r t = TU = 0.5. Thus, in part (1), thesmall investor could update his belief about rt at t =1. However, with the possible existenceof the uninformed trader the small investor is now unsure of who he is dealing with. Hecannot update his beliefs about rt as accurately at time 1. If no announcement is made attime 2, then the small investor will still be uncertain (although he will be able to eliminatesome of the possible states). The uncertainty that exists with the possibility of theuninformed trader entering the market causes both prices to be lower. Since the uninformedtrader tries to manipulate the market, the informed trader's actions are 'muddied'. Thepooling which occurs slows down the price discovery process.(ii)^Given the above values, the expected profits of the large traders are:Ei[Profit] = 0.7113,Eu[Profit] = 1.6099.39Thus, the informed trader's expected profit decreases with the possible entrance of theuninformed trader (from 1.3597 to 0.7113). The expected final payoff of 44.4, now mustbe shared among three participants instead of two. Therefore, with the possible entrance ofthe uninformed trader, the expected profit is redistributed in favour of the uninformed trader.(iii) The expected utility of the small investor given he invests in the risky project is now:Esi[Utility 1 Risky Project] = 3.6995.His expected payoff and variance of payoff are:EsI[PaYoff 1 Risky Project] = 43.5989Var[Payoffsi 1 Risky Project] = 143.6092.Comparing these results to those in part (1), we see that the expected payoff of thesmall investor increases, as does the variance of payoff. The overall effect is that theexpected utility of the small investor decreases. Since the small investor is risk averse heis concerned about not only his expected return from the project but also about the highermoments associated with the expected return. The presence of the uninformed traderchanges the distribution of the payoffs, adversely affecting the small investor's expectedutility.(iv) Before investing in the risky project the small investor will compare his expectedutility from the risky project with that of the riskfree project. The small investor's utilityfrom investing in the riskfree project is still 3.701302. Therefore, the small investor will40want to invest in the riskfree project if the uninformed trader sets b(U) = 1 (i.e. if theuninformed trader always buys at time 1 when chosen by Nature). The uninformed trader'sactions discourage the small investor from investing in the risky project. This results in aloss to the economy. Since the small investor does not invest in the risky project theexpected profits of the large traders fall to zero. And for the small investor:Es/Utility i Riskfree Project] = 3.701302Es/Payoff i Riskfree Project] = 40.5Var[Payoffsl Riskfree Project] = 0The small investor is willing to decrease his expected payoff (from 43.5989 to 40.5) inreturn for a large decrease in variance (from 143.609 to 0). Looking at the market as awhole, the total expected payoff falls from:0.9(0.7113) + 0.1(1.6099) + 43.5989 = 44.4to 40.5. The total expected utility for this economy falls from:0.9(0.7113) + 0.1 (1.6099) + 3.6995 = 4.5007to 3.7013. Thus, the equilibrium, resulting from the presence of the manipulator, involvesinvesting in the sub-optimal project.(3)One way to convince the small investor to invest in the risky project is for theuninformed trader to reduce b(U), the probability of buying at time 1, to the point where thesmall investor will once again be willing to invest in the risky project.' In this example,20 However, we will show later that this strategy does not result in an equilibrium.41if the uninformed trader reduces b(U) to 0.51 then the small investor's expected utility fromthe risky project will increase to 3.701344, and he will want to invest in the risky projectonce again. The graph in Appendix C shows the relationship between b(U) and the smallinvestor's expected utility.(i) The prices are calculated in the same way as in part (2) except that b(U) is fixed at0.51. b(I) = 1 still maximizes the informed agent's expected profits. And,= 37.2640,P2 = 43.8259.These prices are greater than those in part (2) because there is less chance that theuninformed trader will try to manipulate the market and therefore there is a higherprobability that given the large trader buys at time 1 it is the informed trader.(ii) Under this scenario, the expected profits of the large traders are:El[Profit] = 0.9538,Eu[Profit] = 1.0040.Since there is less chance that the uninformed trader will disguise himself as theinformed trader, the informed trader's actions are more quickly reflected in the prices.Furthermore, the redistribution of payoff is not as large. The informed trader's expectedprofit is greater, while the uninformed trader's expected profit is less.42(iii) As stated above the small investor's expected utility from investing in the riskyproject increases to 3.701344. However, we can show that this solution is not anequilibrium. Once the small investor decides to invest in the risky project, the uninformedtrader will want to defect from b(U) = 0.51 to b(U) = 1. In this way, the uninformedtrader can increase his expected profit from 1.0040 to 1.6099. However, the small investorwill know before hand that the uninformed trader will want to defect and will therefore notinvest in the risky project. The uninformed trader has no way of legitimately signalling thathe will not defect. Thus, this solution is not an equilibrium and a regulator will be neededto ensure that the risky project is chosen.(4)In order to reach an equilibrium in which the risky project is chosen, we will needthe intervention of the regulator. The regulator's objective is to maximize the total expectedutility of the market participants. As we will see, in this example, the regulator can inducethe small investor to invest in the risky project by setting the probability of trading halts, ir>0. The final payoffs to the market participants are presented in Table 4.43Table 4 - Final Payoffs Given the Regulator May Halt TradingState t=0 Probability Uninformed Informed Small InvestorUl 0.05(1-b(U)) 0 0 50U2 0.05(1-b(U)) 0 0 10U3 0.05b(U)71" 0.3(50-P1) 0 50+0.3(111-50)U4 0.05b(U)r 0.3(10-P1) 0 10+0.3(P1-10)U5 0.05b(U)(1-r) 0.3(P2-P1) 0 50 +0.3(P1-P2)U6 0.05b(U)(1-w) 0.3(P2-P1) 0 10 +0.3(PcP2)Il 0.81b(I)(1-r) 0 0.3(P2-P1) 50+0.3(P1-132)12 0.09b(I)(1-ir) 0 0.3(10-P1) 10+0.3(P1-10)13 0.81b(I)r 0 0.3(50-P1)-w 50+0.3(P1-50)14 0.09b(I)ir 0 0.3(10-P1)-w 10+0.3(P1-10)15 0.81(1-b(I)) 0 0 5016 0.09(1-b(I)) 0 0 1044(i)^Again, if the small investor decides to invest in the risky project then the large tradert will maximize his expected profit with respect to b(t), given the optimal 7r. The objectivefunctions of the large traders are as follows:Maxb(1) E1 [Profit] = b(1){(1-10[7-1(P2 - PI )B + (1 -7-1)(L - Pi )B]+ ir[7-1 ((H - POB -w)+(1- ri)((L - Pi )B -w)1}= b(/){(1 -7r)[0.9(P2 -P1)0.3 +0.1(10 -P1)0.3]+7[0.9(50 -P1)0.3+0.1(10 -P1)0.3 -3.0134]}^Maxbm Eu [Profit] =^b(U)tr[ru (H - Pi )B + (1 - r u) (L - Pi ).13]+ (1 - w) (P2 - PI)B}^=^b( U){7r[0.5 (50 -P1)0.3 +0.5(10 -P1)0.3}+(1 - 7r) (P2 -Pi) 0.3}45(1 -0)b(U)ru^=^0.05 b(U)ru5 =(1 - 0)b(U) + Ob MT'^0 .1b (U) + 0 .81b (I)r, =^(1-0)b(U)(1-Tu)^0.05b(U)(1 - 0)b(U) + 0 b (1)7-1^0 .1b (U) +0 .81b (I)where:Pus(/' [wu5]so +r,u, [wu6] io 4- r„ ui [ wil ] sop = ^ru5 u, [vu5 ] + ru6 vi [wu6] + r„ vi [ w„ ]r„P1G.B.A UL1=====0 b (1)T1 .^0 .81b (I)(1-0)b(U)+0b(I)T'^0 .1b (U) + 0 .81b (1)Auk (Gu3 50 +B u4 10) + (1 - 7)(Gu5 50 + Bu6 10)]+ All'ir (G13 50 + 1114 10) +(1 - ir) (G11 50 +13,2 10)]Aupr(Gu3 + B u4) + ( 1 -7) (Gu5 + B u6)1+ Al[ir (G13 + 1314 ) +(1 - ir)(Gn +B12 )]ri IP [W.](1 -7-')U1 [W.](1 -0)b(U)^0.1b(U)(1 - 0)b(U) + 0 b (I)0 b (I)0.1b (U) + 0.9 b(I).^0.9 b (I)(1 - 0)b(U) + Ob(I) 0.1b(U) + 0.9 b (I)and Ws is the final payoff of the small investor in state s.The regulator will set 7 to maximize the total expected utility of the economy. Thegraphs in Appendix D show the relationships between 7 and the small investor's expectedutility, 71 and the large traders' expected utilities or profits, and 7r and the sum of expectedutilities. In this problem, we have to solve simultaneously for b(U), b(I), P1, P2, and 71.The maximization of the large traders' expected profits depend on 7*; however, 7* alsodepends on the maximization of the large trader's expected profits, or bt (I) and b*(U). Inthis example, we obtain the following solution:= 0.18,^b*(U) = 1,^b*(I) = 1,P1 = 35.2944,^P2 = 40.0820.(ii) The expected profits of the large traders are:E1[Profit] = 0.4734,Eu[Profit] = 0.8918.The expected profit of the informed trader decreases as 71 increases because of the illiquiditycost, w, imposed on him by the halts. The uninformed trader's expected profit is lowerbecause, given he buys at time 1, 18% of the time he will be revealed before he can closehis position.(iii) For the small investor:Es1Utility 1 Risky Project] = 3.701392^Us1[Y=40.5]Esi[Payoff 1 Risky Project] = 43.396647Var[Payoffsi 1 Risky Project] = 135.2591.(iv)^This is an equilibrium as no one is tempted to defect. Given T=0.18, the largetraders maximize their profits by setting b* (U) = 1, and b* (I) = 1, and the small investorreceives a slightly higher expected utility by investing in the risky project. Although theincrease in r causes the expected payoff of the small investor to decrease, it also causes thevariance of payoff to decrease. Again, the risk aversion of the small investor means that theeffect on the higher moments associated with the expected return are important to the smallinvestor.From this example, we have shown that the regulator can encourage capital formationthrough the use of trading halts when there is the possibility of trade-based manipulation inthe market. The total expected utility increases from 3.7013 (when the riskfree project waschosen) to:0.9(0.4734) + 0.1(0.8918) + 3.7014 = 4.2166.However, there is a deadweight loss with the use of trading halts. Under this last scenario,the total expected payoff is now:0.9(0.4734) + 0.1(0.8918) + 43.3966 = 43.9118.Although, this is greater than the payoff from the riskfree project, 40.5, it is less than theoriginal expected payoff of the risky project or 44.4. The loss comes from the cost, w,imposed on the informed trader for having to wait until time 3 to sell, and equals Oirw =480.4882. Thus, if the small investor is willing to invest in the risky project even with thepossible presence of the uninformed trader then the regulator should not intervene in themarket with trading halts, given her objectives are those stated above. If the regulator doesset some level of trading halts in this instance, she is only imposing an unnecessary cost onthe informed trader. Furthermore, because of the illiquidity cost that trading halts impose,the regulator will only want to intervene to the point where the small investor is indifferentbetween the 2 projects. The regulator's objective in this example does not coincide withdriving the manipulator out of the market.(5)The preceding example, allows us to comment on another result from our model. Ifwe were to assume that neither of the large traders ever bought at time 1 or that b(U) = b(I)= 0, then the small investor if choosing the risky project would not be able to share any ofthe risk. In this particular example, this would lead to the small investor investing in theriskfree project since investing in the risky project would result in an expected utility of3.686702 which is less than that from the riskfree project. Although, the small investorwould have an expected payoff of 44.4 from investing in the risky project, the variance ofthe payoff, 192.64, would be too high for the risk averse investor to bear. Thus, theexistence of the informed trader helps lower the variance of the small investor's payoff.When the risk neutral informed trader trades with the small investor, he takes on some ofthe risk from the project which makes the small investor more willing to invest in the riskyproject.49II. DiscussionA regulator who must contend with trade-based manipulation in the market must tryto ensure that the manipulative activity does not discourage capital formation which isallocatively efficient. Thus, if an investor would invest in a project in the absence ofmanipulation but not in the presence of manipulation, then the manipulator's actionscontribute to an inefficient allocation of resources. The regulator would then want tointervene in some way in order to discourage manipulation and encourage investment.In our model, the presence of the manipulator (or b(U) > 0) causes the expectedutility of the small investor to be lower than in the absence of the manipulator. Since thesmall investor is risk averse, the noise created by the possible presence of the manipulatornegatively affects the small investor's expected utility from investing in the risky project.In some cases the effect may be large enough to discourage the small investor from the riskyproject. Since there is no way for the manipulator to legitimately signal that he will limithis presence in the market in order to reduce the noise somewhat, the regulator will want tointroduce the possibility of trading halts in order to discourage manipulation throughdecreased profits, and encourage investment through decreased noise. However, tradinghalts can impose illiquidity costs on some. In our model, the informed trader is harmed bytrading halts. The regulator has to ensure that the informed trader does not want to leavethe market because of the trading halts. If he does then the small investor might once againchoose the riskfree asset since he cannot share the risk of the risky project with anyone else.Thus, the trade-off that the regulator faces is between the benefits derived from encouraging50efficient capital formation by the small investor and the costs imposed on the informed traderbecause of the possible reduction in liquidity. In the next chapter, we discuss some of themodel's assumptions and their importance to the results.51Chapter 4Sensitivity of the AssumptionsOur model contains several assumptions which are quite restrictive. Although someare required in order to achieve our results, in some instances they can be relaxed to acertain extent and still produce the same conclusions. In this chapter, we discuss thesensitivity of the more important assumptions on our results.I. The RegulatorIn our model, we assume that there is only one regulator; however, in reality thereare normally 2 levels of regulation in the securities market. On one level, the stockexchange is a self-regulatory body in that it is made up of member brokerage houses and setsregulations which it imposes on itself. On the second level, the government monitors theexchanges and sets further regulations to ensure their policy objectives are met. Forexample, in British Columbia, the Vancouver Stock Exchange is monitored by the B.C.Securities Commission.It has been argued by Easterbrook (1986) and Edwards and Edwards (1984) that inthe presence of manipulative activity, exchanges are capable of optimally restrictingmanipulation without further help from government. The social costs of manipulation areinternalized by an exchange, either directly or indirectly. To the extent that manipulationforces investors out of the market, either because they perceive it to be unfair or because the52extra noise makes it less useful, an exchange is affected directly through lower tradingvolumes, and therefore, less revenues. To the extent that manipulation decreases allocativeefficiency, an exchange is affected indirectly. The government which acts in the publicinterest will put pressure on an exchange when it feels that the exchange is compromisingallocative efficiency. This pressure forces an exchange to internalize the costs which do notaffect them directly. Thus, an exchange will optimally set regulation in order to limitmanipulation. Since the government and the exchange's goals are basically aligned withregards to manipulation, we have assumed in our model that there is only one regulator.II. The Illiquidity Cost Imposed on the Large, Informed TraderIf w, the illiquidity cost imposed on the informed trader, were not large enough topersuade the informed trader to sell at time 2 then the uninformed trader would not earn anyprofits. If it were optimal for the informed trader to wait until time 3 to sell but theuninformed trader still sold at time 2 then the small investor would know for certain thatthey were trading with the uninformed trader at time 2 and that 7t=ru =0.5. P2 would thenbe less than PI because P 1 would be partially a function of 71 which is greater than 71 .Therefore, the uninformed trader would face a loss. Furthermore, if the uninformed traderwere to also wait until time 3 to liquidate his position, then he would again face a loss sinceP1 would be greater than Tufl + (l-r")L, the expected liquidating dividend at time 3 for theuninformed trader. This again follows because P 1 is partially a function of T1, where r' >r". Therefore, in order to expect positive earnings, the uninformed trader requires the53illiquidity cost imposed on the informed trader to be large enough to make him want to sellat time 2.In order to find the break even point for w, where the informed trader is indifferentbetween selling at time 2 and time 3 we must look at his payoffs from doing both. Giventhat bad news is not announced at time 2, if the informed trader were to sell at time 2, hisearnings would be (P2 - P1)B, and if he were to sell at time 3, his earnings would be (H -P1)B - w. Therefore, it must be the case that w (H - P 2)B in order for it to be optimalfor the informed trader to always sell at time 2. 21III. An illiquidity Cost Imposed on the Small InvestorIn our model, we assumed that the small investor does not face an illiquidity costwhen the regulator imposes random trading halts. As in Allen and Gale (1992), we couldassume that the small investor plans to invest in a project for the long term and that he is apassive player in the market. However, if the opposite were true and the small investorwere to face an illiquidity cost in the presence of possible trading halts, then his expectedutility would be negatively affected. 22 If the cost were large enough then it could offset thebenefits from trading halts, namely, the reduction in noise created by the possible presenceof the manipulator, and cause the expected utility to decrease as ir increased. In this case,the regulator's actions would not be of benefit to the market and the optimal solution would21 If bad news is announced at time 2, then the informed trader will always want to sell at time 2 as long as w isnon-negative. This is because the payoff from selling at time 2 -- - Pi)B -- will be higher than that from selling attime 3 --(L- Pi)B - w.22 A table of the small investor's final payoff in each state given the existence of the illiquidity cost is presentedin Appendix E.54be to keep 7 = 0 even if this meant that the riskfree project would be chosen. Using theexogenous variables from the example in Chapter 3, the graph in Appendix E shows therelationship between the small investor's expected utility and 7, as the illiquidity cost to thesmall investor, c, is increased. For some values of c, the small investor's expected utilitystill increases with 7, however, at a slower rate. In these instances, the regulator wouldhave to set T at a higher value (than if there were no illiquidity cost, c) in order to convincethe small investor to invest in the risky project. As long as the informed trader is stillwilling to participate at the higher level of 7, this would be an optimal strategy. Thus, thepresence of an illiquidity cost imposed on the small investor can mitigate the benefits oftrading halts and might even make them useless in the face of manipulation.IV. Information StructureOur information structure is very similar to that of Allen and Gale (1992). In theirpaper, they provide as an example in support of their choice of structure, a company in itsdevelopmental stage. Developing a product or a manufacturing technique requires many testbefore it can be determined if it is a viable product or process. An early test which fails isbad news and can be announced; however, it is not until after many tests that success canbe announced. As another example, suppose that a company is facing a possible lawsuit andthe informed trader finds out that it is unlikely that the lawsuit will be filed. The longer theperiod that a lawsuit is not announced, the greater the chance that no lawsuit will be filed.Thus, bad news (i.e. the announcement of the lawsuit) will occur earlier than good news (i.e.55the realization of no lawsuit). We can, therefore, think of situations where this type ofstructure exists.In our model, we only examine the profitability of 'long' manipulation, where theuninformed trader buys first and then sells. It seems reasonable to assume that 'short'manipulation is also possible if the structure were changed to good news before bad news.However, this is not the case. As Allen and Gale (1992) argue, under the currentframework, a bear raid would not be successful since "the sale of stock at date 1 w[ould]lower the price below the expected value at date 2." 23 The reason for this is that the riskwould be loaded on the risk averse small investor instead of the risk neutral large trader.The small investor would only purchase at time 1 and take on the risk at a relatively lowprice. In practice, evidence shows that 'short' manipulation (bear raids) are less frequentthan 'long' manipulation, possibly because of the additional cost associated with marginaccounts when shorting a security.'Our information structure is restrictive, and our results must be considered with thisin mind. We have only looked at one specific scenario where manipulation is profitable andcan cause economic inefficiency. It is unclear how disruptive manipulation might be underother circumstances and how effective trading halts might be in these cases.23 Allen and Gale (1992), pg. 518.24 See Edwards and Edwards (1984).56V. Risk Aversion of Small InvestorIn this model, as in Allen and Gale's (1992) model, the small investor must be morerisk averse than the large trader in order for manipulation to be profitable. If this were notthe case, then the informed trader would never enter because he would always trade at a lossin the possible presence of the manipulator. Consequently, the manipulator would not beable to pool with the informed trader and deceive the small investors. In Appendix F, weprove that when the small investor is risk neutral, the informed trader's expected profit isnon-positive. Thus, the difference in risk aversion among the market participants, bymotivating trade in the first place, is important to our results.VI. Correlation Between Large Trader Type and TtIn order to distinguish between the informed and uninformed large trader, we attacheda different probability of good news to each. By setting the probability of good news giventhe uninformed trader, rU = 0.5, the uninformed trader has the least possible precision inhis information (i.e. when there are 2 possible payoffs, the greatest variance of payoffsoccurs when probabilities are set at 0.5 and 0.5). Thus, the informed trader has greaterprecision as long as his probability of good news is not 0.5. Unfortunately, in a binomialdistribution this difference in precision creates a difference in mean payoff. If Naturechooses the informed trader, then the project's expected payoff is higher. Is this correlationplausible in practice? As one example, consider the existence of short-selling constraints.In this case, an informed trader will only be interested in seeking out good news about aproject. Thus, if an informed trader is chosen, it does seem plausible that the expected57payoff will be higher than if the uninformed trader were chosen. As another example,suppose the project involves a resource company which has staked a piece of land. Withprobability 0 this land is rich in minerals. If it is, then a truly informed miner will knowthat it is and will be willing to buy. However, if it is not rich in minerals then theuninformed manipulator may want to deceive the market into believing that it is a valuableresource site. As long as the small investor is unable to distinguish between the informedminer and the uninformed manipulator then the pooling equilibrium described in our modelwill hold. Again, it seems reasonable that in the presence of the informed trader theexpected payoff could be higher.VII. ConclusionOur model contains some restrictive assumptions so care should be taken in applyingour results. They cannot be easily generalized to other situations. Since such restrictiveassumptions appear necessary for profitable manipulation, it suggests that, in practice, trade-based manipulation may not be profitable under a lot of circumstances.58Chapter 5Policy Implications and ConclusionI.^Policy ImplicationsOur model and the numerical example in Chapter 3 show how the use of randomtrading halts can be used to encourage allocative efficiency by mitigating the negative effectsof trade-based manipulation. The optimal strategy does not necessarily result in the completeelimination of manipulative activity. Allocative efficiency can exist in a market that is notcompletely devoid of trade-based manipulation. Thus, the regulators' objectives of creatinga fair 'playing field' and of promoting economic efficiency do not necessarily require thesame response. Creating a fair 'playing field' might require the complete elimination oftrade-based manipulation, while promoting allocative efficiency might only require preventivemeasures which mitigate the effects of manipulation. In this case, regulators must weightheir objectives before the optimal policy can be designed.Our model also demonstrates the competing interests that a regulator of a securitiesmarket must contend with. The possible presence of manipulative activity can force someinvestors out of the market leaving the market more illiquid and also threatening allocativeefficiency. The regulator's response in this instance might be to use random trading haltsto reduce the noise created by the manipulator and convince those marginal investors toremain in the market. However, this will come at a cost to other participants who areaffected by the illiquidity that the trading halts create. There is a conflict of interest between59those who are most affected by the manipulative activity and those who are most affected bythe trading halts. The regulator must consider how best to balance these conflictingconcerns. The optimal strategy is one where the marginal social benefit of restrictingmanipulation equals the marginal social cost resulting from the policy created to mitigatemanipulation or its effects. In our model, the regulator's response became one of interferingas little as possible in order to achieve her objective.The regulator's strategy in our model appears quite simple. She only needs to setrandom trading halts in order to reduce the effect of manipulation in the market. However,determining when and with what probability is a complicated issue and requires knowledgeof the probability of manipulation in the market at any particular time. This appears to bea difficult, if not an impossible obstacle to overcome. In practice, regulators monitor marketactivity: both volume and price changes. From this data, they make inferences about thepossible presence of a manipulator and halt trading when suspicious trading activity occurs.Our model demonstrates that if done correctly, trading halts may be an effective weaponagainst trade-based manipulation.II. Future ResearchAlthough we have only concentrated on the simplest form of trading halts, other typesof halts, such as position limits or price limits, may also be effective in reducing the noisecreated by manipulative activity. A model similar to ours could be developed in order toanalyze their impact on the problem of trade-based manipulation. Empirically, these60different types of halts can be studied to try to ascertain which is the most effective at theleast cost.Trading halts initiated by exchanges could also be analyzed to determine if there areany common denominators with regards to the type of information revealed, the presence ofblock trades, or the price movement around the halts. The more that is learned about thetools available to regulators, the more effective the regulators can be at designing policy.Finally, as mentioned in the previous chapter, we have only looked at one specificinstance where profitable manipulation can curtail investment. Our results cannot begeneralized to other circumstances. It is, therefore, unclear how disruptive trade-basedmanipulation is over all and how effective the use of trading halts would be in mitigating anyresulting effects.III. Concluding RemarksBecause trade-based manipulation is difficult to verify the threat of prosecution maynot be an effective tool in preventing it. Trading halts, on the other hand, interfere directlywith the manipulator's activity and therefore the possibility of random trading halts may beenough to limit the entrance of manipulators, or at least reduce the negative effects ofmanipulation. In this paper, we only consider the simplest form of trading halts. However,to the extent that price and position limits are forms of trading halts, they too may beeffective.61Trade-based manipulation creates noise or misinformation in the market because itinterferes with the actions of the truly informed trader. The price discovery process ishampered and the true value of a security is not revealed as quickly. Our model describesa situation where trade-based manipulation can cause inefficiencies through the curtailmentof investment. It also demonstrates how the introduction of random trading halts canmitigate the negative effects of manipulation. In some instances, there appears to be anequilibrium which fosters economic efficiency even with the continuing existence ofmanipulative activity. However, trading halts also increase the cost of trading for someparticipants because they introduce additional illiquidity to the market. Regulators must beconscious of the trade-off between these two competing interests when setting policy to dealwith manipulation.62ReferencesAllen, Franklin, and Douglas Gale, "Stock-Price Manipulation," Review of FinancialStudies, 1992, Vol. 5, No. 3, pg. 503-529.Ausubel, Lawrence M., "Insider Trading in a Rational Expectations Economy," AmericanEconomic Review, Dec. 1990 Vol. 80, No. 5, pg. 1022-41.Bernhardt, Dan, Burton Hollifield, and Eric Hughson, "Investment and Insider Trading,"Manuscript, Sept 1992.Brander, James A., Government Policy Toward Business, Toronto: Butterworths CanadaLtd., 1988.Chichilnisky, Graciela, "Manipulation and Repeated Games in Futures Markets," Chapter6 in The Industrial Organization of Futures Markets,  ed. Ronald W. Anderson, Lexington:D.C. Heath and Company, 1982.Coleman, Thomas C., R. Steven Wunsch, and Robert R. Davis, Panel Discussion onTrading Halts and Price Limits, Review of Futures Markets, Vol. 7, No. 3, 1988, pg 435-50.Coleman, William D., "Financial Services Reform in Canada: The Evolution of PolicyDissension," Canadian Public Policy, XVIII:2, pg 139-52.Cooper, David J., and R. Glen Donaldson, "Manipulating Futures Markets and CommodityPrices by Corner and Squeeze," Draft: January 31, 1993.Donaldson, R. Glen, "Some Economic Effects of Price Manipulation in Futures Markets,"Manuscript, January 22, 1993.Easterbrook, Frank H., "Monopoly, Manipulation, and the Regulation of the FuturesMarkets," Journal of Business, 1986, Vol. 59, No. 2, Pt. 2, pg. S103-S127.Edwards, Linda N., and Franklin R. Edwards, "A Legal and Economic Analysis ofManipulation in Futures Markets," Journal of Futures Markets, 1984, Vol. 4, No. 3, pg.333-366.Fischel, Daniel R., and David J. Ross, ^"Should the Law Prohibit 'Manipulation' inFinancial Markets?" 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Heath and Company, 1982.Vila, Jean-Luc, "The Role of Information in the Manipulation of Futures Markets," Draft:Oct. 1988.Vila, Jean-Luc, "Simple Games of Market Manipulation," Economics Letters 29, 1989, pg21-26.64Appendix AH = high payoff of project,L = low payoff of project,V8 = liquidating dividend in state s, V 8 E [L or H],We = final payoff of small investor in state s,0 = probability that the agent is informed,rt = probability that the project will payoff H given the large trader t ischosen, where t E T = {I, U},b(t) = probability that large trader t issues a buy order at time 1,7r = probability that the regulator will halt trading at time 2, given the riskneutral trader buys at time 1,w = the cost imposed on the informed agent of waiting until time 3 to sell.65rs = conditional probability of state s occurring given the large trader buysat time 1 and no announcement is made at time 2, s E [U5, U6, II],(1 - e)b(U)ru rU5 = (1 - 0)b (U) + Ob (1)7-1rU6 =^(1-0)b(U)(1-7-u)(1 - 0)b(U) + eb(1)710 b (Or'r„ =1 - e)b(U) + 0 3 b (I) riAt = conditional probability of large trader t buying at time 1 given that alarge trader buys at time 1.A = ^(1 - 0)b(U) u^(1- 0)b(U)+0b(1)A = ^0 b (I) I^(1 - 0)b (U) + Ob (I)66Figure B.1 t■1 t-2 t■3Appendix B - Model of Manipulation and Trading Halts6 1.Appendix CFigure C.1 - Small Investor's Expected Utility vs. b(U)As b(U) increases, the small investor's expected utility decreases. At approximatelyb(U) = 0.51 the small investor becomes indifferent between the two projects.68Appendix DFigure D.1 - Small Investor's Expected Utility vs. wAs the probability of halts, 1r, increases, the small investor's expected utility alsoincreases. At approximately 7 = 0.18 the small investor becomes indifferent between thetwo projects.69Figure D.2 - Large Traders' Expected Utilities vs. wThe large traders' utility function is discontinuous where the small investor is indifferentbetween the 2 projects.70Figure D.3 - Sum of Expected Utilities vs. 7The function is equal to:0 Eprofit] + (1-0) Eu[Profit] + Es/Utility]The optimal level of w occurs where the small investor is indifferent between the 2projects.710.070^0.01^0.02^0.03^0.04^0.05^0.06Probability of Halta-0 -111- CO 1^c-0.2^c-0.3 ^c-0.40.06 0.09 0.1Small Investor's Expected UtilityGiven Different Levels of Illiquidity Cost3.70159.7013.70053.73.69963.6993.6886c-O 5--x-Appendix EFigure E.1 - An Illiquidity Cost Imposed on the Small InvestorAn illiquidity cost imposed on the small investor reduces the benefits from trading halts.At a certain level, the cost completely offsets the benefits and the expected utilitydecreases with an increase in '71".72Table E.1 - The Small Investor's Final Payoffs Given an Illiquidity CostState^ Final Payoff^Ul HU2^ LU3^ H + (P1-H)B - cU4^ L + (P1-L)B - cU5^ H + (P1-P2)BU6^ L + (P1-P2)BIl^ H + (P1-P2)B12^ L + (P1-L)B13^ H + (P1-H)B - c14^ L + (P1-L)B - c15^ H16^ L73Appendix FIf the small investor were risk neutral then the informed trader would never be ableto trade at a profit in the possible presence of the manipulator. To begin, the equilibriumprices would be as follows:P1 = (1 - x)[ru H + (1 - ru )L] + x[r'H + (1 - r )1,]x b (l)(1 - 0)b (U) + 0 b (I)P2^(1 - ATUH + (1 - TU)L] + yH0 b (I) Ti(1 - 0)b (U) + Ab(I)r'where y < x.To prove this, we can show that:0 b ^0 b (I) (1 - 0)b (U) + 0 b (l)r1^(1 - 0)b (U) + 0 b (I)r1[(1 - 0)b (U) + 0 b (I)] < (1 - 0)b (U) + 0 b (I)r1r (1 - 0)6 (U)^(1 -6)b(U)The last line is true as long as Ti < 1.Now, in order to prove that the informed trader cannot expect to profit when thesmall investor is risk neutral, we show that his expected value of the asset at time 2, ED/2]],=74is less than the price at time 1. We will only prove this in the instance where w = 0. Inother words, we will show that:EIV2] = TI P2 + (1-r') L < Pi .Proof:E i [V2 ] =^74(1 -y)(ru H + (1 - ru )L) +y Hi+ (1 - r1)L= [ri ru (1 - y) + rly]I- +[r (1 -y)( 1- ru)+( 1- r1)]LP1^= [(1 - x) ru +x7-111 +[(1 - x)(1 - ru) +x(1 - r1)]LIn order to show that ED/ 2] < P1 , we only need to show that:(1-y) T1 TU^y T < (1-x) TU + X TI .Since y < x, then y^< x 7', and it is sufficient to prove that:(1-y) 7-1 TU < (1-x) TU.Or:(1 - 0)b (U)r ru^<^(1 - 0)b (U)ru(1- 0)b(U) + Ob(I)r'^(1 - 0)b (U) + Ob(I)71(1 - 0)b (U) + 0 b (I)] < (1 - 0)b (U) + Ob(I)r'r'(1 - 0)b (U)^(1 -0)b(U)Again the last line is true as long as Ti < 1. Thus, we have shown that the informedtrader's expected value of the asset at time 2 is less than the price of the asset at time 1,when the small investor is risk neutral. Therefore, he can not expect to profit by tradingwith the risk neutral small investor. Since the presence of the regulator imposes an75illiquidity cost on the informed trader, his losses only get worse when the regulatorintervenes with random trading halts (given the illiquidity cost is sufficiently large).76


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