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Relative value analysis Ney, David James 1968

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RELATIVE VALUE ANALYSIS by DAVID JAMES NYE B.Com., University of B r i t i s h Columbia, 1965 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION i n the Department of Commerce and Business Administration We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June 1968 i i i In presenting t h i s thesis i n p a r t i a l f u l f i l l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. David J . Nye Department of Commerce and Business Administration The University of B r i t i s h Columbia, Vancouver 8, Canada. Date August 13, 1968. ABSTRACT This study i s an empirical analysis of a technical stock s e l e c t i o n technique. A random sample i s studied for the period 1956 - 1967. P o r t f o l i o s are constructed and managed by building a model containing three v a r i a b l e s — r e l a t i v e earnings, r e l a t i v e price-earnings and r e l a t i v e p r i c e s . The objective of the study i s to gather evidence which w i l l test the hypothesis that r e l a t i v e value analysis selects p o r t f o l i o s whose rate of appreciation i s greater than that of a buy-and-hold strategy or that of the market. The r e s u l t s of the analysis support the hypothesis. With few exceptions the s t r a t e g i e s ' rates of appreciation are up to several percentage points higher than the rate of appreciation of both the market and the buy-and-hold strategy. Secondly, p o r t f o l i o s which are constructed using both fund amental analysis and r e l a t i v e value analysis show even higher rates of appreciation. As a consequence of the r e s u l t s obtained, a general conclusion and several s p e c i f i c conclusions are reached. The general conclusion formed i s that r e l a t i v e value analysis i s a p r o f i t a b l e stock s e l e c t i o n technique. More s p e c i f i c a l l y , i t i s concluded that: (a) Trends i n stock prices do e x i s t . (b) Fundamental analysis serves an important function i n sel e c t i n g s e c u r i t i e s to maximize p o r t f o l i o returns. (c) The analyst who uses the r e l a t i v e value method w i l l make buy and s e l l decisions which r e s u l t i n the selected p o r t f o l i o outperforming the market. TABLE OP CONTENTS CHAPTER PAGE I. INTRODUCTION . 1 Purpose and Scope of the Study 2 D e f i n i t i o n of Terms Used 4 I I . THE CONCEPT OF RELATIVE VALUE ANALYSIS 15 The Five-Stage Theory 15 Risk 22 I I I . RELATIVE VALUE - REVIEW OF THE LITERATURE . . . 2? IV. DEVELOPMENT OF THE MODEL 61 Development of the Model 6 l Results of the Test ?2 V. CONCLUSIONS 82 BIBLIOGRAPHY 86 APPENDIX i : EXCHANGE LISTING REQUIREMENTS . . . . 89 APPENDIX I I . TABLES 10 - 13 . . . . 91 APPENDIX I I I . GRAPHS A - D 100 LIST OF TABLES TABLE PAGE 1. Summary of Whitbeck & Kisor Test Results . . . 36 2. Summary of R. Levy's Test Results . . . . . . 42 3. Results of Testing the V a l i d i t y of the Five-Stage Hypothesis ; • . . 45 4. T r a n s i t i o n Matrix . . . . : . 47 5. Study No. 1 - Test Results 1952-1963 . . : . . 49 6. Results of Multiple Regression Analysis . . . 56 7. Percent of T o t a l Number of Purchases Executed During I n i t i a l 20% of Sample Time Period 71 8. Summary of Results of Study No. 1 - 1964-1967. 72 9. Compound Growth Rate of Study No. 1 on a Dollar Commitment Basis 79 10-13. Appendix II 91 LIST OP FIGURES FIGURE PAGE A. Graph of Superior Earnings Performance . . . . . 5 B. Graph of Average Earnings Performance . . . . . 5 C. Graph of Below Average Earnings Performance . . . 5 D. Graph of Five-Stage Cycle . . . . . . . . . . . . 14 E. Expected D i s t r i b u t i o n of Relative Price i n Period t+1 Given a Level of y i n Year t . . . . 25 F. Relative Price - Dynamic and Static Models . . . 60 G. S. & P. Composite p-e Ratio 69 CHAPTER I INTRODUCTION T r a d i t i o n a l l y , each investor has had one or more of the following objectives: (a) The preservation of c a p i t a l . (b) The preservation of the purchasing power of the d o l l a r . (c) To earn an adequate return on investment. (d) To maximize return on investment. Various techniques have been suggested i n order that an investor may properly manage his p o r t f o l i o and thereby achieve his objectives. T r a d i t i o n a l l y , f i r s t of a l l one evaluated stocks on the basis of either fundamental analysis i or technical a n a l y s i s . More recently, however, the Theory of Random Walk has been gaining acceptance as a good pre d i c t o r of security price f l u c t u a t i o n s . As a r e s u l t , the Theory has been used to c r i t i c i z e the use of technical analysis, since the l a t t e r assumes the existence of trends i n stock price movements. The next step i n the management of p o r t f o l i o s was to determine not only the percent d i s t r i b u t i o n of s e c u r i t i e s i n i & < i p i e a S e r e f e r to Section II of t h i s chapter f o r d e f i n i t i o n of termsL 2 the p o r t f o l i o hut also how thi s d i s t r i b u t i o n should vary over time. In spite of the large amounts of e f f o r t which have been devoted to determining the best a l l o c a t i o n of investor resources i n order to meet s p e c i f i c objectives, there i s a notable lack of investment techniques which are able to s a t i s f y the investor whose aim i t i s to "outperform" the market.3 I. PURPOSE AND SCOPE OP THE STUDY Purpose. This study was undertaken i n order (1) to investigate the hypothesis that r e l a t i v e value analysis enables the investor to make buy and s e l l decisions which permit him to a t t a i n h i s objective of outperforming the market; (2) to off e r support to the "tr e n d i s t " school, which advocates that technical analysis of stock price data i s a pr o f i t a b l e technique; (3) to answer c r i t i c i s m s ^ of my previous study.5 3"Outperforming" the market i s an expression used to indicate that the selected p o r t f o l i o exhibited a greater growth rate than the market, as measured by an Index. ^The conclusion reached i n thi s study was that i t was possible to consistently outperform the market. This conclusion was challenged on two grounds. F i r s t of a l l , the time period selected (1952-1963) was one of generally r i s i n g price-earnings r a t i o s and therefore one did not need th i s technique to out perform the market. Secondly, the universe of firms from which the sample was selected was neither s u f f i c i e n t l y large ( i t contained only 70 firms) nor was i t representative of the stock market as a whole. ^Davld J . Nye, Relative Value Analysis, unpublished Bachelor of Commerce Thesis, University of B r i t i s h Columbia, Vancouver, May, 1965. 3 The scope of the study i s very narrow but i s never theless of considerable s i g n i f i c a n c e . Importance of the Study. The study i s important because, f i r s t of a l l , i t explores a stock s e l e c t i o n technique which has not been thoroughly investigated to date. It deals with the " a r t " of investing and attempts to contribute to the body of knowledge i n t h i s area. The word "a r t " i s used rather than science for the following reason. Given that the stock market approaches the economist's i d e a l of a perfect market, i . e . , excluding those who have both the means and the a b i l i t y to maintain^ a market i n a p a r t i c u l a r security or act on the basis of "inside" information, the successful investor i s more of a behaviorlst than a s c i e n t i s t . The past ten years has seen a notable Increase i n the use of quantitative techniques i n security valuation and s e l e c t i o n and they may safely be c a l l e d progress. However, the most sophisticated model must s t i l l include one important v a r i a b l e — p e o p l e and t h e i r expectations. Our present l e v e l of technology i s improving i n i t s a b i l i t y to understand, measure and predict the actions of people but much remains to be done. This, of course, excludes the " s p e c i a l i s t s " employed by the New York Stock Exchange, whose function i t i s to maintain an orderly market for the benefit of a l l investors. See Baumol, The Stock Market and Economic E f f i c i e n c y . A second reason why thi s study is important i s the Implication which successful technical analysis has with regard to the r o l e of fundamental analysis of s e c u r i t i e s . If p r o f i t s , i . e . , appreciation i n the price of a security, can be earned which are equal to or better than those a t t a i n  able by the use of fundamental analysis i n stock evaluation, then the a l l o c a t i o n annually of substantial resources by the investment Industry could be c r i t i c i z e d on the grounds that the funds are not being put to t h e i r most productive use. I I . DEFINITION OF TERMS USED Relative Earnings: Relative earnings are defined as the earnings per share of the firm for a 12-month period divided by the earnings per share of the market index for the same 12-month period. Mathematically, t h i s may be expressed as: X i t = ^ l t E t Where: X = the 12-month r e l a t i v e earnings per share of the i th security at time t e l t = earnings per share of the i th company's stock for the 12-months ending at time t E t = the earnings per share of the market index for the 12 months ending at time t Relative earnings may be computed for a series of time periods and plotted on semi-log graph paper, as shown i n the following figures: A B C Superior Earnings Average Earnings Below Average Performance Performance Earnings Performance Relative Value (Log scale) Time As i s shown i n the fi g u r e s , X may be trending upward, downward or h o r i z o n t a l l y , i . e . , the slope of the r e l a t i v e earnings l i n e may be p o s i t i v e , negative or zero. Consider the following, i f we l e t : e = de = the rate of change of the firm's earnings dt with respect to time. E = dE = the rate of change of the Index's earnings dt with respect to time. Then: Case (a) arises when (I) e > £ ( l i ) -e > -E Case (b) arises when ( i ) e = £ ( i i ) -e = -E Case (c) arises when ( i ) e < E ( i i ) -e < -E Then dX w i l l be positive (Case (a) ) when ( i ) e > E, dt ( i i ) -e > -E. S i m i l a r l y , dX w i l l be negative (Case (c) ) dt when ( i ) e < S or ( i i ) -e < -E and dX w i l l equal zero when dt ( i ) e = E or ( i i ) -e = -E. Relative Price: Relative price i s defined as the price of a stock at a pa r t i c u l a r point i n time divided by the price of a market index at that same point i n time. For purposes of this study, r e l a t i v e price i s repre sented as and i s equal to p ^ where: *T p l t = the price of the 1 th security at time t P t = the price of the market index at time period t . As indicated i n the case of r e l a t i v e earnings, the slope of the r e l a t i v e price l i n e dY may be either p o s i t i v e , dt negative or zero. By determining whether dY i s greater than dt or less than zero, the analyst i s able to measure whether a security i s outperforming the market. Thus, i f dY i s > 0 dt f o r a security, then that security i s outperforming the market Relative Price-Earnings Ratio: The r e l a t i v e p r i c e - earnings r a t i o i s defined as the price earnings r a t i o of the stock divided by the price-earnings r a t i o of the market index. 7 i t should be noted that dY may be po s i t i v e , although dt the change inp^. f o r the same period i s negative and vice versa This may be expressed mathematically as: Z i t = P e l t PE t Where: p e l t = the price-earnings r a t i o of the i th security at time t PE. = the price-earnings r a t i o of the market index. The slope of the r e l a t i v e price-earnings l i n e (defined as dZ) dt offers a reasonably good measure of investor "enthusiasm" for a secur i t y . If dZ i s positive for a reasonably long period dt of time, e.g., 2-3 years, the slope of the l i n e indicates that the security enjoyed investor popularity during that period of time. Conversely, i f dZ i s negative for a similar dt period, t h i s i s good evidence that the stock i s out of favour and therefore should be avoided i n most cases. Relative Value Analysis: Relative value analysis i s the use of the variables ( r e l a t i v e earnings, r e l a t i v e price and r e l a t i v e price-earnings) to decide when a stock should be included and when i t should be eliminated from a p o r t f o l i o . Fundamental Analysis: Fundamental analysis i s the analysis and forecasting of economic, industry and firm factors i n order to determine the i n t r i n s i c or t h e o r e t i c a l value of a security at a s p e c i f i c point i n time. The logic behind t h i s method i s that i f the th e o r e t i c a l value i s greater than market price, the stock should be purchased. Conversely, 8 i t should be sold i f the i n t r i n s i c value i s less than the market value. Opposed to th i s idea are the membeis of the techni c a l analysis school. Technical Analysis: Technical analysis i s the study of security prices only i n order to make an investment decision. This analysis i s founded upon the b e l i e f that a l l factors a f f e c t i n g a security are r e f l e c t e d i n i t s price eventually and one has only to interpret c o r r e c t l y the stock's price trend i n order to predict accurately i t s price f l u c t u a t i o n s . This method of analysis assumes the existence of trends i n successive price differences. Lately, t h i s assumption has been severely c r i t i c i z e d by some members of the academic community, who have proposed, as an a l t e r n a t i v e , the Theory of Random Walk. Random Walk Theory: B r i e f l y , the Random Walk Theory is defined here to mean that price changes of a stock are s t a t i s t i c a l l y independent of each other. Nothing can be learned about the future by looking at the stock's price s e r i e s . Thus, buying a stock based on signals from a price chart w i l l produce r e s u l t s no better than those from repeated f l i p p i n g of a f a i r coin. 9 Growth Stock; Since the concept of a growth stock i s quite important to the Theory of Relative Value Analysis, more space than usual i s devoted to i t s d e f i n i t i o n . As i n other areas of finance, the theories of d e f i n i t i o n and valuation of growth common stocks have moved from a generally q u a l i t a t i v e approach, such as that taken by Jenks, Kotler and Bernstein, to a quantitative method, such as that suggested by B u r r e l l , Solomon, and, more recently, Mao. Bernstein^ makes an important d i s t i n c t i o n between a growth company and a growth stock. To him, a growth company i s not one whose sales and earnings increase merely as a r e s u l t of the firm's response to favourable external factors, such as population increase; rather, he sees true growth as being "inner directed." In other words, the management of a growth firm i s the d r i v i n g force. "The a b i l i t y to create i t s own market i s the s t r a t e g i c , the dominating, and the single most disti n g u i s h i n g c h a r a c t e r i s t i c of a true growth company."9 Opposed to th i s view i s Kotler's somewhat loose d e f i n i t i o n of a growth s i t u a t i o n . "... a growth stock i s the stock of a company which has shown for a number of years and/or i s showing annual percentage increases i n net earnings which °P. Bernstein, "Growth Companies versus Growth Stocks," Harvard Business Review, v o l . 34, No. 5 (September-October 1956), pp. 87-98. 9 I b i d . , p. 91. s u b s t a n t i a l l y exceed the long run growth rate i n the economy A® 11 To Jenks, x a growth company means "a company that w i l l eventually be successful and that is now i n or entering a phase of rapid development." He enumerates several character i s t i c s of growth companies such as high multiples, low y i e l d s , plus several other technical price patterns. Although the a r t i c l e i s easy to read, i t i s at a low l e v e l and does not represent a s i g n i f i c a n t contribution to the theory. B u r r e l l , ^ writing In I960, suggests that two Important factors i n valuing growth companies are the h i s t o r i c a l growth rate of the dividend and investor expectations. He suggests that a measure of investor expectations i s the past r e l a t i o n  ship of dividends to market price with an a d d i t i o n a l indicator being current stock market l e v e l s . The current price i s the sum of the present values of two elements—the present value of the s e l l i n g price at some future date plus the present value of an annuity of the i U P . Kotler, "Elements i n a Theory of Growth Stock Valuation," Readings i n F i n a n c i a l Analysis and Investment  Management. (Ed. E, M. Lerner). Homewood, I l l i n o i s , Richard D. Irwin, Inc., 1963, pp. 355. H j . C. Jenks, "Investing i n Growth Stocks," i b i d . , P. 325. 1 2 0 . K. B u r r e l l , "A Mathematical Approach to Growth Stock Valuation," i b i d . , p. 338. expected increasing dividends. Thus, B u r r e l l must assume a growth rate i n dividends, the duration of the growth, an appropriate c a p i t a l i z a t i o n rate and an appropriate discount r a t e . According to B u r r e l l , the current market price i s then equal to: ' P 0 = D (l+ff? n + £ D 0 /l±_f r D ( l + r ) n 1=1 \l+rj Where: P Q = the proper price to pay for the stock today D 0 = the current dividend per share r Q = the rate which an i n d i v i d u a l investor uses to c a p i t a l i z e a constant size income stream i n perpetuity r = the discount rate which an i n d i v i d u a l investor applies to a future d o l l a r The f i r s t term i s an estimate of the present value of the stock's expected market price i n years hence and the second term i s an estimate of the present value of the expected dividend income over the period. A more current d e f i n i t i o n of a growth company i s that of Mao's: "... a company which has s p e c i f i c opportunities to invest funds at a perpetual after-tax annual return of r , where r i s greater than the stockholder's required rate of return, y ."*3 He summarizes two models of permanent growth 13James C. T. Mao, Quantitative Analysis of F i n a n c i a l  Decisions. unpublished manuscript, University of B r i t i s h Columbia, 1968. Chapter 10, p. 30. as developed "by Solomon*^ and Modigliani and M i l l e r ^ ^ and then develops a model which incorporates exponential growth of earnings, constant growth and dec l i n i n g growth. It i s important to note that these models recognize and incorporate the investment opportunities approach. Thus, i n the f i n a l analysis, dividends are a function of earnings, which i n turn are a function of the opportunity of the firm to invest i t s funds at a rate greater than y. Solomon, The Theory of F i n a n c i a l Management, New York, Columbia University Press, 1963. 15 f. Modigliani and M. M i l l e r , "Dividend Policy Growth, and the Valuation of Shares," Journal of Business, v o l . 34 (October 196l), pp. 421-449. CHAPTER II THE CONCEPT OF RELATIVE VALUE ANALYSIS In Chapter I the hypothesis was stated, and i n t h i s chapter the underlying theory which led to the hypothesis w i l l be given. In addition, the concept of r i s k and i t s r e l a t i o n to r e l a t i v e value w i l l be discussed. I. THE FIVE-STAGE THEORY This theory states that, given a s i t u a t i o n of increasing r e l a t i v e earnings, the market i n i t i a l l y f a i l s to respond favourably to the improved earnings, and then responds i n an exaggerated manner. In other words, the theory rests upon the premise that human beings i n general react i n a manner which i s not proportionate to the o r i g i n a l s t i m u l i . Benjamin F. Graham expressed e s s e n t i a l l y the same idea when he said: One thing badly needed by investors—and a quality they r a r e l y seem to h a v e — i s a sense of f i n a n c i a l history. 1 ° Yet the market tends to greet each upsurge as i f i t were the beginning of an endless growth and each decline i n earnings as i f i t pressaged ultimate extinction. * 7 1 D B . Graham, The I n t e l l i g e n t Investor, 3rd e d i t i o n , Harper & Row, New York (1965), p. 13. 1 ? I b l d . . p. 14. 14 In order to better understand th i s idea, i t i s con venient to divide this process of under and over-reaction Into f i v e stages, as shown i n Figure D. FIGURE D Graph of 5-Stage Cycle Stage 1 2 3 4 5 Relative Value (Log Scale) Time During Stage 1, r e l a t i v e earnings are p o s i t i v e l y sloped while the r e l a t i v e price-earnings l i n e has a negative slope. This means that the firm's earnings are growing at a greater rate than those of the index. At the same time, a f a l l i n g r e l a t i v e price-earnings l i n e indicates that the firm's multiple i s r i s i n g at a slower rate than the multiple of the market i s r i s i n g . On the other hand, i t may indicate that the firm's multiple i s f a l l i n g at a rate greater than that of the market. The impact of the r e l a t i v e earnings and r e l a t i v e price-earnings change upon r e l a t i v e price w i l l depend upon th e i r comparative movements. This idea may be expressed mathematically i n the following manner. As indicated i n Chapter I, we have: X^t = the r e l a t i v e earnings per share of the i th security at time t = the r e l a t i v e price of the i th security at time t = the r e l a t i v e price earnings r a t i o of the i th security at time t . Values of X, Y and Z for a number of time periods may be calculated. Having calculated these values and plotted them on semi-logarithmic graph paper as i n Figure D, i t i s possible to regress these values against time and obtain an equation of the form y = a + bx. In our case we would obtain the following: (1) X = a +o<T (2) Y = b + £ T (3) Z = c + T T Where: a, b and c are constants. oC = the slope of the r e l a t i v e earnings l i n e . ^ = the slope of the r e l a t i v e price l i n e . i f = the slope of the r e l a t i v e price=earnlngs l i n e . 16 Then i f : (a) ©< = ~Y . P = o (b) << > 1$ ; £ > 0 (o) c< < nr ; ? < 0 Stage 1 has been c a l l e d a "base b u i l d i n g " stage since the market largely ignores the improving earnings picture of the firm. This i s an i n t e r e s t i n g occurrence from a behavioural point of view and bears further discussion. Proceeding from the position that an earnings increase i s "better" from the point of view of an investor seeking an outlet for his funds, why should ^ be negative? In other words, why should investors be w i l l i n g to pay r e l a t i v e l y less for increasing earnings? The p o s s i b i l i t y that they are not aware of the increase can safely be ignored. Another p o s s i b i l i t y i s that they are aware of the s i t u a t i o n but believe the Increase to be only a temporary reversal of a long term downtrend as evidenced by previous data. This could be case (c) mentioned previously, where °< K if and the security price i s being adjusted downwards on the basis of revised long term expectations. In case (a), <=*£. = 1$ , i . e . , the slope of l i n e X i s equal to the slope of l i n e Z. Under these conditions, investors appear to believe that earnings w i l l return to a "normal" l e v e l and therefore, the adjustment i n B reflects these expectations. In case (b) i t could be argued that some investors believe the increase to be a fundamental improvement and, on t h i s basis, the f a l l i n g r e l a t i v e price earnings r a t i o does not completely o f f s e t the r i s i n g r e l a t i v e earnings. In t h i s s i t u a t i o n there are enough "believers" to more than of f s e t the "disbelievers" and as a r e s u l t Q i s p o s i t i v e . Expectations are for continued improved earnings but they are by no means unanimous. By focussing on r e l a t i v e earnings, we have excluded many other explanatory variables and they must now be mention ed. According to K i n g , ^ market and industry factors are very important i n the explanation of security price changes. However, by d i v i d i n g firm data by market data, we have excluded the market and industry impact. This brings us once more to the firm and the impact that other variables such as dividends, cash flow and leverage w i l l have on security prices. Rather than attempting to determine the influence of each of these variables as stock price determinants, they are merely mentioned and the discussion w i l l continue to be centered on earnings as an important variable i n determining stock price changes. • L OBenjamin F. King, "Market and Industry Factors i n Stock Price Behaviour," Journal of Finance, v o l . 39, No. 1, Part II (January 1966), p. 139. 18 A good discussion of the concept of changed earnings and Investor expectations i s provided by Whitbeck and K i s o r . 1 ? In t h e i r paper they point out that during a business cycle the multiples of many firms behave i n a c o n t r a - c y c l i c a l manner. Thus, as earnings r i s e , the multiple f a l l s and vice versa. Obviously investors have some notion of "normal" earnings for the firm and the occurrence of a Stage 1 merely indicates that they expect the firm to continue to behave i n a c y c l i c a l fashion. As earnings r i s e , t h e i r expectations do not change and, as a r e s u l t , the price of the security remains f a i r l y constant and the multiple contracts. When earnings f a l l because of a decline i n economic a c t i v i t y , investors expect them to increase when the economy resumes i t s growth. Therefore, security prices are maintained and the multiple expands. Stage 2 i s defined as one i n which r e l a t i v e earnings continue to increase ( i . e . °< > 0) but the r e l a t i v e price earnings r a t i o remains constant ( Y = 0). This stage i n the cycle indicates that investors are r e v i s i n g t h e i r expectations about the future earnings of the firm and as a r e s u l t are w i l l i n g to pay r e l a t i v e l y more for each share i n the b e l i e f !9v. S. Whitbeck and M. Klsor, J r . , "A New Tool i n Investment Decision Making." Reprinted i n Frontiers of  Investment Analysis (Ed. E. Bruce Fredrikson). Scranton, Pennsylvania, International Textbook Company, 1965, pp. 335-350. 19 that r e l a t i v e earnings w i l l continue to expand. As w i l l "be Indicated l a t e r , t h i s stage does not play a s i g n i f i c a n t role i n the concept mainly because of d e f i n i t i o n a l inadequacies. During Stage 3 r e l a t i v e earnings continues to expand and, i n addition, the r e l a t i v e price earnings r a t i o expands, r e s u l t i n g i n r e l a t i v e price substantially outperforming the market. During t h i s stage i n the cycle investors appear to have confirmed t h e i r b e l i e f that t h i s i s a growth firm. They believe that t h i s above average earnings growth i s going to continue u and are, therefore, w i l l i n g to pay more for each share. Stage 3 i s in t e r e s t i n g to consider with reference to the Whitbeck and Kisor theory and the behaviourallst approach. It would appear that investors view the firm from a c y c l i c a l point of view u n t i l Stage 3 occurs. At this time, the over- reaction takes place and the value of the r e l a t i v e price earnings r a t i o increases to a l e v e l which i s not j u s t i f i a b l e when subjected to r a t i o n a l a n a l y s i s . Stage k i s defined as having stable r e l a t i v e earnings, while r e l a t i v e price earnings continue to increase. Thus, a stock i n t h i s stage w i l l continue to outperform the market as i n Stages 2 and 3 (and possibly i n Stage 1 also) but the above average performance i s due s o l e l y to an increasing multiple ^ u I t i s d i f f i c u l t to determine what i s each investor's time horizon for t h i s expected growth. 20 and i s thus a pote n t i a l l y dangerous s i t u a t i o n from the stockholder's point of view. The reasoning behind the occurrence of Stage 4 i s as follows. As r e l a t i v e earnings increase, through Stages 1, 2 and 3> an Increasing number of investors become aware of the superior earnings gains being reported by the firm. As th i s number becomes s u f f i c i e n t  l y large, demand for the stock i s i n i t i a l l y less than supply, then equal, and f i n a l l y exceeds supply. Stage k r e f l e c t s the s i t u a t i o n of continuing excess demand r e s u l t i n g i n the expanding multiple. What i s the reason for t h i s apparent excess demand? It i s suggested that i t i s again the r e s u l t of favourable investor expectations. If expectations are influenced by h i s t o r i c a l data (and i t would appear that they are) then investors, noting the uptrend i n earnings, continue to purchase the stock i n the expectation that t h i s uptrend w i l l continue. Stage 5 occurs when both r e l a t i v e earnings and r e l a t i v e price earnings slope downward, r e s u l t i n g i n a substantial decline i n share value to those holding the security during t h i s stage. As i s inev i t a b l e , almost a l l firms experience an earnings decline at some time or another. When such a r e l a t i v e earnings decline i s experienced, concurrent with i t i s a r e l a t i v e price earnings r a t i o d e c l i n e — a g a i n the r e s u l t of revised expectations based on new information. 21 In a l l probability i t i s u n r e a l i s t i c to think that investors never expect a firm's earnings to decline since the mathematical implications of a high growth rate compounded for even a large f i n i t e time period are absurd. The question then becomes: why would the security continue to be purchased during Stage kl Obviously the answer i s timing. Investors expect earnings to decline eventually but not i n the r e l a t i v e l y near fu t u r e i When the decline occurs, the downward sloping r e l a t i v e price earnings r a t i o implies that the downtrend i n r e l a t i v e earnings i s expected to continue for a time. Other wise, r e l a t i v e price earnings would increase, based on the b e l i e f that the r e l a t i v e earnings decline was only temporary ?1 and that the growth would quickly be resumed. This i s the very broad framework within which we s h a l l be dealing and i t i s expected that there w i l l be exceptions which are not explained by thi s theory. Indeed, i t would be very naive to claim that security price movements can be explained by only one var i a b l e . However, we s h a l l attempt to a t t a i n the previously mentioned objective by means of r e l a t i v e value a n a l y s i s . One of the points to be noted here i s that r e l a t i v e value analysis i s not, nor i s i t claimed to be, a method by which stocks may be valued. Rather, i t focuses on the problem •^"•Some support i s lent to t h i s by B. Graham's previously mentioned statement (see footnote 17). 22 that, given a c e r t a i n security and i t s p r i c e , w i l l i t be a p r o f i t a b l e investment, i . e . , w i l l i t outperform the market? We are not r e a l l y concerned with whether the stock i s under valued or overvalued but only whether that security, i f purchased, w i l l r i s e i n price more than the market or f a l l i n price less than the market. I I . RISK No discussion of investments i s complete without con sidering r i s k , and i n t h i s section r i s k w i l l be studied within the context of r e l a t i v e values. For our purposes the investor may be said to face two kinds of r i s k . F i r s t of a l l , he faces what we w i l l c a l l Internal r i s k op and t h i s r i s k i s defined as the chance of the firm f a i l i n g . The use of the word "chance 0 implies some known probability of the firm f a i l i n g . However, when one considers that Internal 2 1 r i s k includes both business r i s k and f i n a n c i a l r i s k , J the d e r i v a t i o n of a p r o b a b i l i t y function i s a complex, but not impossible, task. Internal r i s k i s reduced to the extent 2 2 " F a i l u r e " i s defined as the condition where the firm has i n s u f f i c i e n t resources to meet obligations as they f a l l due, or, i n Donaldson's words, there exists a s i t u a t i o n of "cash insolvency." 23"Business r i s k " and " f i n a n c i a l r i s k " have the t r a d i t i o n a l meaning. 23 possible by l i m i t i n g stocks e l i g i b l e for i n c l u s i o n i n the sample to those l i s t e d on the New York Stock Exchange as at June 30, 1955»2^ No attempt w i l l be made i n t h i s project to quantify i n t e r n a l r i s k . To the extent that a l l firms must meet these minimum standards, the probability of f a i l u r e i s maximized at a c e r t a i n l e v e l with the larger firms presumably having a probability lower than t h i s maximum. In addi t i o n to i n t e r n a l r i s k * the investor also faces external r i s k , which i s defined as the r i s k of a decline i n the value of the firm due to a l l factors other than Internal r i s k ! The two types of r i s k may be measured by the variance i n the market price of the security. In some work to be d i s  cussed i n a l a t e r chapter i t i s evident that security price fluctuations are a function of market, industry and firm factors. Thus, even though an investor may purchase an interest i n a firm, not only because of i t s demonstrated earning power but also because of i t s opportunities for p r o f i t a b l e investment, he nevertheless i s exposed to the r i s k of a decline i n the value of his shares due to forces external to the firm. He thus faces, for example, the following anomaly; l e t us assume 24N.Y.S .E. l i s t i n g requirements are summarized i n Appendix I i n addition to the requirements of the smaller, regional exchanges. I t i s i n t e r e s t i n g to note that the f i r s t N.Y.S.E. L i s t i n g Committee was formed i n 1866 and, over the years, standards have gradually been r a i s e d . However, since no e x i s t i n g contract i s bound by l a t e r agreements, the im proved standards applied only to the l a t e s t agreements and, l e g a l l y , a previously l i s t e d firm was not bound by the new standards. 2k that our investor i s one of those g i f t e d individuals who i s t r u l y able to forecast the future better than most as a r e s u l t of h i s excellent analytic a b i l i t y , both with respect to economic factors and human behavior. Our investor has bought an interest i n a firm based on his forecast of p r o f i t  able investment opportunities available to the firm. Subsequently a government department announces a policy change which i s expected to adversely a f f e c t this p a r t i c u l a r industry. This announcement r e s u l t s i n changed expectations of present and potential investors and, consequently, the supply of t h i s security exceeds demand, r e s u l t i n g i n a new, lower p r i c e . However, to what extent would investors' expectations be revised as a r e s u l t of l o g i c a l analysis? This i s an extremely d i f f i c u l t question on which to obtain empirical evidence but, i n t u i t i v e l y , we would say not enough. Our investor has assessed the s i t u a t i o n , however, and i s of the opinion that factors exist which w i l l mitigate the effects of the policy change. Although the investor's analysis may be correct, he w i l l suffer a loss or have his p r o f i t s reduced, should he be forced to l i q u i d a t e his holdings before market price has adjusted to the " t h e o r e t i c a l " or " i n t r i n s i c " p r i c e . Recognizing t h i s external r i s k , the investor's objective i s not to minimize variance but to choose a security whose expected d i s t r i b u t i o n of future r e l a t i v e prices i s negatively skewed, (see Figure E) during the time he owns shares i n that company. FIGURE E Expected D i s t r i b u t i o n of Relative Price i n period t+1 given a l e v e l of y i n year t Frequency X H Hooe As Markowitz pointed out, variance i s not a true measure of r i s k since t h i s Implies that deviations on both sides of the regression l i n e are equally undesirable. However, positive deviations are i n f i n i t e l y more desirable than negative ones. Thus, a measure such as the semi-variance i s more meaningful but i t i s also a much more complex programming problem. In t h i s chapter the concept of r e l a t i v e value has been given and, i n addition, the notion of r i s k has been related to the subject of the study. In the next chapter the l i t e r a t u r e on r e l a t i v e value w i l l be reviewed and the subsequent chapter w i l l explain the development of the model. CHAPTER III RELATIVE VALUE - REVIEW OF THE LITERATURE Although the use of r e l a t i v e values i s an intuitively- appealing concept, a review of the l i t e r a t u r e indicates that very few writers have dealt with the subject e x p l i c i t l y . Most investors r e a l i z e that performance must be measured against some standard and one need only r e f e r , for example, to the prospectus of any mutual fund or investment advisory service to see the use of r e l a t i v e value. However, the i n t e r e s t i n g point to note i s that very few investors appear to have investigated the r e l a t i o n s h i p between the security and the standard i n order to determine i f a meaningful and consistent pattern e x i s t s . The e a r l i e s t reference t h i s writer was able to f i n d was that of Rose,25 where r e l a t i v e values were used more as a descriptive t o o l , rather than an a n a l y t i c a l s e l e c t i o n technique. Rose Rose's main purpose was to study the rates of return achieved by f i n a n c i a l i n s t i t u t i o n s on t h e i r s e c u r i t i e s p o r t f o l i o and his r e l a t i v e value technique i s shown i n an 2^Dwight C. Rose, A S c i e n t i f i c Approach to Investment  Management. New York, Harper & Brothers, 1928. 28 appendix e n t i t l e d "Relation of Stock Price Trends i n Each Major Industry to the Price Trend of a l l Stocks." As the heading implies, Rose summed the market value of the stocks i n a p a r t i c u l a r group, divided t h i s sum by the market and plotted t h i s r a t i o on semi-log charts for the period January 1, 1918—December 31, 1927. In addition, he employed a scale on the v e r t i c a l axis which indicated the percent v a r i a t i o n of the group from a l l the stocks. One must suppose that the charts were useful to Rose as indicators of past performance of a group, e.g., his automobile group included: 1. General Motors 6. Chrysler Motors 2. Willys Overland 7. Chandler Cleveland Preference 3. Studebaker Corp. 8. Mack Truck 4. White Motor 9. Pierce Arrow 5. Packard Motor Car 10. Hupp Motor Car However, the v a l i d i t y of his index would be open to question because of the weighting system he used. Apparently i t did not occur to him that he should study further the relationships involved to see i f anything meaningful could be uncovered. By 'meaningful' I have i n mind a s e l e c t i o n technique able to choose stocks which w i l l outperform the market. Rhea The discovery of an apparently meaningful r e l a t i o n s h i p ^°Rose did not Indicate, however, which stock market index he used. was made by Robert Rhea, who reported i n a 1933 issue of Barron's^? that he had had some success i n using a r e l a t i v e value technique. Rhea began with the simple observation that during the course of a stock market cycle some issues fluctuate more widely than others i n r e l a t i o n to the Dow-Jones I n d u s t r i a l Average. A stock's v o l a t i l i t y was measured by i t s Index number and Rhea assumed that a stock which h i s t o r i c a l l y had been v o l a t i l e would continue to exhibit v o l a t i l i t y . The security price was related to the market through the use of an appreciation index number derived as follows: (1) Determine the percentage change i n the security f o r time period t (2) Determine the percentage change i n the industry index f o r time period t (3) Divide (1) by (2); then (3) indicates the gain which would have been made on an investment i n the security r e l a t i v e to the gain recorded by the index. Example $ Change ( t ^ - t ) % Change ( t ^ - t Q ) Security 105i75 - 94:25 12.00 (1) Index 24i65 - 20;90 17.94 (2) (1) \ (2) = 12.00 _ I7.9Z4. - » o b ° Thus, t h i s security did r e l a t i v e l y poorer than the index CfRi Hi Rhea, "Stock Habits - A Simple Method to Follow Issues that Fluctuate More Widely than the Averages," Barron's, New York, May 8, 1933, P» !• 30 since, for every $51.00 appreciation of the index, the stock went up only $ .668. A s i m i l a r figure can be derived for declines i n the index. Rhea then determined these index numbers for the 10 declines and 10 r a l l i e s 2 ^ which had occurred i n the 15-month period January 1, 1932—May, 1933* He averaged these figures to a r r i v e at one advance index and one decline index for each stock. These stocks were then divided into three groups of '15 each, according to the following c r i t e r i a . Group I - " l i v e l y " stocks—those that move with the market but with greater v a r i a t i o n i n advances than declines. C h a r a c t e r i s t i c s : (a) absence of dividend payers (b) "heavy" leverage Group II - Price v a r i a t i o n "approximates" that of the average. C h a r a c t e r i s t i c s : (a) mostly dividend payers Group III - Price v a r i a t i o n i s usually less than that of the average. C h a r a c t e r i s t i c s : (a) includes many higher priced stocks (b) dividend payers are i n the majority The re s u l t s of his test were as follows: Group I showed a $3.00 gain for every $1.00 gain.recorded by.Group I I I . ^°A peak was said to have occurred i f the index declined more than 10$ from a given l e v e l . This decline was said to have continued u n t i l the index had r i s e n 10% from a given l e v e l . 31 Although Rhea's method i s not at a l l rigorous and a n a l y t i c a l , i t does take the f i r s t step i n using r e l a t i v e values as a technique to a i d i n the s e l e c t i o n of above average s e c u r i t i e s as well as describing t h e i r h i s t o r i c a l performance. Kourday Although i t i s possible that many investors may have used r e l a t i v e values to a i d t h e i r investment decision making, apparently none of them f e l t i n c l i n e d to report i t , since the next a r t i c l e did not appear u n t i l the early 1960's. At that time M. Kourday published an a r t i c l e 2 ^ i n the F i n a n c i a l  Analysts Journal. His purpose i n writing was to publicize a hypothesis which he had developed and tested during his career as a security analyst. He feels that r e l a t i v e value analysis Is a usefu l technique for comparing s e c u r i t i e s with one another, se l e c t i n g the best one, i . e . , the stock which w i l l outperform the averages, and determining when an issue should be eliminated from a p o r t f o l i o . However, he also states that t h i s analysis should not be the sole decision making t o o l but that i t i s best used i n conjunction with fundamental a n a l y s i s . His basic premise i s that security prices are a function of earnings. As earnings increase, so should the stock's 29 M . Kourday, "Relative Values r- A Method for Outperforming the Market," F i n a n c i a l Analysts Journal, v o l . 19, No. 6 (November-December 1963), p. 35. 32 p r i c e i S i m i l a r l y , as r e l a t i v e earnings increase, r e l a t i v e price should also r i s e . Thus, the share price of the company whose earnings are growing faster than average should show better than average price performance. This c o r r e l a t i o n also exists for the opposite s i t u a t i o n , so Kourday claims. A r e l a t i v e earnings decline should be r e f l e c t e d i n a r e l a t i v e price decline; Where a c o r r e l a t i o n does not e x i s t , then there exists an opportunity to buy or s e l l . For example, i f r e l a t i v e earnings are i n an uptrend but r e l a t i v e price has not shown any growth,3° the stock should be purchased. However, Kourday's apparently flagrant claim of a good and consistent c o r r e l a t i o n over time i s q u a l i f i e d by a d d i t i o n a l hypotheses disguised as " f a c t s " i n other sections of his paper. Thus,"As i s well known, even though there may be a time lag i n earnings reports, the r e l a t i v e market performance of a stock can r e f l e c t a material change."3l The r e l a t i v e price-earnings r a t i o i s a measure of the under or overvaluation of a security. Thus, the amount by which the r e l a t i v e price-earnings r a t i o i s greater than 100$ provides a measure of the premium which investors are paying. This may be compared to the analysts' and others' forecasts of share price to determine whether the premium, i n t h e i r 3° The reader w i l l remember that t h i s has been defined as Stage 1. 3 % i Kourday, op. c i t . , p. 36. opinion, i s j u s t i f i e d . The user of Kourday*s method i s required to forecast not only the earnings of the security under study but also the earnings of the Dow-Jones I n d u s t r i a l Average. For example, i n September the analyst should forecast the l a s t quarter earnings and also the following year's earnings.3 2 From t h i s data, and using current prices, he may determine r e l a t i v e values and evaluate the security from a r e l a t i v e standpoint. Kourday's paper i s very inte r e s t i n g to read; however, he i s not able to provide any s i g n i f i c a n t empirical support for h i s hypothesis other than a few examples mentioned i n the text of h i s paper. In addition, his reasoning proceeds from basic assumptions, for which there i s not empirical evidence. However, as mentioned e a r l i e r , the theory i s i n t u i t i v e l y appealing and deserving of a d d i t i o n a l thought and t e s t i n g . Whitbeck and Klsor Whitbeck and K i s o r ^ u t i l i z e d the r e l a t i v e earnings concept i n t h e i r empirical work which was reported i n 196ji They addressed themselves to the problem of how much to pay 3 2The accuracy of t h e i r forecasts i s i n considerable doubt. See the a r t i c l e by J , G. Cragg and B. C. M a l k i e l . 3 3V. S. Whitbeck and M. Kisor, J r . , "A New 'Tool Investment Decision-making," F i n a n c i a l Analysts Journal, v o l . 19, No. 3 (May-June 1963), pp. 55-62. 34 for a given stock and determining what the proper multiple should be. By p l o t t i n g earnings per share over time on a log arithmic scale and f i t t i n g a least squares l i n e , they determine the slope of the l i n e , i . e . , the average annual growth i n earnings per share and the v a r i a b i l i t y of the earnings as measured by the standard deviation. Proceeding from the assertion that r e l a t i v e earnings and r e l a t i v e price earnings move i n a contracycIleal fashion, they i n f e r that the market has a concept of "normal" or " c y c l i c a l average" earnings for the firm i n question. This "normal" earnings l e v e l i s defined as "... that l e v e l of net income which would p r e v a i l currently i f the economy as a whole were experiencing m i d - c y c l i c a l business conditions.3 ^ Working i n the b e l i e f that there should be a r e l a t i o n  ship between the projected rate of earnings growth and the p-e r a t i o , the authors conducted the following t e s t . For 135 stocks of "general investment i n t e r e s t , " the expected earnings growth rate was plotted along the x axis and the "normalized" p-e r a t i o along the y a x i s . The "normalized" p-e r a t i o was determined by d i v i d i n g current (6/8/62) price by "normalized" earnings. A regression l i n e was then f i t t e d , which yielded 31+Whitbeck and Kisor, i b i d . , p. 158. 35 the following:35 Y = 9.3 + 1.5X In this case Investors were apparently w i l l i n g to pay 9»3X earnings for a firm with no projected growth and, af t e r that, each percentage point of growth was worth an ad d i t i o n a l 1.5 multiples. The second part of t h e i r empirical work consisted of regressing what they consider to be the three p r i n c i p a l factors of common stock valuation, growth, s t a b i l i t y and payout upon the p-e r a t i o . Their analysis produced the following equation:36 y = 8.2 + 1.5*! + 6.7x2 - O.2X2 Where: y = price-earnings r a t i o x^ = growth rate x 2 = payout = standard deviation of earnings Having determined the "proper" multiple with which to multiply "normal" earnings, Whitbeck and Kisor are able to a r r i v e at the t h e o r e t i c a l price of the secur i t y . This price may be expressed as a r a t i o of current actual price and they 35since no value for r 2 was given we can only assume that i t was not s i g n i f i c a n t . 36 S ee footnote 35 f ° r comment regarding the r ^ value. 36 thus have an index with which to measure under or over valuation. Given t h i s t h e o r e t i c a l price, t h e i r hypothesis then becomes "... the market price of the stock w i l l seek this l e v e l faster than the t h e o r e t i c a l price i t s e l f w i l l change . . ."3? Why? Because "... changes i n market psychology come, by and large, i n a slow and orderly fashion . . . " 3 8 To test t h e i r hypothesis, they divided the stocks into the following groups: (a) Undervalued group: Market Price  Theoretical Price * (b) Overvalued group: Market Price i > 1 e Theoretical Price i»±5 The re s u l t s of the study are shown i n Table 1 . TABLE 1 Undervalued Group S & P 500 Overvalued Group 3 months' Cumulative 3 months'' Cumulative 3 months' Cumulative Date Change Change Change Change Change Change % % % %• % 9 / 2 3 / 6 0 n ; 9 1 1 . 9 6 . 6 6 . 6 5 .7 5-7 1 2 / 2 3 / 6 0 1 6 . 8 3 0 . 7 12 .3 1 9 . 7 8 . 3 14.5 3/24/61 3 i 0 3 4 . 6 1 . 0 2 0 . 9 ( 1 . 4 ) 1 2 . 9 6 / 2 3 / 6 I 3 .2 3 8 . 9 2 . 4 2 3 . 8 2 . 1 15.3 Whitbeck and Kisor, op. c i t . , p. 6 0 3 8 I b i d . Thus, for each three-month period, the undervalued group outperformed the S. & P. 500, which i n turn out performed the overvalued group. Smllen and Safian In 1964 K. B. Smilen and K. Safian39 discussed t h e i r concept and use of r e l a t i v e earnings. They en t h u s i a s t i c a l l y support the concept of r e l a t i v e earnings but argue that not a l l companies should be related to one stock market average. To r e l a t e a c y c l i c a l firm and a growth firm to the same average i s u n f a i r . Thus they originated t h e i r concept of the Dual Market P r i n c i p l e . They developed the C y c l i c a l Average of the Dual Market P r i n c i p l e , which i s composed of a representative group of 23 prime c y c l i c a l s e c u r i t i e s whose earnings are clo s e l y related to the l e v e l of economic a c t i v i t y . For example, automobile firms would be compared to the C y c l i c a l Average. Their Dual Market Principle,*s Growth Average i s com posed of 25 s e c u r i t i e s which the authors consider to have varying degrees of growth p o t e n t i a l . In the case of firms whose earnings are dependent upon external factors, these are c l a s s i f i e d as s a t e l l i t e firms and are also related to the Growth Average. 3 9K. B. Smilen and K. Safian, "Relative Earnings - A Fresh Perspective," F i n a n c i a l Analysts Journal (September- October 1964), v o l . 20: No. 5, pp. 104-107. Apparently believing that t h e i r terms have been adequately defined, they then proceed, aided and abetted by hindsight, to analyze a firm's earnings and make t h e i r investment decisions. In addition to the absence of empirical support, the reasoning of Smilen and Safian i s f a u l t y . In t h i s writer's opinion they have f a i l e d to j u s t i f y the use of two averages with which to compare firms; We w i l l proceed from the basic premise that the fundamental purpose of r e l a t i v e values Is  to enable the user to compare a l l firms^ Smilen and Safian, using t h e i r method, are unable to do t h i s . To compare a c y c l i c a l firm to a c y c l i c a l average is;to study a subset of the universe. I t c a r r i e s with i t an implied assumption that the user has already decided that he w i l l include a firm from a p a r t i c u l a r industry i n his p o r t f o l i o and that h i s decision now i s which one to include. Obviously, t h i s i s putting the cart before the horse. I t i s possible to conceive of a s i t u a t i o n where a firm's earnings may be increasing r e l a t i v e to the C y c l i c a l Average but decreasing r e l a t i v e to the market. In t h i s case they would make an incorrect investment de c i s i o n i R u s s e l l In the book A.Treasury of Wall Street.. Wisdom H. D. Schultz, A Treasury of Wall Street Wisdom (Edi Samson Coslow), Palisades Park, New Jersey, Investors Press, I n c i , 1966, pp. 90-92. t 39 Richard R u s s e l l has a short s e l e c t i o n on the use of r e l a t i v e strength as an investment s e l e c t i o n c r i t e r i o n . B a s i c a l l y , h i s suggested procedure i s as follows: (a) Select those groups of stocks which have shown the best r e l a t i v e strength, i . e . , those groups which are now s t a r t i n g to increase a f t e r long declines. (b) From these groups pick the stocks with the best r e l a t i v e strength. (c) From these stocks pick those with the best actual technical patterns. Those stocks selected should be sold when any of the following situations occurs (a) The stocks no longer outperform the market. (b) When the r e l a t i v e strength l i n e reverses. (c) When the general market re g i s t e r s a s e l l s i g n a l . Although Russell's technique sounds very l o g i c a l and p r o f i t a b l e , i t lacks rigorous d e f i n i t i o n and empirical support. However, the present study attempts to correct several of these d e f i c i e n c i e s . Levy's Study Perhaps the most i n t e r e s t i n g r e l a t i v e value study reported, to date i s that of Levy ' s ^ which.offers strong Robert A. Levy, "Relative Strength as a C r i t e r i o n for Investment Selection," Journal of Finance, v o l ; 22, No. 4, (December, 1967)* PPi 595-610. support i n favour of the Trendists. Although he has not refuted the Random Walk Theory, he has been able to e f f e c t a possible r e c o n c i l i a t i o n between the two opposing camps. Generally speaking, Levy found that a s e r i a l c o r r e l a t i o n study of performance ranks rather than successive f i r s t differences detected the existence of trends over the long term (26 weeks) but not over the short term (4 weeks). Thus the "co-movement" of stock prices, found by King, 2 4 , 2 could i n fact conceal e x i s t i n g dependencies i n successive price changes. Then, Levy suggests that, by using ranks which measure r e l a t i v e strength, the v e i l of the general market movements may be parted and the underlying structure analyzed. In order to investigate his hypothesis, Levy randomly chose 200 stocks and studied them over the 260-week period October 24, i960—October 15, 1965. He constructed r a t i o s designed to measure h i s t o r i c a l strength and future performance. Thus he used h i s t o r i c a l strength as a means for s e l e c t i o n at time period t and subsequent r a t i o s as a measure of his investment r e s u l t s . A f t e r c a l c u l a t i n g the following three price r a t i o s : (a) C/A 26 - current week's price divided by the average of 26 previous weeks' price and including the current week. Benjamin P. King, "Market and Industry Factors i n Stock Price Behaviour," Journal"of Business, v o l . 39» No. 1, Part II (January 1966), pp. 139-190. 41 (b) 4/C - current week's price divided into the price 4 weeks subsequent to the current price; (c) 26/C - current week's price divided into the price 26 weeks subsequent to the current week: The ranks l i s t e d below were determined f o r the 200 stocks: (1) Relative Strength Ranks - the highest r a t i o was given a rank of 000. (2) V o l a t i l i t y Ranks - the c o e f f i c i e n t of v a r i a t i o n defined as was used as a ranking c r i t e r i o n with the highest r a t i o receiving the lowest rank (000): (3) Market Ranks - each week the C/A 26 r a t i o s were summed and the t o t a l s ranked. (4) Divergence Ranks - the difference between the average of the C/A 26 r a t i o s of the 20 strongest stocks and the average of the 200 stocks was determined and ranked with the largest divergence receiving a rank of 001. S i m i l a r l y , the long term weak divergence ranks were determined. Levy's r e s u l t s were extremely enlightening: T r a d i t i o n a l l y , i t has. been maintained that h i s t o r i c r e l a t i v e strength tends to continue for a period of time: Although the 4/C ranks and r a t i o s did not support t h i s hypothesis, the 26/C ranks and r a t i o s showed that the 10% h i s t o r i c a l l y strong stocks gained on average 9*6% while the 10% weakest gained on average only 2l9%i In addition, he found good c o r r e l a t i o n between past performance groupings and 26-week future perform ance groupings, as shown i n Table 21 kz TABLE 2 C/A 2 6 Relative Group Performance Indicator Based Upon Strength 26/C Average 26/C Average Rank Group Number Group Ratios Group Ranks  1 1 1 2 2 2 3 3 3 7 6 5 6 8 8 7 5 5 8 6 7 9 9 9 10 10 10 r* = . 8 7 . 9 2 Further i n v e s t i g a t i o n of his preliminary r e s u l t s led Levy to the following conclusions: (a) Selection of stocks which h i s t o r i c a l l y had been both r e l a t i v e l y strong and r e l a t i v e l y v o l a t i l e resulted i n p r o f i t s greater than those possible by random selection^ (b) Following from the r e s u l t s f i t s t mentioned, he found that superior performance could be achieved by purchasing stocks i n a market which h i s t o r i c a l l y had been strongi Thus continuation of r e l a t i v e strength appears to apply to the general case (the market) as well as to i n d i v i d u a l s e c u r i t i e s I Nye-Study No: 1 The next study to be considered i s the author's BiComm. graduating essay. The Five-Stage Theory described e a r l i e r was f o r i t s v a l i d i t y and f o r i t s a b i l i t y to outperform the market. The sample consisted of 30 U.S. i n d u s t r i a l s l i s t e d on the N.Y.S.E. These companies were being followed by the 43 Research Department of Eastman D i l l o n , Union Securities and Company, a large United States investment house based i n New York, and included firms from almost a l l major ind u s t r i e s . For purposes of t h i s t e s t , a given stage was said to have occurred i f the trend of r e l a t i v e earnings or r e l a t i v e price earnings was established f o r a minimum of four quarters. Although t h i s was an a r b i t r a r y figure i t was f e l t that to take any period less than that might not permit a trend to be c l e a r l y enough established, whereas to postpone the decisions past four quarters might r e s u l t i n l o s t investment opportunities. In order to test for v a l i d i t y , a p a r t i c u l a r stage was f i r s t of a l l chosen and then the movements of r e l a t i v e earnings and r e l a t i v e price earnings were studied, both before and a f t e r the occurrence of the given stage. The re s u l t s of t h i s test w i l l be given i n the next section; The next portion of the study was devoted to t e s t i n g the a b i l i t y of the system to achieve above average investment r e s u l t s . F i r s t of a l l , t h i r t y charts were randomly chosen and coded from the o r i g i n a l seventy. Following t h i s , quarterly plottings of r e l a t i v e earnings, r e l a t i v e price earnings and r e l a t i v e price were made from the coded charts onto new charts by an Impartial participant i n the study. It should be pointed out that the author did not know the name of the company whose figures were on the chart nor was he aware of 44 the year f o r which the figures were being plottedi A f t e r each p l o t t i n g , the charts were given to the author, who studied them, made buy or s e l l decisions i f indicated and returned the charts to the participant, who then made another quarterly p l o t t i n g . In thi s way, seven years of data were plotted on the charts and studied. Buy and s e l l decisions were based on the following c r i t e r i a , A stock was purchased at the end of Stage 1 and held i n the p o r t f o l i o u n t i l Stage 5 had occurred. One further question was also studied. This was the e f f e c t , i f any, of the l e v e l of r e l a t i v e price-earnings at the time of purchase on the performance of the p o r t f o l i o . Thus two tests were car r i e d out: The f i r s t one consisted of buying on a Stage 1 with r e l a t i v e price-earnings at any l e v e l , while the second test consisted of buying a f t e r Stage 1 only i f r e l a t i v e price-earnings were less than 100: Results 8 F i r s t of a l l , the res u l t s of the test of the v a l i d i t y of the 5-stage hypothesis are summarized i n Table 3 on the page following. 45 TABLE 3 Results of Testing the V a l i d i t y of the Five-Stage Hypothesis Stage 1 (a) Prior (b) After Stage 2 (a) Prior (b) A f t e r Stage 3 (a) Prior (b) A f t e r Stage 4 (a) Prior (b) A f t e r Stage 5 (a) Prior (b) A f t e r % Frequency R.P.E. R.E. Increased Stable Decreased Increased Stable Decreased 78 4 18 17 12 ?1 80 10 10 40 22 38 29 96 67 4 15 27 30 7 55 66 20 13 10 4 70 83 57 57 3 5 40 38 67 36 4 28 29 36 67 30 12 7 21 60 87 56 3 11 10 33 60 52 13 5 27 43 Stage 1 was most often preceded by Increasing r e l a t i v e price earnings (R.P.E.) and decreasing r e l a t i v e earnings (R.E.). This tendency was very strong, as the figures indicate; A f t e r Stage 1, R.P.E. increased 80$ of the time, while the R i E i movements indicated no strong trend i n either d i r e c t i o n ! Stage 2 of the charts studied was most often preceded by declining R.P.E. and Increasing RiE. Following Stage 2, 21 out of 22 cases showed an R.P.E. increase while RiEi was more or less evenly d i s t r i b u t e d between increasing, stable, and decreasing movements. Stage 3.was preceded by declining or stable R.P.E. 85$ of the time. During t h i s period RiEi was increasing with a frequency of 67$. A f t e r Stage 3 R i P i E i and R.E. decreased 66$ and 60$ of the time, res p e c t i v e l y ! Movements pr i o r to Stage 4 indicate that de c l i n i n g R.P.E. and increasing R.E. were predominant; This was also the case f o r movements of RiPiE . and RiEi a f t e r Stage hi' Movements of R.P.E. p r i o r to Stage 5 were roughly divided between increases and decreases, whereas RiE. either increased or remained stable 73$ of the timei A f t e r Stage 5 had occurred, R.P.E. increases were made s l i g h t l y more than h a l f the time and RiE. movements were f a i r l y evenly mixed between increases and decreasesi The theory of Markov chains was used to generate a t r a n s i t i o n a l matrixi Thus, given a c e r t a i n movement of R.Ei 47 and B.P.E., i t was possible to determine the probability of another stage following the given stage. These p r o b a b i l i t i e s are summarized i n Table 4. TABLE 4 T r a n s i t i o n Matrix To Stage From Stage 1 2 3 4 5 1 .02 .05 • 35 .50 .08 2 .00 .00 .36 .59 .05 3 .34 .00 .00 .31 .35 4 .45 .00 .09 .09 .37 5 . .38 .00 .14 .43 .05 figures were calculated using the data from the sample charts. Given Stage 1, Table 4 shows that there was a probability of i85 that either Stage 3 or 4 would follow. This would indicate that an investment at the end of Stage 1 would have a very good chance of outperforming the market, while the chance of substantial loss, i . e . , Stage 5> was only 8%, Given Stage 2, the re s u l t s are even more in t e r e s t i n g since the prob a b i l i t y of gain through either Stage 3 or 4 was .95* A f t e r the development of Stage 3 there was almost an even chance of either Stage 1, 4 or 5» Again, given Stage 4, 48 the most l i k e l y outcome was either Stage 1 or 5« I*1 Stage 5» the p r o b a b i l i t y was .81 for either Stage 1 or 4. These figures Indicate that given Stage 1 or 2, the probability of above average re s u l t s was very high. However, an investment at the end of Stage 3 had a greatly reduced probability of substantial gain since the chance of Stage 4 was only •31i This p r o b a b i l i t y was further reduced at the end of Stage 4, when the combined p r o b a b i l i t y of either Stage 3 °r 4 was only i18• As might be expected, an investment at the end of Stage 5 had a good chance of performing as well as or better than the market! The r e s u l t s of the 2 tests are shown on the following page i n Table 5* In c a l c u l a t i n g the r e s u l t s of the t e s t , two d i f f e r e n t bases were used. F i r s t of a l l , the r e s u l t s were calculated on a per share basis. Thus whenever a buy s i g n a l was indicated, one share of that stock was purchased. The second basis of c a l c u l a t i o n was that of d o l l a r commitments. In t h i s case, when a buy signal was given, i t was assumed that $1,000 worth of stock was purchased. In addition, as long as the stock was held, i t was assumed that $1,000 was invested i n the stock every January 1st. Also of note was the fact that a l l gains shown represent c a p i t a l appreciation i n the value of the stock plus stock dividends but exclude a l l cash dividends. 49 TABLE 5 Study No. 1 - Test Results I952-I963 Per Share Dollar Commitment Test #1 Test #2 Test #1 Test #2 Market 1 9 5 2 5 .7 1 1 . 2 11.7 1 9 5 3 4.5 8 . 7 (0.3) 1 9 5 4 9 3 . 2 41 .2 4 3 . 8 1 9 5 5 55.0 104.0 4 7 . 0 9 1 . 0 2 0 . 2 1 9 5 6 28.2 19.3 36.O 36.I 3.6 1 9 5 7 33.5 ( 1 1 . 1 ) 1 2 . 1 ( 7 . 4 ) ( 1 2 . 2 ) 1 9 5 8 84.2 9 3 . 2 6 9 . 0 5 8 . 9 3 4 . 0 1 9 5 9 55.0 42 .2 52.0 36.I 1 5 . 2 I 9 6 0 12 .6 36.6 14.0 42.7 10.0 1 9 6 1 51.3 62.5 27.0 55.1 17.4 1 9 6 2 ( 2 2 . 6 ) 2 2 . 0 35.0 30.1 (10 .0) 1 9 6 3 23 .0 42.7 30.0 31.1 I 6 . 5 Average Annual Gain 35.3 45 .7 31.9 41.5 12.5 Of the 2? stocks purchased at one time or another during the period 1952-1963, 22 or 85$ of the purchases appreciated i n value. Considering the test #1 r e s u l t s f i r s t , these show that the p o r t f o l i o outperformed the market i n 10 out of 12 years. Using the arithmetic mean of the annual r e s u l t s , the average gain per year was 35*3$ while the market's average gain per year was only 12.5$; Calculated on a d o l l a r commitment basis, the res u l t s show that the port f o l i o again outperformed the average i n 10 out of 12 years but the mean gain was 31*9$ or 3.4$ less than the per share method: The test #2 r e s u l t s show that both methods of c a l  c u l a t i o n resulted i n the p o r t f o l i o outperforming the market i n nine out of nine years. In both cases the average yearly gain was better under test #2 than under test #1; The per share basis showed a gain of 45.7$ vs. 35:3$ while the d o l l a r commitment basis showed a 41.5$ v s i a 31.9$ gain; Conclusions s The r e s u l t s of the sequence v a l i d i t y test showed that a 1-3-5 series of movements was more l i k e l y . However, the point to be noted was that an investment made at the end of Stage 1 had a high probability of outperforming the market since a move into either Stage 2, 3 or 4 w i l l usually r e s u l t i n above average returns. This type of analysis permitted 51 an Introduction of a q u a l i t a t i v e judgment concerning r i s k since, once the stock had moved through Stages 1 to 4, the r e l a t i v e price earnings was quite high and as a r e s u l t the stock price was vulnerable! It may be argued that the reason for t h i s was that the market was discounting expected future earnings increases; Thus, i f they did not materialize, the best that could be hoped fo r was an average market performance! On the other hand, the company's f a i l u r e to achieve the expected earnings would l i k e l y r e s u l t i n a multiple contraction with i t s r e s u l t i n g c a p i t a l losses! S i m i l a r l y , we may say that an investment made at Stage 3 i s subject to a higher r i s k than the same investment made at Stage 1. Good r e s u l t s may occur a f t e r Stage 5 because the r e l a t i v e price-earnings r a t i o usually increases: However, the r i s k s t i l l exists that t h i s increase may be off s e t by a further decline i n r e l a t i v e earnings! On the basis of the res u l t s of tests #1 and #2, i t was shown that r e l a t i v e value analysis was a u s e f u l technique i n achieving an above average investment performance: It appeared that, regardless of the method.of Investing, i . e . , either on a per share basis or a d o l l a r commitment basis, or the l e v e l of the r e l a t i v e price earnings, t h i s technique permitted the investor to outperform the market. 52 The study i s , however, open to several major c r i t i c i s m s . These are the time period during which i t was undertaken, possible biases i n the sample and imprecise d e f i n i t i o n of vari a b l e s ! In the f i r s t place, the time period of the study was one i n which stock prices underwent a substantial r e - evaluation by investors. Large amounts of funds were committed to the stock market by the public, not only i n d i v i d u a l l y but through other channels such as Mutual Funds and Pension Funds. As a r e s u l t , the price-earnings r a t i o of the S. & P. Composite rose from 10;3 i n 1953 to 22.? i n 1961 but by 1963 had declined to 17i8. Thus, one could argue that the success of the r e l a t i v e value technique was due i n a large part to thi s multiple expansion; Secondly, the test sample was biased i n that i t con tained only firms which one investment house perceived to be growth firms! They were h i s t o r i c a l l y successful companies, which had been operating for many years and had a proven earnings record! Therefore i t i s quite possible that one could have achieved the same re s u l t s by merely randomly selecting a p o r t f o l i o from the group of 70 s e c u r i t i e s . T h i r d l y , the slope of the r e l a t i v e earnings and r e l a t i v e price-earnings l i n e s was determined v i s u a l l y and as a r e s u l t i t was not possible to increase the s e l e c t i v i t y of the buy c r i t e r i a and determine i t s Impact. 53 Nye-Study No: 2 In order to further investigate the r e l a t i o n s h i p between earnings and the p-e multiple, a second study was undertaken * This study was conducted i n an e f f o r t to determine the predictive significance of two variables i n forecasting quarterly changes i n security p r i c e s . For each of 35 companies the change i n price of the stock at the end of quarter t + 1 was predicted at the end of the t th quarter! The change i n price was measured i n d o l l a r s and, i f accurately predicted, then price i n period t plus the change i n price from t to t + 1 should give a reasonably good estimate of what the price of the security w i l l be at the end of period t + l i This prediction of change i n price involved f o r e  casting the earnings per share of the company i n question! This forecast was f o r the percentage change i n earnings per share from period t to t + 1 and was made at the end of period t i This prediction thus implied an ad d i t i o n a l f o r e c a s t — t h a t of the earnings per share at the end of period t . For example, at September 30 the percentage change i n earnings per share from the end of September to December 31 must be forecasted! This means that the earnings per share for the period ending September 30 must be known but, since the firm w i l l not yet have published t h i s data, an estimate must be made. 54 Relevant to t h i s discussion i s the work done by Green and 43 S e g a l l . J In th e i r a r t i c l e they developed and tested s i x d i f f e r e n t models to forecast earnings per share. The s i x models were: (a) Annual 1: (b) Annual 2: (c) Annual 3: E P 3 t + 1 = EPS t EPS t+1 = EPS + (EPS t « EPS t_ 1) EPS t + 1 = EPS t ± (EP3 t - E P S j ^ ) ) r E p s t - i (d) Interim 1: EPS t = 4 (1st Quarter EPS t) (e) Interim 2: E P S t + 1 = EPS t + (I Q. E P S t + 1 - I Q. EPS t) I Q.EPSt ( _ _ _ ) (f) Interim 3: Regress I Q. EPS^. on previous f i v e quarters. They concluded that forecasts using f i r s t quarter interim reports are not c l e a r l y superior to those using only annual data! However, they stated that some knowledge ( i i e i , three months* earnings) i s better than a twelve-month forecast; Also they found that, i n companies with r e l a t i v e l y large changes i n earnings per share, the Interim 3 model provided the best r e s u l t s . ^Di Green and J . S e g a l l , "The.Predictive Power of F i r s t Quarter Earnings Report," Journal of Business, v o l i 40, Noi 1 (January, 1967), pp. 44-55! 55 Hypothesis: The hypothesis offered was that the change i n price of common stocks i s a function of two v a r i a b l e s — t h e percentage change i n earnings per share of the stock and the l e v e l of i t s r e l a t i v e price-earnings r a t i o i Thus, for a given security: f ( l E P S t + l - l E F S t ; i f t ) ( iEP3 t I P E t ) the change i n price of the i th security from period t to t+1 the percentage change i n earnings per share of the i th security from period t to t+1 lrat = the price-earnings r a t i o of the security j P E t at the end of period t divided by the price-earnings r a t i o of the Dow-Jones In d u s t r i a l Average at the end of period t i The data used was quarterly price and earnings per share as at March Jl, June 30> September 30, and December Jl f o r the period i960 to the second quarter of 1967, for a t o t a l of 30 observations f o r each of the 35 companies studied. S i m i l a r l y , data f o r the Dow-Jones was used for the same dates. To test the hypothesis, the computer was used to run a multiple regression on the data of each of the 35 companies. i p t + l = Where: ^P^+i = i E F S t + l " j 5 1 5 ^ iEPS t Thus an equation of the form shown below was obtained f o r each company*s stock: j X 0 t + l = jA + ^ 1X 1 t + 1 + i b 2 ±X2 t Where: .X (t+1) = the d o l l a r change i n price from period t 1 0 to t+1 of the i th security! jX.. (t+1) = the percentage change i n earnings per share of the i th security from period t to t+1 .X2 (t) = the l e v e l of the r e l a t i v e price-earnings r a t i o at period t : = a constant ^0 + ^bg = regression c o e f f i c i e n t s The r e s u l t s of the regression are shown i n Table 6, TABLE 6 Results of Multiple Regression Analysis C ompany Constant Regression C o e f f i c i e n t s X l X2 2 r Abbot Laboratories 8.7 .45 -.06 .07 A l l i e d Chemical Company -7.8 .23 .07 .13 American Home Products 55.1 -1.7 -.3 .13 Armstrong Cork 6.2 .04 -.02 .003 B r i s t o l Myers - .66 .90 .004 .01 Celanese -5.1 - .16 .13 .08 Chrysler Corporation 19.8 .32 -.27 .42 Cluett Peabody 22.6 .18 -.28 .24 5? TABLE 6 (continued) Company Constant Regression Coef f i c i e n t s X l X2 r 2 Corn Products 17.6 -.10 -.13 .10 Dupont 54.0 .81 -.41 .10 P.M.C. Corporation 30.0 • 38 -.20 .15 General Cable -7.0 -.03 .16 .19 General Motors 17.2 -.003 -.20 .06 Georgia P a c i f i c 26.1 .19 -.23 .21 Honeywell Inc. 38.4 -.70 -.21 : i3 Inland S t e e l -105.7 -1.08 1.16 .02 International T. & T. -2.82 -.39 .05 .03 Jones & Laughlin -.17 -.06 .006 .06 Lockheed A i r c r a f t 3.5 .16 -.04 .06 Magnavox 36.6. .08 -.27 .37 Monsanto Chemical 8.7 • 56 -.09 .12 North American A v i a t i o n 3.47 .006 -.05 .02 Owen I l l i n o i s Glass 29.1 .63 -.27 .27 Pepsi 9.3 .12 -.06 .05 Polaroid 37.0 .21 -.10 .10 R.C .A. 19.6 .26 -.14 :i4 R. J . Reynolds 9.0 .71 -.10 .09 Safeway 12.3 .29 -.14 .14 Smith, Kline & French 29.2 .80 -.21 .27 Standard O i l 4.8 .10 -.06 .04 58 TABLE 6 (continued) Regression Constant C o e f f i c i e n t s X« X„ Td Company 1 S t e r l i n g Drug 12.0 .44 -.08 .05 Textron -2.5 -.02 .09 ;12 U.S. Freight 37.0 .18 -.34 :28 Warner-Lambert 10.1 -.30 -.06 .06 Xerox 72.0 -.01 -.14 .17 In general, the r e s u l t s indicate that t h i s model has no predictive value and therefore the hypothesis as i t i s presently formulated must be rejected. Looking f i r s t at the c o r r e l a t i o n c o e f f i c i e n t s , no s i g n i f i c a n t r e l a t i o n s h i p was exhibited between P and X^, P and X 2 or X^ and Xgi The range of r f o r P and was - i 2 5 t o ;59 with 15 negative signs and 20 positive signsi For P and X 2, the range was -!60 to i43 with 28 negative signs and 7 positive signs. S i m i l a r l y , for X^ and X 2» r ranged from — i39 to i72 with 15 negative signs and 20 positive signs; Thus, i n some cases, the variables moved i n opposite d i r e c t i o n to each other while i n the remaining cases they moved together i n the same d i r e c t i o n , but there was no consistency i n the r e s u l t s . In addition, the highest r was .72 and almost a l l others were f a i r l y close to zero, thus indicating that they varied randomly. Looking at the values, the range was .003 to i42, indi c a t i n g that the best " f i t " explained only k-2% of the t o t a l error. Considering the P-ratlos, at a 5$ l e v e l of significance the value of F had to exceed 4;5» At values greater than 4! 5 we can conclude that there i s regression i n the population and the improvement brought about by f i t t i n g the regression plane was not due to chance. The following l i s t shows the frequency of F values greater than 4;5: X l - 3 oases *2 " 5 cases ~2 „ 2 Chrysler .42 Cluett-Peabody !24 Owens-Illinois Glass .27 General Cable i l 9 Smith, Kline & French .27 Georgia-Pacific ;21 Magnavox •37 U.S. Freight i28 Although the F - l e v e l d i d indicate an improvement, which was not due to chance, i n a small number of cases the r 2 figures show that i t was not a s i g n i f i c a n t improvement. Conclusion: As mentioned e a r l i e r , the results of tes t i n g the hypothesis show that i t had no predictive value; In fact several cases resulted i n the standard deviation of the pre dicted value being greater than the standard deviation of the mean! 60 Perhaps the reason the r e s u l t s compared so unfavourably with the r e s u l t s of Study No. 1 previously mentioned was that the former model i s a s t a t i c one whereas the l a t t e r i s dynamic; Thus, because the variables have a wide movsment over time, the " f i t " of the l i n e i s not good. On the other hand, the r e l a t i v e value system appears to be able to permit the user to take advantage of these v a r i a t i o n s ; Figure F i l l u s t r a t e s t h i s point; FIGURE F Relative Price - Dynamic and Static Models Dynamic Model Relative Price Sta t i c Model Time Although the s t a t i c regression model was not valuable as a predictive t o o l , these "stages" s t i l l occur and, i f i t i s possible to develop a dynamic model, then the re s u l t s might be improved; CHAPTER IV DEVELOPMENT OF THE MODEL AND THE TEST OF THE HYPOTHESIS I. DEVELOPMENT OF THE MODEL Description of the Test As mentioned previously, the Study No. 2 r e s u l t s tended to support the r e l a t i v e value hypothesis. However, as a r e s u l t of the e a r l i e r mentioned c r i t i c i s m s , the Study No. 1 test was f i r s t of a l l continued to the second quarter of 1967. In addition, because of the p o s s i b i l i t y that the sample was biased i n favour of successful companies whose shares were eagerly sought by investors, a new sample of firms was chosen. The test was then conducted from the second quarter of 1956 to the second quarter of 1967» providing a time span of more than ten years. Selection of the Sample The Standard & Poor's '500' index was chosen as repre sentative of the market rather than the Dow-Jones In d u s t r i a l Average i n view of the recognized d e f i c i e n c i e s of the l a t t e r . In order that a l l selected p o r t f o l i o s could be compared with the market, only those stocks which were included i n the 62 S; & P. index as at December 31, 1966 as l i s t e d i n Standard  & Poor's Trade and Securities S t a t i s t i c s , 1966 e d i t i o n were e l i g i b l e f or inc l u s i o n i n the sample. Having thus defined the universe, a t o t a l of 50 firms was selected f o r the sample. The procedure was as follows: each stock i n the Index was assigned a number from 001 to 500. A Random Number Table was then used to generate the sample. Once picked by a random number, the stock had to be l i s t e d on the N.Y.S.E. for the entire time period. In addition, i t must have been included i n Moody's Handbook of Common Stocks, Second Quarterly 1956 ed i t i o n , and also the Third Quarterly  1967 e d i t i o n . In addition, quarterly earnings figures had to be a v a i l a b l e . If the stock f a i l e d to meet any of these requirements i t was excluded from the sample and another security was randomly chosen. Oh this basis the stocks of the following companies were included i n the sample: Abbot Laboratories, Inc. Addressograph-Multigraph Corp. A i r Reduction Company, Inc. Alpha Portland Cement Company Aluminum Co. of America Amerada Petroleum Corp. American A i r l i n e s , Inc. American Bakeries Company American Potash & Chemical Corp. American Smelting & Refining Co. American Tobacco Company Archer-Daniels-Midland Company Beatrice Foods Company Beckman Instruments, Inc. B e n e f i c i a l Finance Company Bucyrus-Erie Company Dupont (E.I.) De Nemours and Co. Foremost Dairies General Foods Corporation General Instrument Corporation General Portland Cement Company Goodrich (B.F.) Company Grant (W.T.) Company Gulf O i l Corporation Hudson's Bay Mining & Smelting Company, Ltd. Keebler Company Lockheed A i r c r a f t Corporation May Department Stores Company Merck & Company, Inc. Motorola, Incorporated North American Aviation, Inc. 63 Burlington Industries, Inc. Peabody Coal Company Burroughs Corporation Penn-Dixie Cement Corporation Case (J.I.) Company Proctor & Gamble Company Chemetr.on Corporation S c o v i l l Manufacturing Company Colgate-Palmolive Company Sears, Roebuck and Company Columbia Broadcasting System, S h e l l O i l Company Inc. Superior O i l Company Consolidated Edison Company Westinghouse E l e c t r i c Corporation . of New York, Inc. Whirlpool Corporation D i s t i l l e r s Corporation-Seagrams, Wrigley (Wm.) J r . Company Ltd. Dr. Pepper Company These firms comprise 24 industries with one or two firms from each industry. However, there i s a concentration of Food Producing and Processing firms (8) and Petroleum companies (4). The sample Includes firms i n both c y c l i c a l industries (Building Materials) and r e l a t i v e l y n on-cyclical industries (Food). In addition, growth industries are repre sented (Office Equipment, Electronics) while stable or de c l i n i n g industries (Coal) are also a part of the sample. Since the firm's stock had to be l i s t e d i n both 1956 and 1967J the sample Is biased towards firms which have been able to remain i n business during that time. Thus the r i s k of a complete loss of c a p i t a l through bankruptcy has been avoided. However, the sample does not contain only successful firms since the raw data shows that many of them, although they were able to maintain t h e i r l i s t i n g s , experienced d e f i c i t earnings. In some cases these d e f i c i t s occurred as frequently as s i x out of the eleven years and t h e i r share prices suffered accordingly. Data Quarterly data for the period 1955 to the second quarter 1967 for the S. & P. Composite was obtained from Standard & Poor's Trade and Securities S t a t i s t i c s (1966 e d i t i o n ) . The data included 12-month earnings for the quarters ending March 31, June 30, September 30 and December 30. The l e v e l of the Index was also obtained for corresponding periods, as was i t s price-earnings r a t i o . Quarterly prices for each stock were obtained from Barron's and were checked from that source to ensure that no recording errors had been made. In addition, random checks were made using the Wall Street Journal to guard against possible p r i n t i n g errors. It was decided that the most repre sentative price was the average of the Bid and Ask prices and consequently t h i s was determined i n each case and recorded. Although i t i s possible that either the Bid or Ask price would have been acceptable since most of the stocks were a c t i v e l y traded, some s e c u r i t i e s did exhibit a f a i r l y wide spread and therefore i t was decided to use the arithmetic mean. A l l prices were adjusted for stock s p l i t s and stock dividends. Quarterly earnings data was obtained from various issues of Moody's Handbook of Common Stocks and was adjusted for stock s p l i t s and stock dividends. Eight of the companies had a f i s c a l year d i f f e r e n t from the calendar year and this presented c e r t a i n 65 data problems. The eight companies were: Addressograph-Multigraph Corporation Beatrice Foods Company Case (J.I.) Company D i s t i l l e r s Corporation-Seagrams, Ltd. General Instrument Corporation Grant (W.T.) Company May Department Stores Company Sears, Roebuck and Company In the case where the firm's quarter ended on either January Jl or February 28, the data was compared to the Index's March 31 data. Thus an implied forecast of the Index and i t s earnings was made. It could be argued that a better method would have been to r e l a t e the data to the December 31 f i g u r e s . However, the main objection to t h i s i s that i t would have increased considerably the complexity of the computer programming while providing only doubtful returns. Methodology The f i r s t step was to define the variables. These were Relative Earnings, Relative Price and the Relative Price- Earnings Ratio. From the raw data the computer was instructed to calculate the three r e l a t i v e values for each quarterly time period. The logarithmic values of these r e l a t i v e figures were then determined and these values were then regressed against time on a four-quarter basis. To repeat from Chapter I, l e t : e i t = the 12-month earnings per share of the 1 th security at time period t 66 p i t = the price of the i th security at time period t p e i t = t h e P r i c e " " e a r n i n s s r a t i o of the i th security at time period t = the 12-month earnings per share of the S. & P. Index at time period t P+. = the price of the Index at the end of time period Z t PE. = the price-earnings r a t i o of the Index at time period t Then; f i t E = X.. = the 12-month r e l a t i v e earnings per share £ of the i th security at time period t % t p — = Y.. = the r e l a t i v e price of the i th security t at time period t p e i t pg = Z- t = the r e l a t i v e price-earnings r a t i o of the t i th security at time,period t For the time period 1 < t £ 4, log X^, log log &^ + 2 a n ( ^ 1°8 xit+ 3 w e r e regressed to obtain an equation of the form X^ _ + ^ ^ T where o<^ i s the slope of the r e l a t i v e earnings l i n e of the i th security for 1 < t < 4 and T i s time. S i m i l a r l y ! Y^ = ~b± + P^T where ^ equals the slope of for 1 < t < 4 = + Y j T where Y ^ equals the slope of Zj_ for 1 < t < 4 Values of ^ j_ and " Y ^ were s i m i l a r l y computed for the time periods 2 < t < 5, 3 < t < 6, . . . , . 4-2' < t < 45. 67 The buy and s e l l c r i t e r i a were then defined so as to evaluate a t o t a l of 120 Strategies and to attempt to determine the optimum combination of buy and s e l l decisions i n order to meet the two objectives of outperforming the market and maximizing return. The c r i t e r i a were as follows: As before, two tests were conducted—one where the l e v e l of Z^ was ignored and the other where Z^ f; 1.0, i . e . , the multiple of the i th security had to be equal to or less than the multiple of the S. & P. Index. The c r i t e r i a are then: Strategy No. Buy i f S e l l i f « i Y i \ « i 1 >.10 >0 <0 <l.o£ <-.05 2 " " » » <-.10 4 >.15 " » <-!o5 5 H " " <-.io 6 " " " " <-.l5 7 >.20 " " M <-.05 8 " " » " <-.10 9 « I I I I it ^-.15 10 >.25 " " " <-!o5 11 " " » " c-.io 12 " " M " <-.l5 13 >.30 " " " <-'.05 14 » •» » <-.io 15 " " " " <-.i5 16 >.io " <i.o <-.05 17 " " •• " <-.io 18 " " " " <-.i5 19 >.15 " " " <-.05 20 " H " <-.io 21 " " " » <-.i5 22 >.20 " " " <-.05 23 *» » » M <-.io 24 " " " <-.15 25 >.25 » » » <-.05 26 w " » » <-.io 27 " M 11 " <-.i5 28 >.30 " M •» <-!o5 29 " n " " -.10 30 M .l568 The remaining 30 Strategies were formulated i n a s i m i l a r manner except for a data time lag, the reason for which w i l l be discussed f i r s t . As the data i s presently formulated, Firm data for time period t i s compared with Index data for time period t . However, t h i s involves the use of hindsight. For example, on September 30, 1966 the l a t e s t earnings which would be avai l a b l e would be those for the period ending June 30, 1966. Thus the variables were re-defined to account fo r this time l a g . Let: X.. = e i t _ i = the 12-month r e l a t i v e earnings per share E ^ of the i th security at time period t = p ^ = the r e l a t i v e price of the i th security • 5 — at time period t * t ~ = ^ e r e l a t i v e price-earnings r a t i o of e l t - l the i th security at the end of time p period t E t - 1 With the variables re-defined as above, the same combinations of c r i t e r i a were applied and these addi t i o n a l 30 Strategies may be considered as more r e a l i s t i c than the previous 30. For the next series of tests the time period was shortened from 1956> second quarter—1 9 6 ? , second quarter, to 1958, second quarter—1967* second quarter, and reference to. Figure G w i l l indicate the reason why. J J G U H E - J G . 70 One of the c r i t i c i s m s of the previous study was that i t was conducted during a period of generally r i s i n g p-e r a t i o s . Under such circumstances favourable r e s u l t s might be expected, regardless of the a b i l i t y of the model to select superior s e c u r i t i e s . The present tests have been conducted during a time when the S. & P. Composite multiple rose from 13*77 to 17-01. An analysis of the computer output for the i n i t i a l series of tests (see Table 7) shows that, on average, hjfo of a l l purchases were made i n the f i r s t 20$ of the t o t a l test period. Therefore, i t was decided to conduct the test during a period when the beginning and ending p-e r a t i o was the same. When a buy si g n a l occurred, the computer was instructed to purchase $1,000 worth of the security and to hold i t u n t i l a s e l l s i g n a l occurred. TABLE ? Percent of To t a l Number of Purchases Executed During I n i t i a l 20% of Sample Time Period tegy No. 1 1 41 2 46 3 53 4 36 5 36 6 38 7 48 8 48 9 48 10 45 11 45 12 45 13 40 14 40 15 40 16 41 17 45 18 51 19 34 20 34 21 37 22 45 23 45 24 45 25 45 26 45 27 45 28 40 29 40 30 40 I I . RESULTS OF THE TEST 72 Table 8 shows the res u l t s of updating the o r i g i n a l test to the second quarter of 19&7• Test #1 again supports the r e l a t i v e value method since, i n each year, the technique outperformed the market quite substantially and the average annual gain was greatly superior to that of the market. The average annual gain of test #2 was s l i g h t l y lower than that of the market, even though the technique outperformed the market i n two of the four time periods; These r e s u l t s were not superior and do not lend support to the r e l a t i v e value technique. TABLE 8 Summary of Results of Study #1 (1964-1967. 2nd Quarter) TEST #1 TEST #2 MARKET Qtly.Avge. Annual Qtly.Avge. Annual Qtly.Avge. Annual % % % % % % 1964 1.6 6.6 (1.14) (4.48) 0.10 0.4 1965 8.7 39.6 3.2 13.4 1.7 7.0 1966 (0.11) (0.52) (5.96) (21.79) (4.79) (17.83) 1967* 11:5 24.3 8.2 17.1 5.1 10.4 Average Annual Change 16.5 0.15 0.5 * F i r s t two quarters only. 73 In an e a r l i e r chapter the method of c a l c u l a t i n g the res u l t s of the f i r s t study was indicated and one point should be emphasized. By assuming that $1,000 was invested i n the security every January 1, the entire p o r t f o l i o was sold on December 31 and repurchased the following day—an obviously absurd assumption. In addition, the re s u l t s were based on a p o r t f o l i o which at no time contained a cash reserve. Thus the r e s u l t s were attainable only by assuming a continuous 100$ commitment i n stocks. When bu i l d i n g the present model, the a r b i t r a r y nature of the previous assumptions was kept i n mind and avoided. But, as i s true i n any s i t u a t i o n , the elimination of some problems creates new ones. Prom an o v e r a l l point of view, however, the present test i s more r e a l i s t i c : the p o r t f o l i o was not turned over at year end; and provision was made for determining cash balances at any point i n time. Ideally, the r e s u l t s should be measured i n such a way that a meaningful Indicator of performance i s used and, at the same time, some measure of r i s k i s indicated. The computer output for the f i r s t series of tests l i s t e d the amount of external funds required for purchases at any p a r t i c u l a r time period, the amount of cash on hand, and the market value of s e c u r i t i e s held. The cash account was viewed as a Current Account and, as such, was not considered to earn Interest. As w i l l be shown l a t e r , this had a d e t r i  mental e f f e c t on r e s u l t s since, In c e r t a i n cases, substantial cash balances resulted from the sale of s e c u r i t i e s and the u n a v a i l a b i l i t y of addi t i o n a l Investment opportunities. Since the prime objective of t h i s test i s to out perform the market through appreciation i n the value of the p o r t f o l i o , dividends were not included i n ca l c u l a t i n g the r e s u l t s ; In addition, since dividends are not considered i n measuring the performance of the Index, the comparability of r e s u l t s i s enhanced. In attempting to a r r i v e at a meaningful measure of performance i n the current study, the method used i n Study No: 1 was discarded for reasons mentioned previously. Next, a form of price index was considered. It was hoped that a base-weighted aggregative index, such as that developed by Paasche, would be u s e f u l . His modified formula was of the form: Index = p-^  X 10 Where: p^ = the current market price of the security Q-^ = the number of shares currently outstanding of the security p = the average price i n the base period of the security QQ = the number of shares outstanding of the security i n the base period 75 An index of t h i s type would have yielded a measure of performance and, i n addition, could have been regressed against time i n order to measure the variance and thus obtain a measure of r i s k . Upon study, however, i t became apparent that the index would not have resulted i n a meaningful measure of performance. The following example w i l l explain why! Consider a p o r t f o l i o which was started i n time period t . During the next f i v e periods various s e c u r i t i e s were purchased and soldi In period t + 6 security x i s purchased, and at time period t + 7 we wish to measure the performance of the p o r t f o l i o from period t + 6 to t + 7. By using the index formula the p o r t f o l i o performance for t + 6 to t + 7 would be influenced by the price change of security x from period t to t + 7 and i s therefore an unsatisfactory measure. The measure f i n a l l y decided upon y i e l d s a figure which r e f l e c t s r e a l i s t i c a l l y the r e s u l t of each strategy. The approach taken i s that of an investment project, i . e . , for an amount of$x required i n time period t = 1, the Strategy yielded an amount of $y i n time period t = 45. By using the r a t i o = p, one i s able to determine the com pound rate of interest for which $1 i n t = 1 i s equal to ftp i n t = 45. The amount of $x for each strategy was determined by discounting the funds required i n period t over and above 76 the cash on hand i n period t . Thus i n each strategy the investor's beginning equity was $0 but through trading he was able to generate cash for h i s subsequent investment opportunities: Any addi t i o n a l funds required were assumed to be a v a i l a b l e at no out-of-pocket cost, e i g . , Savings Account deposits, estate funds or " r i c h benevolent Uncles." Table 10 (see Appendix II) shows the results of t h i s f i r s t e f f o r t . The f i r s t point to note i s that the system achieved an annual growth rate greater than that of the market, with the exception of Strategy 13. In addition, the growth rate of the buy and hold strategy was less than those of a l l the other strategies (again with the exception of Strategy 13)• In terms of maximizing returns, Strategy 3 yielded the largest d o l l a r amount ($54»253) while Strategy 5 yielded the highest growth rate (12.018$). Studying the strategies themselves, there i s one r e s u l t which was to be expected and another rather unexpected one: Considering the former f i r s t , as the s e l l i n g c r i t e r i a ) was varied from <C-.05 to </-.10, the r e s u l t s , as measured by the growth rate (Column D) and $ returns (Column A minus Column B) improve. The reason for th i s i s that short-term declines from an upward sloping trend l i n e caused the stocks to be sold (In the ^- .05 case) with two e f f e c t s ; (a) an above 77 average security was eliminated from the p o r t f o l i o , and (b) commission costs were unduly large. When was changed to <^-ilO, these two effects were eliminated and the r e s u l t s improved, except for Strategies 16 and 17. By r e d u c i n g ^ t o <-.15» the predominant ef f e c t was that of an improved growth rate . For values of<=*£of >.10 and >!15 and Z at any l e v e l , ^ < -^.10 was the dominant strategy. However, for a l l other combinations the compound annual percentage increase was larger and, i n most cases, the difference was not n e g l i g i b l e . Graphs A-D c l e a r l y show the e f f e c t ; Considering next the r e s u l t s obtained by varying , = > <^ i» i t was found that the optimum slope was >i l5 . Improved re s u l t s were obtained whenc*^ was increased from >.10 to y,15'» However, at values of >.20, >.25 and ^ .30, the r e s u l t s were poorer. It i s suggested that t h i s was due to firms being selected whose earnings experienced wide variations, such as c y c l i c a l companies. As a r e s u l t , t h e i r price performance dominated that of the one or two firms whose R.E. was growing at a s i m i l a r substantial rate but were of better q u a l i t y , i . e . , were more consistent. In addition, the wider price fluctuations meant that the security was sold more frequently than the >.10 and/ >i ! 5 cases. Thus greater amounts of cash were held (see Column E) and t h i s adversely affected performance. 78 It w i l l be remembered that for Strategies 16-30 an a d d i t i o n a l constraint of R.P.E. less than 1.0 was imposed; Comparing Strategies 1-9 with Strategies 16-24 shows that the growth rate f o r the l a t t e r was greater than the former i n s i x out of nine cases. For the remaining strategies there was no difference. This i s a p a r t i c u l a r l y i n t e r e s t i n g r e s u l t i n the l i g h t of returns obtained i n Study No. i . Based on t h i s , one would have expected Strategies I6-3O to exhibit a cl e a r superiority but such was not the case. The previous study's sample was comprised of well researched firms which hindsight had shown to be highly successful and which Eastman- D i l l o n considered would continue to be successful; On the other hand, the present sample was randomly chosen from many indus t r i e s . As a r e s u l t the former was biased i n favour of superior firms and the r e s u l t s appear to have been i n f l a t e d as a r e s u l t of t h i s bias. Evidence for t h i s suggestion i s contained i n Table 9» which shows the r e s u l t s of the o r i g i n a l study calculated on the same basis as the present study; The r e s u l t s are substantially better than any of the r e s u l t s from t h i s study and present e x c i t i n g implications regarding the r o l e of Fundamental Analysis: 79 TABLE 9 Compound Growth Rate of the O r i g i n a l Study on a Dollar Commitment Basis  TEST 1 TEST 2 D0W--JONES Year t fcGain P o r t f o l i o Value* $Gain P o r t f o l i o Value $Gain Value 1952 112 1,112 - - 117 1,117 1953 87 1,199 - - (3) 1,114 1954 412 1,611 - - 438 1,552 1955 470 2,081 910 1,910 202 1,754 1956 36O 2,441 36I 2,271 36 1,740 1957 121 2,562 (74) 2,197 (122) 1,668 1958 690 3,252 589 2,786 340 2,008 1959 520 3,772 361 3,147 152 2,160 I960 140 3,912 427 3,574 100 2,260 1961 270 4,182 551 4,125 174 2,434 1962 350 4,532 301 4,426 (100) 2,334 1963 300 4,832 311 4,737 165 2,499 C om pound Growth Rate** 25.32$ 30.32$ 7.84; * Based on $1,000 o r i g i n a l Investment and $1,000 invested every January 1. ** Compounded annually. Table 11 summarizes the re s u l t s obtained when the test was conducted during a time period when the market's beginning and ending multiple was the same. The res u l t s of Table 10 may be influenced by the fact that the s; & Pi Composite multiple increased from 1956 to 196?» As the reader w i l l remember, t h i s was a major c r i t i c i s m of my f i r s t study and i t s v a l i d i t y had to be investigated; The r e s u l t s vindicate the e a r l i e r findings and dissolve the multiple expansion argument; There are several i n t e r e s t i n g points to note i n these r e s u l t s ! F i r s t l y , the technique outperformed the market (except for Strategies 31> 3^, 37> 40 and 43) even though the beginning and ending multiple of the market was the same. For those Strategies which f a i l e d to outperform the market, the s e l l c r i t e r i o n (^ !05) had a si m i l a r but more dramatic impact on the growth rate mentioned e a r l i e r for Table 10. Considering the re s u l t s i n the f i r s t h a l f of Table 11, those obtained when was greater than ;15 dominated the cases of ^ ^ >;i0, >.20, >.25 and >:30: As w i l l be shown l a t e r (see Tables 12 and 13), t h i s Strategy was dominant i n every case; As i n the case of Table 10, the re s u l t s of the second h a l f of Table 11 were somewhat disappointing i n that only 7 out of the 15 strategies showed higher growth rates than 81 th e i r twin strategy i n the f i r s t h a l f . Also, no patterns or trends appeared which could be considered p a r t i c u l a r l y s i g n i f i c a n t ! Tables 12 and 13 contain the res u l t s of lagging the data; As discussed e a r l i e r , i t was conducted i n order to assess the impact on performance i f the investor applies t h i s technique under actual conditions. The re s u l t s are extremely inte r e s t i n g i n that, i n many cases, the Investor was able to maintain h i s above average performance, while i n cases where the growth rate was lower (10 cases out of 15), only one strategy exhibited a decline of greater than 1% i n the annual growth rate . In the case of Table 12, 1? out of 30 strategies showed no v a r i a t i o n i n the annual growth rate while the re s u l t s reported i n Table 13 showed an increase i n t h i s figure to 24! Of the s i x which did change, four of these showed an increase i n the annual growth rate while only two declined! As before, the growth rate was maximized when ^ was > i l 5 f o r the f i r s t h a l f of Table 12. These strategies were also dominant for the constant multiple case, as shown i n the f i r s t h a l f of Table 13. When the ad d i t i o n a l constraint of r e l a t i v e p r i c e - earnings, being less than 1!0, was added, the r e s u l t s i n Tables 12 and 13 did not vary from those shown i n Tables 10 and 11, respectively! CHAPTER V CONCLUSIONS Preliminary Note and Suggestions for Further Study In the re s u l t s reported i n Chapter IV an unexpected discovery was made. E a r l i e r i n the study i t was suggested that, i f the hypothesis was accepted, then the role of fundamental analysis would he open to question! Although the hypothesis was accepted, i t i s concluded that fundamental analysis has a greater rather than a lesser r o l e since the rates of appreciation of the p o r t f o l i o s chosen from the analyzed sample were subst a n t i a l l y greater than those of the random sample! Proceeding from t h i s f a c t , the next step would be to analyze, say, a group of 50 stocks. These firms would be those which, i n the opinion of the analyst, have expanding opportunities f o r investment. A second sample of 50 stocks would be randomly chosen, as was done i n the present study! The buy and s e l l c r i t e r i a as formulated would then be used to construct p o r t f o l i o s from the two samples and It i s expected that p o r t f o l i o s from sample one would outperform those of sample two and also the market! It should be noted that the test could not be conducted using h i s t o r i c a l data since sample one may be constructed with 83 the benefit of hindsight. Thus, the s t a r t i n g period would be at the time the analyst makes his forecast and would continue into the future for as long as is..desired: Since the area of r i s k was not incorporated i n the model, a further study along the following l i n e s might be undertaken! F i r s t l y , divide the slope of E!E: and RiP.Ei into the following classes - R!E! Slope (CXT i ) R.P.E. Slope ("Y^) 0 — i04999 (:04999) — 0 i05 — .09999 (.09999) - - ( ! 0 5 ) ;10 -- !14999 (.14999) -- (ilO) .15 — .19999 (.19999) — (.15) .20 — .24999 (.24999) — (.20) .25 — .29999 (.29999) ~ (.25) >.30 < (.30000) Using the buy c r i t e r i a defined e a r l i e r i n the model, p o r t f o l i o s would be constructed from a l l possible combinations of the above classes. In addition, a l l possible time periods, i : e ! , s t a r t i n g and ending dates, would be considered. The one major v a r i a t i o n , however, would be that the structure of the p o r t f o l i o would not change over time. Thus, once the p o r t f o l i o had been selected, i t s change i n value could be 84 compared with that of a market index over time and both performance and r i s k evaluated. GENERAL CONCLUSION The r e s u l t s of this research vindicate the conclusion reported i n Study #1 that r e l a t i v e value analysis i s a p r o f i t a b l e stock s e l e c t i o n technique. Sp e c i f i c Conclusions As indicated i n Chapter I, the purpose of the study was: (1) To investigate the hypothesis that r e l a t i v e value analysis enables the Investor to make buy and s e l l decisions which permit him to a t t a i n his objective of outperforming the market. (2) To offer support to the " t r e n d i s t " school, which supports the idea that technical analysis of stock price data i s a p r o f i t a b l e technique. (3) To answer c r i t i c i s m s of my previous study. Considering the t h i r d purpose, the r e s u l t s reported In Chapter IV indicate that these c r i t i c i s m s may have been j u s t i f i e d . The compound growth rate of the p o r t f o l i o s , although lower than that reported for Study No. 1, was never theless higher than that of the market. However, to what extent the lower growth rates are the r e s u l t of the sample being random rather than the lack of a general multiple expansion i s not known. But, considering the r e s u l t s when t = 45 (when there was an o v e r a l l multiple expansion) with 85 the r e s u l t s of Study No. 1, one i s led to suspect that the non-randomness of the Study No. 1 sample i n f l a t e d the r e s u l t s more than the multiple expansion. The second conclusion of t h i s study i s that stock price trends do exist and therefore, as Levy found, i t i s possible to p r o f i t a b l y exploit these trends. Based on conclusion (2) i s the t h i r d conclusion: that the stock market analyst who uses r e l a t i v e value analysis i s able to detect and exploit these trends; and that r e l a t i v e value analysis renders acceptable the theory that the investor can make buy and s e l l decisions which r e s u l t i n the selected p o r t f o l i o outperforming the market. BIBLIOGRAPHY BOOKS Baumol, W. J . The Stock Market and Economic E f f i c i e n c y . New York, Fordham University Press, 1965* Drew, G. A. New Methods for P r o f i t i n the Stock Market. Wells, Vermont, Fraser Publishing Company, 1966. Graham, B. The I n t e l l i g e n t Investor, 3rd revised e d i t i o n . New York, Harper & Row, 1965. , Dodd, D. L., & Cott l e , S. Security Analysis. 4th e d i t i o n , New York, McGraw-Hill Book Company, Inc., 1962. Hayes, D. A. Investments: Analysis and Management. New York, The MacMillan Co., 1966. Mao, J . C. T. Quantitative Analysis of F i n a n c i a l Decisions. Unpublished manuscript, University of B r i t i s h Columbia, 1968. Markowitz, H. M. P o r t f o l i o Selection. New York, John Wiley & Sons, Inc., 1959. McNeel, R. Wi Beating the Stock Market. Wells, Vermont, Fraser Publishing Company, 1963. Rose, D. C. A S c i e n t i f i c Approach to Investment Management. New York, Harper & Brothers, 1928. Schlalfer,. R. Probability and S t a t i s t i c s for Business  Decisions. New York, McGraw-Hill Book Company, Inc., 1959. Schultz, H. D. A Treasury of Wall Street Wisdom. (Ed. Samson Coslow). Palisades Park, New Jersey, Investors Press, Inc., 1966. 87 ARTICLES Barnes, L. "What Difference. Does Knowledge Make to Investors?" F i n a n c i a l Analysts Journal, v o l . 21, No. 5 (September-October, 1965)» PP. 60-68. Bernstein,. P.. L. "Growth Companies versus Growth Stocks." Harvard Business Review, v o l . 34, No. 5 (September- 0ctoner-, 1956), pp. 87-98. Reprinted i n Frontiers  of Investment Analysis (Ed. E. Bruce Fredrikson). Scranton, Pennsylvania, International Textbook Company, September, 1966, 2nd E d i t i o n . Birmingham, J . M. "Is Absolute or Relative Judgement Required?" F i n a n c i a l Analysts Journal, v o l . 20, No. 2 (March-April, 1964), pp. 62-63. , , "Random or Rational:..Stock Price Behaviour and Investment Returns." F i n a n c i a l Analysts Journal, v o l ; 21, No. 5 (September-October, 1965), pp. 52-53- B u r r e l l , 0. K. "A Mathematical Approach to Growth Stock Valuation." Readings i n F i n a n c i a l Analysis and  Investment Management (Ed. E. M. Lerner), Homewood, I l l i n o i s , Richard D. Irwin, Inc., 1963, PP. 338-348. Cragg, J . G. and M a l k i e l , B. C. "The Consensus and Accuracy of Some Predictions of the Growth of Corporate Earnings." Journal of Finance, v o l . XXIII, No. 1 (March, 1968), pp. 67-84. Fisher, L. "Outcomes for Random Investments-, in. Common Stocks Listed on the N.Y.S.E." Journal of Business, v o l . XXXVIII, No. 2 ( A p r i l , I965), pp. 149-161. Green, D. and Segall, J . "The Predictive-Power, of F i r s t Quarter Earnings Reports." Journal of Business, v o l . XXXX, No. 1 (January, 1967), pp. 44-55. Hammel, J . E. & Hodes, D. A.- "Factors.. Influencing Price-. Earnings M u l t i p l e . " F i n a n c i a l Analysts Journal, v o l . 23, No. 1 (January-February, 1967), pp. 90-92. Harkavy, 0. "The Relation between Retained Earnings and Common^Stock Prices for Large, Listed Corporations." Journal of Finance, v o l . v i i i , No. 3 (September, 1953), pp. 283-297. 88 Holt, C... C. "Influence of Growth Duration on Share Prices." Journal of Finance, v o l . XVII, No. 3 (September, 1962), pp. 465-475. King, B. F. "Market and Industry Factors i n Stock Price Behaviour." Journal of Business, v o l . XXXIX, No. 1, Part II (January, 1966), pp. 139-170, Kotler, P. "Elements., i n a Theory, of Growth Stock Valuation." Readings i n F i n a n c i a l Analysis and Investment (Ed. E. M. Lerner). Homewood, I l l i n o i s , Richard D. Irwin, Inc., 1963, pp. 355-369. Kourday, Mi "Relative Values - A Method...of. Outperforming the Market." F i n a n c i a l Analysts Journal, v o l . 19, No. 6 (November-December, I963), pp. 35-44. Levy, R. A. "Relative Strength as.a C r i t e r i o n for Investment Selection." Journal of Finance, v o l . XXII}" No. 4 (December, 1967), pp. 595-610. McWilliams, J . D. "Prices, Earnings and P-E Ratios." F i n a n c i a l Analysts Journal, v o l ; 22, No. 3 (May-June, 1966), pp. 69-75. Molodovsky, N; "Recent Studies of P-E Ratios." F i n a n c i a l  Analysts Journal, v o l . 23, No. 3 (May-June, 1967), pp. 101-108. Smilen, K. B. & Safian, K. "Relative Earnings. - A Fresh Perspective." F i n a n c i a l Analysts Journal, v o l . 20, No. 5 (September-October, 1964), pp. 104-107. T a b e l l , E,_ W. "Case for Technical Analysis." F i n a n c i a l Analysts Journal, v o l . 20, No. 2 (March-April, 1964), ppi o7-76. Whitbeck, V. S. & Kisor, J r . , M. "A New Tool i n Investment Decision Making." Reprinted i n Frontiers of Investment  Analysis (Ed. E. Bruce Fredrikson). Scranton, Pennsylvania, International Textbook Company, I965, PP. 335-350. MICROFILM Zimmer, R. K. "An Empirical Analysis of Stock Market Price Determinants;" Microfilm 65-5697, University Microfilms Library Services, Ann Arbor, Michigan. APPENDIX I LISTING REQUIREMENTS New York Stock Exchange a) Net earnings a f t e r taxes must equal at least $1,000,000 annually over a three-year period. b) Net tangible assets must be at least $10,000,000. c) There must be at least 500,000 shares outstanding d i s t r i b u t e d among 1,500 stockholders, each of which must hold at least 100 shares. American Stock Exchange a) Net earnings a f t e r taxes must be at least $150,000 for the past f i s c a l year and average at least $100,000 for the past three years. b) Net tangible assets must be at least $1,000,000. c) There must be at least 200,000 shares outstanding d i s t r i b u t e d among 750 shareholders, of whom at least 500 must each hold 100 shares or more. Also, the stock must have an aggregate market value of $2,000,000 outstanding and $1,000,000 of publicly held shares. Midwest Stock Exchange a) The company must have an a b i l i t y to show net earnings of at least $100,000. b) Net tangible assets must be at least $2,000,000. c) There must be at least 250,000 shares outstanding d i s t r i b u t e d among 1,000 shareholders. 90 P a c i f i c Coast Exchange a) The company must have demonstrated earning power of $100,000 annually OR b) Tot a l assets of at least $1,000,000. c) At least 250,000 shares must be outstanding, excluding family or concentrated holdings, di s t r i b u t e d among 750 shareholders. Source: Cooke, G i l b e r t W., The Stock Market, Simmons-Boardman Publishing Corporation, New York, 1964, pp. 214-215. APPENDIX II TABLES 10 - 13 92 TABLE 10 RESULTS OF STRATEGIES WITH NO DATA LAG AND t = 45 Strategy Ending Value Funds P r o f i t Annual Average Number of P o r t f o l i o Required Ratio Growth Cash ( $ ) * ( I ) * * C = A Rate($)*** Balance B {% of A) A B D E 1 $ 39,120 $ 15,138 2.5843 8.52 32.9 2 60,416 19,400 3.1143 10.22 7.2 3 81,397' 27.144 2.9987 9.88 2.0 4 24,133 7,089 3.4046 11.06 30.9 5 44,122 11,415 3.8654 12.02 8.1 6 45,517 13,610 3.6827 11.74 3.5 7 13,127 5,304 2.4749 8.13 43.9 8 23,878 8,372 2.8522 9.42 16.6 9 28,361 9,767 2.9037 9.58 8.1 10 5,707 2,739 2.0833 9.56 43.9 11 12,990 4,400 2.9524 9.73 18.2 12 16,913 5,825 2.9034 9.67 6.3 13 3,598 1,884 1.9092 5.79 30.4 14 10,427 3,503 2.9253 9.64 22.3 15 14,123 4,912 2.8751 9.48 7.3 * Less commission of 1% on purchases and sales. ** Discounted at a rate of 6% *** Compounded quarterly. 93 TABLE 10 (continued) Strategy Number 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Ending Value of P o r t f o l i o ( I ) A $ 22,229 28,930 31,673 10,619 14,732 18,022 6,838 7,614 9,363 1,933 3,549 4,803 1,920 3,688 4,754 Funds Required ($) B $8,515 10,762 14,541 2,912 4,064 5,070 2,898 2,898 2,898 942 942 942 942 942 942 Pr o f i t Ratio 2.611 2.688 2.178 3.647 3.625 3.555 2.360 2.627 3.231 2.052 3.767 5.098 2.038 3.915 5.046 Annual Growth Rate($) D 8;6o 8.88 8.98 11.66 11.60 11.42 7.70 8.66 10.55 6.43 11.96 14.70 6.37 12.29 14!25 Average Cash Balanc e E 34.5 12i6 5.6 60.2 16.2 12.5 63.4 46.0 31.3 77.1 47i2 41.7 78.2 50 i 3 43:0 Standard & Poor's Composite 6.53$ Buy and Hold, i . e . , $1,000 worth each of 50 stocks 7.85$ 94 TABLE 11 RESULTS OF STRATEGIES WITH NO DATA LAG AND t = 37 Strategy Ending Value Funds P r o f i t Annual Average Number of P o r t f o l i o Required Ratio Growth Cash (ft)* (ft)** Rate($)*** Balance A B C D (% of A) E 31 ft 23,706 ft 13,187 1.798 6.38 22.9 32 47,108 16,484 2.878 11.50 7.2 33 63,384 19,818 3.198 12.72 3.6 34 15,739 6,795 2.316 11.78 21.9 35 33,653 9,773 3.443 13.56 9.7 36 37,870 10,967 3.453 13.60 6.2 37 9,028 5,803 1.556 4.80 40i9 38 19,832 6,558 3.024 12.46 19.0 39 22,595 7,009 3.224 12.86 12.8 40 4,353 3,954 1.100 1.01 42.5 41 12,419 4,661 2.664 10.73 15.3 42 15,108 5,346 2.826 11.38 5.9 43 3,275 2,923 1.120 1.43 43.5 44 9,928 3,662 2.711 10.93 I8;i 45 12,611 4,347 2.90.1 11.67 7:3 # See Table 10. 11 11 it I* »l »• 95 TABLE Strategy Ending Value Funds Number of P o r t f o l i o Required (!) ($) A B 46 $ 13,933 I 8,535 47 24,075 10,161 48 35,519 12,763 49 6,354 2,877 50 13,745 3,968 51 15,516 3,968 52 3,560 1,900 53 5,945 1,900 54 7,371 1,900 55 .730 1,175 56 3,307 1,615 57 4,734 1,615 58 730 1,155 59 3,267 1,508 60 4,687 1,508 1 (continued) P r o f i t Annual Average R a t i o Growth Cash Rate($) Balance C D E 1.632 5.32 25.2 2.369 9.46 11.1 2.783 11.21 3.2 2.209 8.65 24.8 3.464 13.64 1.1 3.910 14.49 9.5 1.874 6.84 48 .3 3.129 12,53 3.2 3.879 14.88 2.7 .621 - - 2.048 7.82 1.1 2.931 11.78 2.0 .632 - - 2.166 8.43 10.6 3.108 12.42 2.0 Standard & Poor's Composite Buy and Hold 6.98$ 10.52$ 96 TABLE 12 RESULTS OF STRATEGIES WITH DATA LAG AND t = 45 Strategy Ending Value Funds P r o f i t Annual Average Number of P o r t f o l i o {*)• A Required ( 1 ) * * B Ratio C Growth Rate(#)#** D Cash Balance (% of A) E 61 $ 39,035 $ 15,239 2.526 8.31 32:8 62 60,082 21,070 2.852 9.41 6:6 63 81,107 27,076 2.996 9.88 1:8 64 24,048 7,182 3.348 10.88 33i3 65 44,024 11,499 3.829 13:02 6:9 66 49,831 13,552 3.677 11.73 3:4 67 13,127 5,304 2.475 8.13 43i9 68 23,644 8,318 2.843 9.38 I5i3 69 28,070 9,486 2.959 9:08 7.6 70 5,546 2,698 2.056 6.44 41.0 71 12,756 4,346 2.9351 9.61 15.6 72 16,623 5,770 2.881 11.01 4:7 73 3,386 1,680 2.016 6:27 40:7 74 10,014 3,431 2.919 9.62 18:7 75 13,833 4,841 2.857 9i43 5:0 See Table 10. II It II II II II TABLE 12 (continued) 97 Strategy Ending Value Funds Number of P o r t f o l i o Required (*) (•) A B 76 $ 22,229 1 8,515 77 28,930 10,762 78 31,673 14,541 79 10,619 2,912 80 14,732 4,064 81 18,022 5,070 82 6,838 2,898 83 7,614 2,898 84 9,363 2,898 85 1,933 942 86 3,549 942 87 4,803 942 88 1,920 942 89 3,688 942 90 4,754 942 P r o f i t Annual Average R a t i o Growth Cash Rate($) Balance C D (% of A) E 2.611 8.60 34:5 2.688 8.88 12;6 2.178 8.98 5.6 3.647 11.66 60.2 3.625 11.60 16.2 3.555 11.42 12.5 2.360 7.70 63.4 2.627 8.66 46.0 3.231 10.55 31.3 2.052 6.43 77.1 3.767 11.96 47.2 5-098 14.70 41.7 2.038 6.37 78.2 3.915 12.29 50.3 5.046 14.25 43.0 98 TABLE 13 RESULTS OF STRATEGIES WITH DATA LAG AND t = 37 Strategy Ending Value Funds P r o f i t Annual Average Number of Po r t f o l i o Required Ratio Growth Cash ($)* ( ? ) * * Rate($)*** Balance {% of A) A B C D E 91 $ 23,624 $ 13,187 1.792 6.34 23:0 92 47,006 16,354 2.874 11.57 7:2 93 63,282 19,701 3.212 12;78 3.6 94 15,657 6,794 2,304 9.12 22a 95 33,552 9,713 3.454 13.60 9:8 96 37,768 10,822 3.490 13.72 6;2 97 9,028 5,803 1.556 4.80 98 19,832 6,558 3.024 12.46 19.0 99 22,595 7,009 3.224 12.86 12.8 100 4,353 3,954 1.100 1.01 42.5 101 12,419 4,661 2.664 10:73 15.3 102 15,108 5,346 2.826 11.38 5.9 103 3,275 2,923 1.120 1.43 43i5 104 9,928 3,662 2.711 10.93 18;1 105 12,611 4,347 2.901 11.67 7.3 See Table 10 11 11 11 11 11 11 TABLE 13 (continued) Strategy Ending Value Funds Number of Po r t f o l i o Required A B 106 ft 13,933 ft 8,535 107 24,075 10,161 108 35,519 12,763 109 6,354 2,877 110 13,745 3,968 111 15,516 3,968 112 3,560 1,900 113 5,945 1,900 114 7,371 1,900 115 730 1,175 116 3,307 1,615 117 4,734 1,615 118 730 1,155 119 3,267 1,508 120 4,687 1,508 P r o f i t Annual Average Ratio Growth Cash Rate($) Balance {% of. A) C D E 1.632 5.32 25.2 2.369 9,46 11.1 2.783 11.21 3,2 2.209 8.65 24.8 3.464 13.64 1.1 3.910 14.49 9.5 1.874 6.84 48.3 3.129 12.53 3.2 3.879 14.88 2.7 .621 - - 2.048 7.82 1.1 2.931 11.78 2.0 .632 - - 2.166 8.43 10.6 3.108 12.42 2.0 APPENDIX III GRAPHS A - D GI IA] FH A — — — — GR 0_Vi TE _E A3 !E_ \ A£ >.N_ _Q] >< AJ TO. - f t _E )R IB LE _1. 0 ( J ) 1 (c (c L) : ( < •0 r) . : ( S.) •:( h i ) ( k) (1 ):: — 1 4 — !l2 — 10 _.. - • — - — — — /, / / - - — - y — — / 8 / / / ' i 6 — — / — — Jlat 5 ~w .:_ \ — — - - — — -Gr bh r — .% - T - — — T — ?, — — — 0 io: >a<: > 0 >.3P. LO > a 5 0 > 5 .3 0 I. — • — • — - - • — | c >< = the s! Lof De ol ;h< 5 I 2. L. In •; J-R. XV .._|_-E A su and bs eq ue nt g rg .s ar i e re :ac . £ LS' fc >i: - O l js i .... - - i 1 r. Ca se ( a) : Th e i s t pc >ir it re J pi *eser lt£ i : :a' ie o: r \ bh w' i e . t i c < > a 0 an d < 0.5 — — - — Si ml y~ ti i — I f — - J ' 2r 3r Ca id i« II . it — II i II — II H — ti it I I II < io; l a r-3 se -( ~n -b") ' i n i I i r — • i i» II < 1 5 ro r I • — — ..„ — - - - — . -I: — -3-o 1 :...p. . 1: " " t " Ca )' * - 1 — • ..  [—i U J .W.W.AJL. I J I I .... — (-e ) (f ,) 1 Ts ... -:- — - — — — — -•- 1 | 1 i —: — — i. . — -/— i —J-... i & L3 L2 -< — OS ... . TO — / \ re y i . • \ —-\ / "*•« 1 j . < - 5. /. \ r 1 ..  .... — V — I i\ ... i _ l ._ .1 ... -~ i / I \ ! i r -i .. . L . 11 - ... .... — \ 1 .... —- — .— — — — I -: ] Hi a.t 2 1 I' —- i l — ... — .... — of 1.0. l i .j 1 i ! Gro '1 $ fftl -)-•- t i I T " — --- 1 i •~r-i _:4__ i — — r . { -1 — i — 1 ! " T " i .. 7 l • • ! 8 - f / i j .... 1 • i • ] | ... — 1 — - i \ i — --- 7 — • 1 i 7„ • •! / i.... i i 1 — — — : — i i — — \\- .... — — - ! —1— i — i / i / • 7 — i — r i I i 5 i i ..  i — / | i— .. . .... - — ! • j — V Ii . .. — — • — — — i i • —- 3 — • t i i 2. —- — .... i • • T " — i i i i i — .... • :| --— ... .... - — 1 i i • 1 ^1 i I i 1 ! ~ -..  10 >.20 >; 30 —- > ab..> i .20.) >.3'0- •i :..l|0J 1 •i2 0-— •< L . l o-; U< .0-' 1 >.-30- >.: 10- 10- 30 >. 1-0 >; 2-0 >. i i. • | 1 1 e_ R. E, . i 1 1 1 l : i •=!-t he s lb _ C .f_ - L i r i e ' i " : G R A P H C — - 1 • GB T E _ I A T E . A £ mi ic; ?i.< >N. -o: ( -P- DR -T. F T A B L E -1 2 . ..... - (a) •(b)" ( c ) (t i ) 8 ) ( f ) ( g) ':'( h) ) V L) 14 - — 12 10 — e th 8 — 'A / y — - ' - — •• / / — / 6 / — _ 4 r - — 2 — 0 — — •: — > i l 0 5 > >i'20 > >i2 5 i . l o LO > > i-2-0 > i:2 5 0 • — — — - — c — th e -o'l _o.f -L: :n< - - - — — — — — — — — - - - - — - - I t • ;• • • . 

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