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Empirical tests of a market trading rule based on the notion of market disequilibrium Yaworski, Laurie Gerald 1973

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EMPIRICAL TESTS OF A MARKET TRADING RULE BASED ON THE NOTION OF MARKET DISEQUILIBRIUM by LAURIE YAWORSKI B.Sc, University of Saskatchewan, 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION in the Faculty of Commerce and Business Administration We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July, 1973 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver 8, Canada Date ABSTRACT The notion o f beta in the stock market i s a concept o f r i s k that has had wide acceptance in the academic and investment communities as a c o e f f i c i e n t o f n o n - d i v e r s i f i a b l e r i s k . The d e f i n i t i o n of beta and i t s use as a measure of r i s k depends on the empirical v a l i d i t y of the market model. The market model i s a l i n e a r equation of the form y = a + bx + c where b (the slope of the l i n e ) i s the beta c o e f f i c i e n t : I t relates the proportion by which a stock's price w i l l change to a change in the market index. The measurement of the beta value has been tested and proven to be stationary over time. Therefore the estimated values in one period are biased estimates of the future values. Professional managers can s e l e c t a level of uncertainty at which to operate and have tended to remain at that level over the years. A model such as this f o r s e l e c t i n g e f f i c i e n t p o r t f o l i o s i s a very r e l a t i v e component in the development of improved normative procedure f o r investment management. Among the possible uses of an e f f e c t i v e measure of r i s k are: 1) the assessment of r i s k in s p e c i f i c s e c u r i t i e s as well as p o r t f o l i os; 2) measurement of the current r i s k in any group of stocks represented by the various market averages; 3) comparison of the r i s k o f individual s e c u r i t i e s with that o f other s e c u r i t i e s and the market as a whole; i i i i i 4) means of screening in search for undervalued and over-valued stocks; 5) aid to timing in buying and s e l l i n g ; 6) a basis f o r s e l e c t i n g and adjusting p o r t f o l i o r i s k to f i t an investor's requirements; 7) means of adjustment to take advantage of market trends and a l o g i c a l basis f o r investment decision making. In accordance with the above theory of market equilibrium, stock prices would adjust instantaneously in some proportion to the changes in the market index. Given the assumptions of the theory, the length of the period over which beta i s calculated should be i r r e l e v a n t to the measure. The implication i s that beta may be useful in short run investment strategy. I t i s f e l t that the adjustment process i s not instantaneous but incorporates some stocks that may be overpriced and others that may be underpriced. Furthermore stocks may lead or lag the market index into a b u l l i s h or bearish market. Trading rules based on the market s e n s i t i v i t y of stocks in the period June 1959 to June 1969 were used to test the p r o f i t a b i l i t y of short run investment strategy in r i s i n g and f a l l i n g market trends. These trading rules developed in the ex post were applied in the ex ante from June 1969 to June 1972 to determine i f there were any stable r e l a t i o n s h i p s . The empirical evidence does not provide very strong conclusions. The results indicate that the adjustment of a stock p r i c e r e l a t i v e to the market i s not instantaneous. There are stocks that lead and stocks that i v lag the market into e i t h e r an "up" or "down" swing. However these relationships are not stable from one period to the next. Where there i s s t a b i l i t y , the timing i s most uncertain. This indicates that the markets are not t r u l y e f f i c i e n t and thus i t becomes a t e s t of the major assumption of the market model. Despite this lack of s t a b i l i t y the results of the trading rules indicate that beta may be used e f f e c t i v e l y on a continuing basis in a d e c l i n i n g market. The rules which are based on a long term beta help us to i d e n t i f y those stocks which vary widely from t h e i r expected prices allowing us to activate trading which i s p r o f i t a b l e f o r the p o r t f o l i o . The findings indicate that beta may be used in this sense as a " l o s s " minimizing technique. However the obvious l i m i t a t i o n i s that the trading rules cannot be applied symmetrically to both markets i n order to bring the best r e s u l t s . Furthermore there i s the major d i f f i c u l t y of predicting the market. Extreme confidence in the f i l t e r rules i s required. Another problem i s that continuous trading a l t e r s the p o r t f o l i o beta at which the manager has selected to operate. The most useful information obtained from the tests i s that through further study and the development of better trading rules the technique maybequite useful. TABLE OF CONTENTS Chapter Page I INTRODUCTION 1 II THE THEORETICAL RELATIONSHIP OF SECURITY PRICES TO THE MARKET 4 III METHODOLOGY - DESCRIPTION OF DATA AND DATA PROCESSING 12 IV EX POST CONSIDERATIONS 18 V EX ANTE RESULTS 32 VI CONCLUSIONS 43 BIBLIOGRAPHY 47 APPENDIX: TABLES I TO XII 48 v CHAPTER I INTRODUCTION The concept of beta with respect to the stock market i s that i t i s a measure of v o l a t i l i t y of a stock or a p o r t f o l i o , r e l a t i v e to the movement of a market index. I t i s assumed to be stable and stationary through time and to be unaffected by the p a r t i c i p a t i o n of investors in the market place. In theory, the stock would move in the same di r e c t i o n as the market index to a degree proportionate to i t s beta c o e f f i c i e n t . Over long periods the beta i s reasonably accurate but as we shorten the period of i n t e r e s t betas f o r an individual stock become inaccurate rendering them useless f o r t r a d i t i o n a l applications. The implication i s that f o r short run investment strategy the beta has not been able to o f f e r any additional information when used in i t s t r a d i t i o n a l applications f o r sel e c t i n g individual stocks. The beta c o e f f i c i e n t i s a notion of market equilibrium where a l l stock prices instantaneously adjust in some proportion to the change in the market index. Given i t s assumptions this notion i s v a l i d i n theory and the length of the period over which the beta i s calculated should be i r r e l e v a n t to the measure. In a s t a t i s t i c a l sense beta i s most s a t i s f a c t o r y when measured over r e l a t i v e l y long periods of time because shorter period disequilibriums are averaged out. 1 2 The purpose of this paper i s to determine whether betas measured over long periods of time can be used e f f e c t i v e l y on a continuing basis in making short run decisions. Trading rules based on the market sensi-t i v i t y of stocks w i l l be used to see i f some p r o f i t can be made through these short run decisions I t i s f e l t that the time of adjustment of a stock price r e l a t i v e to the market index i s not instantaneous but incor-porates some stocks which w i l l move ahead of the index while others move behind. Therefore we would take the position that in a r i s i n g market we w i l l be able to receive larger gains over shorter periods of time and during a de c l i n i n g market losses would be c u r t a i l e d by holding stocks f o r shorter periods of time. I t i s expected that stocks do not adjust instantaneously but rather there are stocks that may lead or lag the market into an "up" swing or "down" swing. A trading rule that allows one to adjust his p o r t f o l i o in l i g h t of this knowledge would be most p r o f i t a b l e . I f an asset i s underpriced r e l a t i v e to i t s equilibrium p r i c e , i t would be most s a t i s f a c t o r y to acquire this asset and hold i t u n t i l i t reaches i t s peak pric e . I f an asset i s overpriced i t would be p r o f i t a b l e to s e l l the stock before there i s a tendency for i t to f a l l to i t s equilibrium p r i c e . The i n t e r e s t i s focused in two d i s t i n c t time periods. Trading rules are developed in the ex post period and then applied to the ex ante period to determine whether there are any stable relationships. In Chapter II the notion of the beta c o e f f i c i e n t or the theore-t i c a l relationship of security prices to the market are discussed. A hypothesis i s derived from this theoretical r e l a t i o n s h i p . In Chapter III the data and data processing are discussed. In Chapter IV the ex post considerations are presented and dis cussed. In Chapter V the ex ante results are presented and discussed. The ex post and ex ante results are then compared. Chapter VI contains the conclusion. I t also looks at the impl cations, l i m i t a t i o n s and uses of the technique. CHAPTER II THE THEORETICAL RELATIONSHIP OF SECURITY PRICES TO THE MARKET The Capital Asset P r i c i n g Model at t r i b u t a b l e to Sharpe 1 and Lintner presented a theoretical r e l a t i o n s h i p between the prices of se c u r i t i e s i n the capital market. The security prices are related through a common dependency on the market factor and i t i s assumed that this relationship i s . s t a t i o n a r y and stable overtime. A security's expected return i s posited to move in rel a t i o n s h i p with the return of the market factor overtime. The relationship i s defined by a constant which has been c a l l e d systematic r i s k (beta c o e f f i c i e n t ) which i s the proportion by which the security's expected return w i l l vary for a one percent change in the market's expected return. The market return i s the change in the market index ( i . e . T.S.E., D.J.I.A., N.Y.S.E.). The systematic r i s k does not capture the f u l l v a r i a b i l i t y of a security's return. The return i s also influenced by c h a r a c t e r i s t i c s which are unique to that s e c u r i t y . However the changes in a security return caused by these unique c h a r a c t e r i s t i c s of that company and that ^William F. Sharpe, "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk," Journal of Finance, September 1964, 425-42. 2 John Lintner, "The Valuation of Risk Assets and the Selection of Risky Investments in Stock P o r t f o l i o s and Capital Budgets," Review of  Economics and S t a t i s t i c s (1965), 13-37. 4 5 company's industry are assumed to be independent of the market factor and therefore non-systematic. The systematic component which relates price changes to the market factor r e f l e c t s investor psychology towards the general economic, monetary and p o l i t i c a l outlook. This component (beta c o e f f i c i e n t ) i s evident to some degree in a l l stocks and indicates the influence of the stock market on a common stock. I f the systematic component i s viewed as the average relationship of security returns with the market returns overtime, then i t i s reasonable to suppose that when the security return deviates s i g n i f i c a n t l y from i t s expected value, given the market return, i t w i l l have to compensate with greater movements in the opposite d i r e c t i o n to maintain the average r e l a t i o n s h i p . 3 A l i n e a r regression developed by Treynor relates the expected 4 return of a stock to the rate of return of a market index. Sharpe's equation: Rs = a + e(Rm) + e where Rs - Stock Return Rm - Market Return 3 - Beta C o e f f i c i e n t a - Unsystematic r i s k e - Error Term which i s a l e a s t squares equation, i s Treynor's l i n e a r regression model. Graphically Treynor showed what a and 3 are: Jack Treynor, "How to Rate Management of Investment Funds," Harvard Business Review (1965), 63-75. 4 Sharpe, "Capital Asset Prices," op. c i t . 6 ares regression l i n e Beta Beta i s a measure of vo l a t i 1 i ty Alpha i s % change i n asset due to unique factor We understand the equation as saying: (% change in a stock) = alpha + beta (% change in the market index). The slope of th i s regression l i n e i s the value of beta which measures the responsiveness of the stock return to a movement in the market index return. I t i s assumed that beta i s stable and stationary through time and to be unaffected by the p a r t i c i p a t i o n of investors i n the market 5 place. In theory a stock should move in the same d i r e c t i o n as the market index to a degree proportionate to i t s beta c o e f f i c i e n t . Some se c u r i t i e s are more s e n s i t i v e to changes in the market than others. When a security has a B = 1, the stock i s assumed to change with the market. I f 3 < 1» the security i s described as defensive and moves Marshall Blume, "On the Assessment of Risk," Journal of Finance, March 1971, 1-9. 7 less than the typical stock in the market swing. I f 3 > 1, the security is aggressive and moves more than the typical stock. I t i s uncommon for a security not to go along with the market. This i s in agreement with Sharpe's assumption that the percentage change in the price of a security from i t s expected value i s most l i k e l y to equal i t s market s e n s i t i v i t y (beta) times the percentage change in the market from i t s expected value (Rs = 3 ( M ) . Beta i s a long run equilibrium notion that averages out d i s -equilibrium s i t u a t i o n s . Over a long period of time with quarterly obser-vations, the beta i s reasonably accurate because the interperiod lags and leads of stock price movements r e l a t i v e to the index are averaged out. I f a computer i s programmed so that the quarterly c l o s i n g prices of a stock are regressed against the closing prices of a market index, a s t r a i g h t l i n e i s drawn through scattered points. The slope of the l i n e i s the beta c o e f f i c i e n t describing the e f f e c t of market changes and the intercept on the v e r t i c a l axis i s the alpha or that part of the p r i c e change due to unique factors. Beta i s assumed to be stationary overtime. When evaluating a p o r t f o l i o one could use the h i s t o r i c a l value of beta as a future estimate of a stock's beta c o e f f i c i e n t . The reason as pointed out by Blume,^ i s that the errors in taking an average w i l l be less than the errors of the parts that make up the average i f the errors of the parts are independent of each other. Fama^ indicated that this property of 6Blume, "On the Assessment of Risk, op_. c i t . ^Eugene Fama, " P o r t f o l i o Analysis in a Stable Paretian Market," Management Science, January 1965, 404-419. 8 averages i s true for d i s t r i b u t i o n s associated with the stock market. Blume through the use of c o r r e l a t i o n c o e f f i c i e n t s showed that there i s value in using e a r l i e r data in assessing future r i s k . In the context of a p o r t f o l i o , systematic r i s k cannot be diver-s i f i e d away. Therefore beta i s best u t i l i z e d to s e l e c t stocks for the purposes of inclusion in a " f u l l y d i v e r s i f i e d " p o r t f o l i o of stocks. The beta value f o r each security i n the p o r t f o l i o has been established through various ingredients. The values obtained f o r individual s e c u r i -ti e s are combined (weighted sum) to c a l c u l a t e the comparable value f o r a p o r t f o l i o . A stock's beta c o e f f i c i e n t does not measure the r i s k asso-ciated with an asset in i s o l a t i o n but rather indicates the contribution by that asset to the v o l a t i l i t y of a " f u l l y d i v e r s i f i e d " p o r t f o l i o . Therefore the manner in which a manager would u t i l i z e beta would be twof old: 1) He must try to form some expectation of the future level of the market and adjust his p o r t f o l i o beta in this manner. 2) He must i d e n t i f y s e c u r i t i e s which f o r unique reasons w i l l r e a l i z e a return greater than the expected return subject to t h e i r level of systematic r i s k . In p r a c t i c e , markets are not t r u l y e f f i c i e n t and at times a stock may be underpriced (or overpriced) r e l a t i v e to a l l other assets. I f some degree of e f f i c i e n c y e xists in the market, eventually the under-priced asset w i l l r i s e to a level where the expected returns w i l l be commensurate with the level of systematic r i s k - the asset's equilibrium p r i c e . In such a case, i f the asset had been acquired when i t was 9 underpriced and held u n t i l i t reached i t s equilibrium p r i c e , superior performance would be achieved. Theoretically a stock's p r i c e should be in harmony with the expected return. Given that the stock has a value of beta, the stock would s t r i v e to maintain a price equivalent to the adjusted market index. The adjusted market index i s the value of the market index multiplied by the value of the beta c o e f f i c i e n t . According to the equation where RS = 3 *Rm, the return of the stock w i l l equal the return on the market (adjusted by the beta c o e f f i c i e n t ) . The value of alpha ( a ) i s assumed to be nonexistent or zero. The notion of instantaneous adjustment i s v a l i d in theory and the length of the period over which the beta i s calculated should be ir r e l e v a n t to the measure. The value of beta would be s t a t i s t i c a l l y s a t i s f a c t o r y when measured over a r e l a t i v e l y long period of time. How-ever, as we shorten the period and increase the frequency of observation, the beta f o r an individual stock becomes very inaccurate and i s thus rendered useless f o r t r a d i t i o n a l a p p lication. The implication of this i s that f o r short run investment strategy the beta has not been able to o f f e r any additional information when used in i t s t r a d i t i o n a l a p p l i -cations f o r s e l e c t i n g individual stocks. Recognition of measurement error i n the s i z e of the beta c o e f f i -c i e n t suggests that only large deviations of the security return from the expected value should be considered. Any trading rule which attempts to c a p i t a l i z e on temporary deviations from equilibrium w i l l have to incorporate broad screening bands to neutralize the misleading e f f e c t o f measurement error. 10 o Conrad Thomas, indicated that there may be a s i g n i f i c a n t d i f -ference in the short run r i s k associated with a stock and the long run ris k or systematic r i s k as measured by the beta c o e f f i c i e n t . One would be i n c l i n e d to agree with him in that i f a stock i s at the upper end of i t s price range, the p r o b a b i l i t y that i t w i l l f a l l i n price i s greater than the p r o b a b i l i t y that i t w i l l r i s e . This i s in agreement with what was mentioned e a r l i e r about the stock being underpriced (overpriced). Furthermore i t i s in l i n e with the theory that a stock w i l l tend towards i t s average price or return which i s the value Rm*Beta. Morgan's law which indicates that the market w i l l fluctuate lends a hand to the theory that a stock w i l l tend towards i t s average p r i c e . Thomas u t i l i z e s a short term r i s k which we have disregarded. However he does raise some in t e r e s t i n g points i n terms of timing through a market cycle. Deviating somewhat from his study, a d i f f e r e n t approach u t i l i z i n g beta may be quite useful. Hypothesis I f the beta c o e f f i c i e n t i s r e l a t i v e l y stable in the long run, then the reason f o r short term betas being unstable may be that the time of adjustment of a stock price r e l a t i v e to the market index i s not instantaneous but incorporates some stocks which w i l l move ahead of the index while others move behind. In diagram A, the stock i l l u s -trated would appear to be moving behind the market index. In this par-t i c u l a r case i t takes the stock one year to catch up to the market in Conrad Thomas, "Beta Mousetrap," Baron's, February 7, 1972. 10a the upswing. In B, the stock moves ahead of the market. I t would be inte r e s t i n g to see i f there i s a stable lead or lag relationship of the stock to the market from period to period and in addition whether a stock that leads i n the upswing does the same in a downswing. An upswing i s a b u l l i s h market s i t u a t i o n and a downswing i s a bearish market s i t u a t i o n . A Return Return Time Peri od I f these lead and lag relationships are f a i r l y constant they would be predictable i n advance i f the market movement i s c o r r e c t l y predicted. The implication here i s that the leaders can be held when the forecast i s for a strong b u l l market, and those that lag the market can be acquired as the bull market proceeds through time. A related concept i s that i f the stock has not moved r e l a t i v e to the market, i t would be expected to move i n the future. 11 Several firms produce estimates of market s e n s i t i v i t y on a con-tinuing basis. This raises a question - can beta be used e f f e c t i v e l y on a continuing basis - that i s , in making decisions from week to week in order to make p r o f i t s . I t seems that beta would be more useful over a longer period of at l e a s t two years. However, i t would be i n t e r e s t i n g to see i f using beta on a con-tinuous weekly basis would be e f f e c t i v e . Given that the value of beta is a measure of market s e n s i t i v i t y , w i l l this concept be e f f e c t i v e in short run decisions. For example, even i f 3 = 2.5 (which may be des-cribed as being very s e n s i t i v e ) , i t may not be very s e n s i t i v e in a sub period where that stock has already reached i t s plateau given that there i s an upswing in the market. Furthermore can trading rules based on the notion of market disequilibrium be used e f f e c t i v e l y ? 1 CHAPTER III METHODOLOGY - DESCRIPTION OF DATA AND DATA PROCESSING The purpose of this chapter i s to present the data and to b r i e f l y describe the s t a t i s t i c a l tests performed. The results of the tests -namely the ex post considerations and the ex ante results w i l l be con-sidered i n the following chapters. 3.1 Data Selection The study began by screening 101 stocks out of a possible 200 stocks in which pensions plans have traded i n . The screen was designed to include only those stocks which had a ten year price history from 1959 to 1969 i n c l u s i v e . The 101 stocks used were chosen at random from the l i s t of stocks that met the requirement of thi s ten year price history. The stocks chosen represent a number of various i n d u s t r i e s . (Table I.) There were 101 stocks used i n the ex post but only 99 used i n the ex ante because 2 stocks f a i l e d to appear on the Toronto Stock Exchange a f t e r June 1969. 3.2 Beta Calculation Once the stocks were chosen the quarterly stock prices and d i v i -dends for each of the stocks were c o l l e c t e d and the beta f o r each stock was calculated from the quarterly returns over the period June 1959 to 12 13 June 1969. This calculation was done by using the TRIP regression pack-age at the U.B.C. Computer Centre. The quarterly return of each stock was regressed against the quarterly return of the market. The market return was calculated from the Toronto Stock Exchange industrial index. The value of each stock's beta (e) appears on Table I along side each stock's number and name. The value of beta was derived from the regression: Rg = a + 3(Rm) where Rg = quarterly stock return 3 = beta R = quarterly market on T.S.E. return a = intercept of the regression equation. The values of the betas vary. Fifty percent of the stocks have a beta value less than one and the other 50% have a beta value greater than one. This is an indication of the variety of stocks chosen. 3.3 Ex Post Market Trends The statistical tests began by analyzing the monthly T.S.E. industrial price index. Within the ten year period two definite market trends were observed from a plot of the monthly T.S.E. index. The monthly returns were used because in this way the weekly returns would be averaged out. In this manner, more definite trends could be defined. A rising and a falling market were first observed from a graphi-cal plot of the T.S.E. index. The rising market was defined as a market trend where there were continuous positive returns. The beginning of this market trend was indicated by a monthly return of 5% which was followed by continuing returns. We do not pass out of this trend until 14 the market f a l l s by 5% in one month and i s followed by a stable or de-c l i n i n g market. The f a l l i n g market was defined as a market trend where there was a continuous negative or very small p o s i t i v e return. We were con-sidered to be in a declining market when there was a negative return in two consecutive periods. We remain in this trend as long as negative returns p e r s i s t or as long as the returns are close to zero. We do not pass out of a d e c l i n i n g market u n t i l a d e f i n i t e p o s i t i v e trend i s i n d i -cated. Such a trend was defined as a 5% return followed by continuing p o s i t i v e returns. The periods chosen were those that represented these trends the best. I t was f e l t that a trend averaging about one year in length would best s u i t the purposes of our t e s t s . The r i s i n g market was defined as the period from March 29, 1968 to A p r i l 1, 1969. The f a l l i n g market was defined as the period from September 24, 1965 to October 14, 1966. I t i s these periods that were examined to measure the lead or lag of each stock r e l a t i v e to the market index movement. 3.4 Ex Post Computer Calculations The weekly closing prices within the periods defined were c o l -lected f o r each of the stocks. The weekly arithmetic returns and the cumulative weekly returns were calculated. This weekly return did not take into account dividends because our i n t e r e s t l i e s mainly i n capital appreciation (depreciation). The T.S.E. index prices were also c o l l e c t e d on a weekly basis and the weekly return also calculated. This w i l l be referred to as 15 the market return. The weekly market return was then multiplied by that p a r t i c u l a r stock's beta c o e f f i c i e n t to derive an expected return for that stock. T h e o r e t i c a l l y , as pointed out in the l a s t chapter, this i s the return the stock should have achieved given i t s value of the beta c o e f f i c i e n t . The cumulative weekly sum of t h i s expected value (R m*3) was calculated. The actual cumulative weekly returns were also calculated for each stock. In this way the actual cumulative values and the expected cumulative values could be compared. For comparison sake, the expected cumulative values were subtracted from the actual cumulative values to derive the cumulative difference between them. In this manner we examined each stock in each period and measured the lead or lag r e l a t i v e to the market index movement. 3.5 Ex Post Testing Procedure The next step in the testing procedure was to devise a set of trading rules through a t r i a l and error method. These rules incorporated the use of the information that has already been derived. These trading rules were applied i n an ex post manner to the 101 stocks. The trading rules were applied to both the r i s i n g and f a l l i n g market. In this manner we derived an ex post expected return which we could compare with the actual return f o r each stock. The purpose in mind was to see i f we could make an extra p r o f i t or c u r t a i l losses. There i s an i m p l i c i t assumption that there i s a zero return at the beginning of each market trend to which the trading rules are applied. 16 With each stock's return a v a i l a b l e , we then looked at that stock's contribution to the whole p o r t f o l i o . The s t r i c t hold p o r t f o l i o or the combined actual return of the 101 stocks was compared to the trade port-f o l i o ' s return. These ex post considerations w i l l be discussed in the following chapter. 3.6 Ex Ante Market Trends The next step in our s t a t i s t i c a l tests involved looking at the ex ante. For the purposes of this paper, the ex ante i s defined as being the period from June 1969 to June 1972. The purpose we had in mind was to see i f the trend observed in the ex post would hold in the ex ante. In the same manner as in the p r i o r 10 year period, two d e f i n i t e trends in the market were observed graphically. The weekly T.S.E. market returns were tested to see i f these trends met the requirements defined in the ex post. Within this 3 year period we so defined the f a l l i n g market as being the period from March 5, 1971 to November 5, 1971. The r i s i n g market was defined as the period from October 8, 1971 to March 31, 1972. The overlapping of the two periods presents no d i f f i c u l t y as we assume that we are at a s t a r t i n g position in each period where we are holding the stocks and there i s a zero return. The d e f i n i t i o n of these trends allows us to pass out of them when the requirements are met. 3.7 Ex Ante Calculations Once again as i n the ex post sense, the weekly prices f o r the stocks were c o l l e c t e d and the weekly returns calculated in the same 17 manner as in the prior period. We calculated the cumulative weekly market return and without making any adjustment in the beta coefficient, we calculated the theoretical or expected return (R m*e). Once again the cumulative expected return was calculated and the cumulative dif-ferences for each stock derived. In this manner, we could observe i f there was indeed a relation-ship that existed and given that there was, was there any relationship to the ex post. Furthermore i t could be observed to see whether the stocks which lagged behind the market movement would eventually respond in f u l l as would be expected by their respective betas. 3.8 Ex Ante Testing Procedure The particular notion of trading rules that was used with the ex post data was applied ex ante. The rules were activated once the beginning of a market trend was determined. As we moved out of the market trend, the trading rules no longer applied. The screening of the T.S.E. index returns determined when we were passing out of a market trend. The ex post results were compared with the ex ante results to determine i f any relationships existed or i f any profits were made. In the ex ante each stock was observed individually by looking at i t s contribution to the whole portfolio of stocks studied. The com-bined actual return of the 99 stocks was compared to the trade port-folio's return. This was done in both the rising and declining market. The results appear in Chapter V. CHAPTER IV EX-POST CONSIDERATIONS In working with the ex post data the computer was used to per-form the c a l c u l a t i o n s . An example w i l l indicate the heading under which the calculated results appeared. An i l l u s t r a t i o n of stock number f i v e in the declining market i s shown in I l l u s t r a t i o n I. With this information a v a i l a b l e , one could look at the l a s t column of figures and determine the number of weeks during the period being studied where there was a lag and the number of weeks where there was a lead in the relationship between the actual and expected r e s u l t s . This was done for both the up market and the down market. The results appear on Table I I . A lead or lag i s indicated by an underlined number Otherwise that stock's movement is random. The checkmark (/) indicate the stocks where a lead i s common to both the r i s i n g , and f a l l i n g market; the cross (x) indicates the lag being common to both market trends. With t h i s information available on the computer output the possi-b i l i t y of various trading rules was explored. The purpose in mind was to e s t a b l i s h a set of rules by which one would adhere to in picking stocks for i n c l u s i o n (or exclusion) in a p o r t f o l i o . Through observation and b a s i c a l l y by t r i a l and error method a set of optimum trading rules were developed. Since there are no rules or standard procedures f o r developing trading rules, i t would seem that the trading rules derived would best s u i t our purposes. 18 ILLUSTRATION I - COMPUTER RESULTS Cumm Stk Cumm Rm* Cumm Wks Stk Rtn Rtn Rtn Mkt Rm*Beta Beta Di f f 5 - Stk No 1.3670 - beta c o e f f i c i e n t 1. .0824 .0824 -.0050 -.0068 -.0068 .0892 2. .0326 .1150 .00 .00 -.0068 .1218 3. -.0366 .0783 .0040 .0055 -.0014 .0797 4. -.0166 .0617 .0050 .0068 .0055 .0563 5. .0444 .1062 .0080 .0109 .0164 .0898 6. .0106 .1168 .0100 .0137 .0301 .0867 7. -.0156 .1012 -.0110 -.0150 -.0150 .0862 8. -.0269 .0743 -.0120 -.0164 -.0014 .0756 9. .00 .0743 -.0120 -.0164 -.0178 .0921 10. %0110 .0853 .0060 .0082 -.0096 .0948 20 To begin with f o r trading purposes, an up-market was indicated by a cumulative expected return of 5% which i s followed by continuing returns. Once i t i s in the r i s i n g market, we do not pass out of i t u n t i l the cumulative expected return f a l l s by 5%. For our purposes the rule i s that there i s no r i s i n g market unless there i s a cumulative expected return of at l e a s t 5%. Otherwise we are considered to be in a stable market. We w i l l be considered to be in a downswing, when there i s a f a l l of 5% in the cumulative expected return over two consecutive periods. Therefore we may not determine whether we are in a f a l l i n g market u n t i l three weeks of returns are experienced. We do not pass out of a declining market unless a d e f i n i t e p o s i t i v e trend i s indicated as was defined e a r l i e r . This would allow us to get by the weekly fluctuations in the market without a l t e r i n g our decisions too much. I t i s important to note " t h a t when market i s mentioned when dealing with the trading rules, we mean the expected return of the market or Rm*Beta. The T.S.E. or true market return was used s o l e l y f o r determining the market trends. We are assuming that we are at a s t a r t i n g position f o r each market trend where we hold 101 shares of each stock. At the beginning of each period, the stock has a zero return. When f i r s t attempting to design the trading rules, the difference between the cumulative actual and the cumulative expected return was experimented with. Buy and s e l l flags were determined as follows: A. Buy stock when cumulative difference has been negative but sta r t s towards a p o s i t i v e position by X% (X + 1/4) over two weeks. 21 i . e . -4% -4% -4% -2% 2% 2% 1% - buy -1% - don't buy 1% - buy I f cumulative difference i s postive and there i s a X% change to increasing p o s i t i v e over two weeks, then buy. B. S e l l 1. I f cumulative difference of actual and expected cumulative totals exceeds (X%) go to rule 2. 2. As long as the cumulative difference i s increasing, hold the stock. As soon as the cumulative difference f a l l s by X% over two weeks, s e l l the stock. In this way we are getting around fluctuations from week to week and are r e a l l y getting the feel for some momentum in the stock. I f the cumulative difference i s f a i r l y constant, then by this rule the stock would not be sold u n t i l a d e f i n i t e downtrend i s established in the expected market return which we w i l l take as covering no more than two weeks. Using these simple rules as the groundwork, a more concrete but not too d i f f i c u l t set of trading rules were designed. The rules designed are i l l u s t r a t e d with diagrams so they w i l l be easier to compre-hend. Trading Rules 1. Look at the cumulative return of the"stock by d i r e c t i o n a) (++ or ->-0)* - Hold unless te s t i n g s e l l decision - When not holding go to (2) b) (-+ or -H-0) - Go to (4) c) (No change) - Go to (2) 22 2. Look at the cumulative return of the market (expected) by d i r e c t i o n . a) (++ or +-0)* - Go to (3b) b) (-+ or -H-0) - Go to (4) c) (No change) - Go to (3c) 3. Look at the cumulative difference f o r two consecutive weeks. a) I f cumulative difference has increased by 5% and cumulative market has f a l l e n - s e l l . Otherwise go to ( c ) . b) I f cumulative difference has increased from -5% or greater -buy: otherwise look at (c) c) I f cumulative difference has decreased 5% in two weeks -sell'. But not i f both stock and market increase in two con-secutive periods - buy; or i f when both the stock and market are both p o s i t i v e , we can look at the cumulative difference and i f i t has increased 5% over the two previous periods -buy. (In simpler terms we use 3a when the market has dropped f a s t e r than the stock; 3c i s used when the stock drops f a s t e r than the market and also when the stock begins to f a l l to meet the market.) 4. a) I f cumulative return of the expected return (Mkt*Beta) has f a l l e n 5% or i f market f a l l s over three consecutive periods -s e l l . (++ or->-0) - Increasing p o s i t i v e or approaching zero from negative side. (-+ or -H-0) - Increasing negative or approaching zero from p o s i t i v e side. 23 b) I f cumulative return of expected return (Mkt*Beta) has f a l l e n 5%, go to 3a. c) I f cumulative return (Mkt*Beta) has increased go to 3b and/ or 3c whichever may apply. d) I f the stocks cumulative return has f a l l e n 5% - go to 3a and/or 3c. Another rule which was l e f t up to the trader's d i s c r e t i o n was the rule of a 0 return. By matter of choice 0 can be taken as being either p o s i t i v e or negative. This choice would depend on the most recent (previous 4 or 5 weeks) history of the stock or market return. Once established these trading rules were tested on the stocks in both the "up" market and the "down" market. I t was hoped that by applying these trading rules more money would be made than i f we j u s t held the stocks. However i t was real i z e d that i t would be most d i f f i c u l t to out perform a s t r i c t hold rule in an "up" market. But then again i t was further real i z e d that i n a "down" market, there should be obvious savings. Furthermore by using the trading rules we would be out of the market f o r periods of a time (minimum two weeks a f t e r s e l l decision) which would free capital for short term lending. Before continuing i t i s necessary to i l l u s t r a t e the manner in which the trading rules were put to use and how they were derived. The following i l l u s t r a t i o n serve this purpose. The diagrams are i l l u s -trated with examples in order that they may more e a s i l y be understood. The equations as they appear in the diagram are the cumulative stock return minus the cumulative market return equals the cumulative difference, 24 I Stock Price ILLUSTRATION II - TRADING RULES UP MARKET tcumm d i f f (-) and -> II Stock Pri ce cumm d i f f (-) but + 0 cumm d i f f (+) and -»• °° r- cumm d i f f (+) - 0 -5 - ( 5) = -10 -8 - (10) = -18 10 - (15) = -25 -8 - (16) = 24 0 - (20) = -20 8 - (25) = -17 20 - (30) = -10 35 - (35) = 0 Time (wks) 5 - ( 5) = 0 15 - (10) - 5 25 - (12) = 13 25 - (15) = 10 25 - (18) = 2 20 - (20) - 0 Twks) III Stock Price cumm d i f f l ( + ) IV Stock Price ,£cumm d i f f (+) and cumm d i f f (-) and + 0 cumm d i f f (+) and -> 0 cumm (-) and cumm d i f f (-) and -> 0 T>ks) 0 - ( 5) = -5 5 - ( 8 = -3 10 - (12 = -2 15 - (15 = 0 20 - (15) = 5 25 - i 1 7 ) = 8 30 - (20 = 10 25 - 08) = 7 20 - [16 = 4 15 - 15 = 0 (wks) 20 - (-5) = 15 10 - ( o) = 10 5 - ( 5) = 0 0 - (10) =-10 -5 - (12) =-17 -10 - (15) =-25 -5 - (20 =-15 15 - (22) = -7 25 - (25) = 0 25 or as i t has been termed i n this study, the actual cumulative return less the expected cumulative return. In the f i r s t set of i l l u s t r a t i o n s of the up market ( I l l u s t r a t i o n II) i n diagram I, we would not want to get into the stock u n t i l the widest divergence has passed because in this case the stock i s lagging behind the market. In diagram I I , the stock i s ahead of the market. In th i s case our aim would be to hold the stock u n t i l the widest divergence. At this point the stock w i l l come down to meet the market so we would l i k e to get out of the stock in order to make the p r o f i t over the shorter period of time. Diagrams III and IV are r e a l l y I and II again. In III we would want to be holding the stock u n t i l i t was at i t s peak return or widest divergence. In IV, we would not hold the stock but we would buy back into i t when the stock has passed i t s low ebb or the point of widest divergence. In the second set of i l l u s t r a t i o n s ( I l l u s t r a t i o n III) of the down market, in diagram I we would not want to be in possession of the stock. As the divergence increases, i t would not be s a t i s f a c t o r y to hold this stock. However once the divergence comes closer to zero and has a tendency to p o s i t i v e we would buy into the stock. In this case the stock leads the market into the downturn. In diagram II the stock lags behind the market into the downturn. Since we would expect the stock to drop f a s t e r at some point to meet the market, we would want to s e l l the stock at i t s maximum divergence from the market. 26 I Stock Price ILLUSTRATION III - TRADING RULES DOWN MARKET -5 -( 0) = -5 -10 -( -2) = -10 -20 -( -5) = -15 -30 -(-10) = -20 -30 -(-15) = -15 -28 -(-20) = -8 -25 -(-25) = 0 cumm d i f f (-) -0 twks) 2 -( 0) = 2 5 -( -2) = 7 10 -( -5) = 15 8 - (-10) = 18 -5 -(-15) = 10 -15 -(-20) = 5 -25 -(-25) = 0 cumm d i f f (+) -0 i n Stock Price cumm d i f f -v 'j cumm d i f f IV Stock Price Cumm d i f f (-) - 0 20 -( 0) = 20 15 -( 5 = 10 10 -(10 = 0 5 -(12 = -7 0 - (15 = -15 -10 -(12) = -22 -5 -(10) - -15 0 - ( 7 - -7 5 -( 5) = 0 Twks) T Cumm d i f f (-) -0 Stk cumm d i f f r (+) -> o cumm d i f f ( - ) - - -Mkt - 5 -( 15) = -20 0 - ( 10) = -10 5 - ( 5) = 0 10 -( o) = 10 5 - ( -5) -10 0 - ( -8) — 8 -5 -(-12) = 7 -10 -(-15) = 5 -18 -(-18 = 0 -20 -(-16) = -4 -22 -(-12) = -10 Twks) 27 In diagram I I I , the stock has f a l l e n f a s t e r than the market index. I f the market forecast i s f o r not much more of a decline, we would expect the stock to come up to meet the market. Therefore, we would buy into the stock when the stock has reached i t s low ebb or when the maximum divergence has passed. In diagram IV, the market i s f a l l i n g f a s t e r than the stock. We would hold the stock u n t i l i t has reached i t s peak or in other words un t i l the maximum divergence has passed. The trading rules were applied to the ex post data. There were 54 weeks in the "up" market and 55 weeks in the "down" market. Table III show the results of the trading rules in these opposing market s i t u -ations. In looking at the relationship of the stock to the market move-ments, in the r i s i n g market there are 71 stocks that lead the market, 24 stocks that lag the market and 6 stocks that have no pattern. This would indicate that 70% of the stocks lead the market i n a r i s i n g market. In 29 of the stocks, there i s no movement with the market. That i s , the stock never moved with the market (defined as being between a -1% and 1% l i m i t ) in these cases. When you observe the d e c l i n i n g or f a l l i n g market, there are 59 stocks that lead the market, 39 that lag the market and 5 that have no pattern. Therefore we could say that 60% of the stocks lead the market into a downturn. In 11 stocks there i s no movement with the market. These results indicate that the sample may be biased. The market i s determined by the average price of the stocks that make up the Toronto 28 Stock Exchange. Since the market i s an average, there w i l l be stocks that lead and stocks that lag the market. Since 70% of the stocks lead the market in the upturn and 60% lead the market in the downturn, the sample may be biased somewhat e s p e c i a l l y i f t h i s r e l a t i o n s h i p holds i n the future. However, since nothing i s known about the s t a b i l i t y of these leads and lags, i t would be wrong to assume that the sample i s biased. In 65 stocks the same relationships to the market holds in both the r i s i n g and declining market. 50 stocks lead the market in both the up and downturns; 15 of the stocks lag the market in both cases. The remaining 36 stocks do not have any set pattern; 12 stocks lag in the r i s i n g market but lead in the declining market; 24 stocks lead in the r i s i n g market but lag in the down market. There i s movement with the market in both the r i s i n g and declining markets i n 64 of the stocks. No movement i s common to 3 stocks in both market trends. Therefore 64 stocks have a tendency to move with the market during a market trend. That i s , i f they lead the market, they w i l l slow down eventually so the market could catch up or i f they lag the market, they w i l l speed up to catch the market. This indicates that the majority of the stocks w i l l s t r i v e to maintain t h e i r average p r i c e . When we look at these f i g u r e s , the 65% indicates that there may be some s t a b i l i t y i n the market in the ex post sense. That i s , a s i m i l a r relationship i s evident in both periods 65% of the time. The 50% s t a b i l i t y of the lead in both market trends attests to the f a c t that the sample i s not biased. Before making any further statement, i t would be necessary to see what the ex ante holds i n store. 29 In u t i l i z i n g the trading rules in the ex post, i t i s obvious that the rules do not work to our advantage in the r i s i n g market. However in the d e c l i n i n g market, our holding period return creates a substantial saving to us. Table IV analyzes the results of the trading rules. The d i f f . return column indicates the return that i s attributed to us not holding the stock. It i s the return the stock had while we were not in possession of i t . The d i f f . weeks column i s the associated time period involved in not holding the stock. Extra p r o f i t means p r o f i t beyond that which we could have had i f we would not have traded in that stock. Extra loss means the same thing in i t s relationship to losses. Less p r o f i t indicates a lower return from trading than from a s t r i c t hold p o l i c y . At times there can be both an extra loss and less p r o f i t . This i s evident where there was a p o s i t i v e return in the s t r i c t hold p o r t f o l i o but a negative return because of trading. The less loss column indicates less losses due to trading. The less loss and extra p r o f i t signs may be evident when a negative return persists in the trade p o r t f o l i o . In the r i s i n g market the results are not impressive. There are only 10 instances where there are extra p r o f i t s made. In only one instance i s there a p r o f i t while there was a loss i n the non-trading or hold port-f o l i o . In 14 instances, there i s an extra loss created through trading. In 8 of these 14 instances, money could have been made i f the stock was j u s t held. In only 3 instances do we save on losses with one of these where we make a p r o f i t . These 3 stocks were in a downtrend while the market was r i s i n g . In the remainder of the stocks, there i s a less 30 p r o f i t sign evident. This persists i n 82 cases. Therefore in 88% of the stocks we had smaller p r o f i t s or an extra loss because of trading. This would suggest that the trading rules are not p r o f i t a b l e i n a bu l l market e s p e c i a l l y for the stocks that have a tendency to follow the market. The d i f f i c u l t y i s that s e l l decisions appear before the stock reaches i t s f u l l p o t e n t i a l . In the declining market the trading rules work to our advantage. In 30 of the stocks we make an extra p r o f i t because of trading. In 21 of these 30 instances we would have had a loss due to non-trading. In 17 cases we had an extra loss due to trading and in 7 of these 17 cases, p r o f i t could have been made had we not traded in that stock. These stocks were sold too early and the buy rules did not allow us to take advantage of the small gains. These stocks seemed to move in more of a random fashion. In 16 cases we made less p r o f i t because of our trading rules - 7 cases ending up in extra losses. Once again these stocks moved in opposition to the market. In 66 instances a less loss sign persists i n d i c a t i n g that 66% of the stocks we traded in had less losses due to the trading rules. Therefore i n 75% of the stocks we eit h e r made an extra p r o f i t or had smaller losses. Therefore the trading rules are used more successfully in a bear market s i t u a t i o n . The rules t e l l us to s e l l well before the majority of the stock reach t h e i r low ebb in th e i r price structure. However 25% of the stocks did not have impressive r e s u l t s . This further indicates that the trading rules cannot be success-f u l l y applied to b u l l i s h type stocks. 31 I f we take a l l the stocks together as a p o r t f o l i o and assume an equal investment in each security our results are as they appear on Table V. As became evident from the analysis of the individual stocks, there i s almost a 15% loss in p r o f i t due to the use of trading rules in the r i s i n g market. However in the declining market, we have a saving of almost 8% due to trading. An i n t e r e s t i n g point in regard to the holding periods i s that in the r i s i n g market we would have 19 weeks to invest the money elsewhere and in the d e c l i n i n g market there would be 31 weeks to invest i t elsewhere. The thought in mind i s that when a stock has been s o l d , the investor i s in possession of a certa i n amount of cash. The trading rules do not allow the p o r t f o l i o to always be at f u l l capacity. Therefore i t can be assumed that there i s a certain minimum amount of cash available. This would allow the p o r t f o l i o manager to invest in short term s e c u r i t i e s such as commercial paper. I t may even be more p r o f i t a b l e at times f o r the investor to be completely out of stocks. However there i s an i m p l i c i t assumption that his main concern i s with p r o f i t s from the stocks and therefore he would be r e s t r i c t e d as to the length of time he can remain t o t a l l y l i q u i d . CHAPTER V EX ANTE RESULTS The purpose of the empirical tests was to see i f the r e l a t i o n -ships that were found to be true in the ex post would be v a l i d in the ex ante. Given that the relationships do e x i s t , they may serve as valu-able information and c r i t e r i a in the decision making process involved in s e l e c t i n g stocks f o r investment. In this chapter the ex ante results are presented and analyzed. A further comparison w i l l be made to the ex post res u l t s to see i f there i s any s t a b i l i t y in the stock relationship to market movements. The good s e c u r i t i e s ex post w i l l be compared to the good s e c u r i t i e s ex ante. The most important aspect of the analysis hinges on the p r o f i t motive. Given that we used the trading rules in the ex ante are there any p r o f i t s that were derived? 5.1 Ex Ante Results The trading rules developed over the ex post period were applied to the ex ante period. There were 25 weeks i n the "up" market and 35 weeks in the "down" market. Table VI shows the results of the trading rules f o r the periods indicated. There i s an implied zero return at the beginning of each trend where we are holding 99 stocks in the p o r t f o l i o . 32 33 As was true f o r the ex post data, the trading rules when applied to the ex ante do not work to our advantage in the r i s i n g market. However in the d e c l i n i n g market, the trading rules help c u r t a i l our losses. The holding period return due to trading i s superior r e l a t i v e to a s t r i c t buy and hold policy in the declining market but not in the r i s i n g market. Table VII analyzes the results of the trading rules as applied in the ex ante. Once again i t i s desirable to define headings on the table to c l a r i f y the method of analysis. The d i f f . return refers to the difference in return between u t i l i z i n g the trading rules and not u t i l i z i n g them. The d i f f . weeks refers to the difference i n the time the stocks are held. This can be referred to as the non-holding period. The extra p r o f i t refers to p r o f i t made over and above any p r o f i t or losses that were available without trading. The extra loss can be defined as losses r e s u l t i n g from trading which are greater than the losses subject to nontrading or to losses from trading when p r o f i t s could be made without trading. Less p r o f i t means that the trading p r o f i t i s less than the nontrading p r o f i t . Less loss means that the losses are c u r t a i l e d because of trading. In the r i s i n g market there are only 11 stocks where the trading rules resulted in an extra p r o f i t ; one of these 11 stocks would have resulted in a loss due to a s t r i c t buy and hold. These stocks lead the market the majority of the time. There are 30 stocks where the trading rules resulted in an extra l o s s ; i f we had not traded in 21 of these stocks but maintained a s t r i c t buy and hold rule there would have been po s i t i v e returns rather than negative returns. The majority of these 34 stocks lagged the market and by s e l l i n g we were not allowing p r o f i t s to run. In only three stocks i s there a curtailment of losses with one stock actually making a p r o f i t . The trading rules resulted in less p r o f i t being made in the r i s i n g market in 75 stocks of which 21 stocks resulted in extra losses. In these stocks the trading rules did not allow the p r o f i t s to run. These results are not very s a t i s f a c t o r y , however they take the same pattern as the r i s i n g market did in the ex post. There were 84 stocks in the ex ante where p r o f i t s were c u r t a i l e d or where losses were evident. This was true of 88 stocks in the ex post. These same stocks would have had better results i f they were not subjected to the trading rules because they do not allow us to capture the stock's f u l l p o t e n t i a l . In the d e c l i n i n g market a curtailment in losses i s most apparent. In 29 stocks an extra p r o f i t was created by following the trading r u l e s ; in 18 of these stocks a p r o f i t would not have resulted had a s t r i c t buy and hold p o l i c y been followed. We sold before the stocks l o s t money. By following the trading rules there were 15 stocks that had extra losses. The majority of these stocks lead the market into the downturn. In 9 of these 15 stocks i f the trading rules had not been applied a p r o f i t would have been made. These stocks were sold too early and therefore we did not take advantage of the small gains. The stocks seemed to move in a random fashion rather than follow the market. The most common occurrence due to the use of trading rules was a reduction in losses. Less loss i s evident in 56 of the stocks traded i n ; 18 of these stocks resulted i n p r o f i t s when a s t r i c t buy and hold policy would have brought a l o s s . The stocks were sold before they reached the low ebb in t h e i r p r i c e structure. 35 These results indicate that i n the declining market, the trading rules are useful. These ex ante results take the same pattern as they did in the ex post. There were 67 stocks i n the ex ante where the trading rules resulted in saving money. This was true of 75 stocks i n the ex post. Just as the trading rules do not allow us to capture the stock's f u l l potential i n the r i s i n g market, they do not allow us to take the f u l l brunt of the stock's decline i n a f a l l i n g market. The trading rules are used more successfully in a bear market s i t u a t i o n . The trading rules do not seem to work well i n b u l l i s h market situations or f o r b u l l i s h type stocks in a declining market. When the stocks are looked at as being part of one p o r t f o l i o , there are some i n t e r e s t i n g results (Table VIII). In the p o r t f o l i o where there was no trading but rather a s t r i c t buy and hold rule adhered to, there was a return of 15.48% in the r i s i n g market. In the dec l i n i n g market th i s same p o r t f o l i o had a loss of 7.55%. In the p o r t f o l i o where the trading rules were adhered to there was a return of 5.79% in the r i s i n g market and .82% in the declining market. These results indicate a reduction i n the p r o f i t s of 9.69% but also a curtailment i n the losses of 8.37%. I f we take both market swings into consideration there i s only a 1.3% reduction i n the p r o f i t s . However in noting this i t must be reali z e d that the two market trends did not involve the same length of time and also i t i s unlikely that the decl i n i n g market f e l l to as great a degree as the r i s i n g market rose (-9.0% and 15.3% r e s p e c t i v e l y ) . 36 A further note of i n t e r e s t i s that by following the trading rules the stocks are held for a shorter time period. This permits the investor to invest his money elsewhere when he has indeed liquidated a portion of his holdings. In the ex ante there are 7 weeks in the r i s i n g market and 18 weeks in the declining market which permits the investor to invest his money elsewhere. Short term investment may be most appropriate. Therefore there would be a guaranteed return which would add to his p r o f i t s . I t i s assumed that this return would not warrant the investor to stay completely out of stocks. There i s an implied assumption that the investor s t r i v e s to maintain some minimum number of stocks in his p o r t f o l i o . He seldom w i l l be 100% out of stocks. At this' point one wonders whether or not a mere random sele c t i o n would be better than adhering to the trading rules. For example, i f the stock market indicates a downtrend and i f by the trading rules we s e l l 10 stocks so that we are at 90% capacity, would i t not be better i f we j u s t randomly selected any number of stocks. The query i s whether a random se l e c t i o n would be more p r o f i t a b l e than a trading rule s e l e c t i o n . Such.an analysis would provide comparative r e s u l t s . However such an analysis i s not the main i n t e r e s t of this paper. The major d i f f i c u l t with a random process i s that i t would have to r e l y e n t i r e l y on the changes i n the market to provide signals to buy and s e l l . The trading rules as indicated in Chapter IV are not e n t i r e l y based on the market. The major component of the rules i s the cumulative difference factor which i s largely determined from the actual returns of each i n -dividual stock. Furthermore the s e l e c t i o n process through the use of 37 trading rules allows the sele c t i o n of certain stocks to s e l l . We know how many to s e l l only a f t e r the rules have been incorporated. Through a random process we would not know the number of stocks to buy and/or s e l l . Table IX indicates the number of stocks that are held in each week i n each of the market trends. The stock position i s shown to vary considerably. Randomly selectin g the same number of stocks as indicated on Table IX would be the best way of comparison. However this would not be a true random s e l e c t i o n . Table X indicates the relat i o n s h i p of the stocks to the market movements in the ex ante. The underlined number indicates whether that stock leads or lags the market. The checkmark (vO indicates the stocks where a lead i s common to both the r i s i n g and f a l l i n g market. The X indicates that the stock lags in both market s i t u a t i o n s . Otherwise the stock movement i s random. In the r i s i n g market there are 45 stocks that lead the market; there are 44 stocks that lag the market; and there are 10 stocks that may e i t h e r lead or lag. There i s movement with the market in a l l but 24 stocks. Movement with the market i s defined as a tendency of the stock to s t r i v e f o r some equilibrium p r i c e as determined by the market times beta. In the declining market the majority of the stocks lag the market. 65 stocks lag the market; 23 stocks lead the market into the downturn; and 11 stocks no d e f i n i t e pattern can be determined. There i s no movement with the market in 35 stocks. These results indicate that our sample i s not biased. Movement with the market i s more of a random process. 38 I t i s possible to compare the relationships between the two ex ante market trends. In 58 of the stocks the same lead or lag re-l a t i o n s h i p exists in both the r i s i n g and declining market. Unlike the ex post where a lead was most prevalent, in the ex ante a lag r e l a t i o n -ship i s common to 41 of the stocks while a lead relationship i s evident in 17 of these stocks. The remaining 41 stocks do not have any set pattern; 30 of these stocks lead in the r i s i n g market but lag in the d e c l i n i n g market; 11 of these stocks lag in the r i s i n g market but lead the market in the downturn. Within the ex ante period, there i s a 58% s t a b i l i t y factor from one market trend to another. Once more these results indicate an unbiased sample where movement of stock prices re-l a t i v e to the market i s a random process. Another i n t e r e s t i n g point i s movement with the market. There are 8 stocks in the r i s i n g market which at no time move in l i n e with the market. This i s true of these same 8 stocks i n the declining market. Movement with the market i s common to both market trends in 49 stocks. This indicates that 50% of the stocks sought t h e i r average p r i c e in both market trends. The number may have been larger had the market trends been longer because the adjustment process may be longer f o r some stocks. 5.2 S t a b i l i t y of Relationship of Individual Security Price  Behavior Relative to Market Movements Table XI compares the ex post and the ex ante in both the r i s i n g and declining market s i t u a t i o n s . There are only 4 s e c u r i t i e s where extra p r o f i t (XP) and less loss (LL) i n the r i s i n g market appear in both the ex post and the ex ante. In 66 stocks lower p r o f i t s (LP) appear 39 in both the ex post and ex ante r i s i n g markets. Extra losses (XL) appeared in this manner in 6 stocks. Therefore in the r i s i n g market 75 of the stocks had the same p r o f i t picture in both the ex post and the ex ante. The trading rules allowed us to make an extra p r o f i t in both periods in only 4 stocks. Therefore i t seems that the trading rules are undesirable in bull market s i t u a t i o n s . The obvious reason i s that they do not allow us to take f u l l advantage of a complete market swing and l e t p r o f i t s run. In the declining market extra p r o f i t s (XP) were evident in only 8 stocks in both the ex post and the ex ante. The most common factor was where there was a curtailment in losses. Less loss (LL) appeared 35 times in the de c l i n i n g market in both periods. Extra losses (XL) and lower p r o f i t s (LP) were common to both periods in two d i f f e r e n t stocks each. Therefore in the de c l i n i n g market 47 of the stocks followed the same pattern in the ex ante as they did in the ex post. The trading rules were used successfully in bear market situations in both the ex post and ex ante. The trading rules allow us to s e l l before the stock reaches i t s low ebb. These relationships allow us to assume that there were only 4 "good" or desirable stocks in the r i s i n g market. These stocks are d e s i r -able in terms of the trading rules. However in the declining market, there were more "good" stocks. In 48 stocks there was e i t h e r an extra p r o f i t or curtailment in losses in both the ex post and ex ante. We would term these 48 stocks as being "good" stocks in the declining market. These stocks can be e a s i l y i d e n t i f i e d by comparing Table XI to Table I. However i t seems that the c h a r a c t e r i s t i c s of each individual stock i s 40 immaterial. The trading rule s e l e c t i o n process i s independent of these c h a r a c t e r i s t i c s . Therefore i t would seem that the rules are not suitable for s e l e c t i o n of stocks f o r inclusion in a s t r i c t buy and hold p o r t f o l i o . They would be more useful in a p o r t f o l i o revision process. However this does not r e s t r i c t us only to the p o r t f o l i o of stocks for the rules can be applied to any number of stocks in or out of a p o r t f o l i o . Since there i s a difference between the s t a b i l i t y in the ex post and the ex ante d e f i n i t e conclusions cannot be made. However the 65% s t a b i l i t y f a c tor in the ex post and the 58% in the ex ante are not that d i f f e r e n t . Some s t a b i l i t y may therefore be evident. A further look at each stock may help c l a r i f y t h i s . Table XII presents a further analysis of these lead and lag relat i o n s h i p s . I t compares the ex post relationships to the ex ante rel a t i o n s h i p s . Each of the market trends i s analyzed. In the r i s i n g market there are 58 stocks which have the same relationship in both the ex post and the ex ante. A lead i s i d e n t i f i e d in 38 stocks and a lag in 20 stocks. In the declining market 40 stocks have the same rel a t i o n s h i p . 26 stocks lag and 14 stocks lead in both the ex post and the ex ante. This indicates a lack of s t a b i l i t y with respect to leads and lags. With respect to the stock moving with the market, there are 55 stocks in the r i s i n g market that at one time or another w i l l move along with the market in both the ex post and the ex ante. The same i s true for 56 stocks i n the declining market. In the r i s i n g market there are 8 stocks which do not move with the market in ei t h e r the ex post or the 41 ex ante. This i s true of only 2 stocks in the ex post and ex ante de-c l i n i n g market. Furthermore our analysis indicates that even when there i s movement with the market within a certain market s i t u a t i o n the timing between the two periods i s not stable in the ex ante. There i s no r e l a t i o n -ship e x i s t i n g in the time i t takes f o r a stock to come within -1% and 1% of the market once the market sta r t s into e i t h e r a "up" or "down" trend. These results indicate that there i s further need to analyze market trends beyond June 1972 to ar r i v e at more d e f i n i t e conclusions in regards to s t a b i l i t y of leads and lags. Our analysis would indicate that movement with the market i s a random process. However this i s a biased conclusion. Despite the lack of s t a b i l i t y from period to period the trading rules are p r o f i t a b l e in a declining market. The rules are able to i d e n t i f y those s e c u r i t i e s which vary widely from t h e i r expected prices allowing us to activate trading which i s p r o f i t a b l e for the p o r t f o l i o . The trading rules that were used are d i f f e r e n t i n that they are derived d i r e c t l y from the theoretical economic relationship of stock prices to the market. As expected the rules were s i g n i f i c a n t l y more p r o f i t a b l e when used i n the f a l l i n g markets. This i s because extraordinary losses were c u r t a i l e d which i s desirable as opposed to extraordinary gains being truncated in the r i s i n g market which i s undesirable. The symmetry of the rules allowed t h i s to happen. The trading rules have incorporated in them buy decisions which require a d e f i n i t e r i s i n g trend to be estab-li s h e d . Only when this i s so can we buy the stock. Therefore we get back into the market only a f t e r the major portion of a p o s i t i v e run 42 has passed. The result i s that the po s i t i v e returns are somewhat smaller. In a r i s i n g market the buy decisions create this d i f f i c u l t y to a larger extent than they do in a dec l i n i n g market. The reason i s simply that there are larger p o s i t i v e gains in the r i s i n g market than in a declining market for the majority of the stocks. The buy rules make i t d i f f i c u l t to get back into the market Smaller gains are thus achieved in the r i s i n g market. This doesn't create a problem in the dec l i n i n g market mostly because there are no p r o f i t s to achieve. On the other hand, s e l l decisions allow us to pass out of a stock quite e a s i l y , thus c u r t a i l i n g losses in the declining market but by the same token truncating p r o f i t s in the r i s i n g market. CHAPTER VI CONCLUSIONS The theory of the relationship of security prices to the market was developed in Chapter I I . Recall that the theory views the beta c o e f f i c i e n t or the systematic r i s k as the average relationship of security returns with market returns over time. I t i s also assumed that when the security return deviates from the expected value given the market return, i t w i l l have to,compensate with greater movement in the opposite d i r e c t i o n to maintain the average r e l a t i o n s h i p . The results of the empirical tests indicate that the adjustment of a stock price r e l a t i v e to the market index i s not instantaneous. Some stocks are found to lead the market while others lag the market. S t i l l other stocks w i l l quite frequently move with the market. Further-more, the analysis indicates that there i s no stable lead or lag re-lationship from one period to another in the majority of the stocks. The d i f f i c u l t y s t i l l remains i n predicting these stocks relationships in advance. The reason being that the timing of a lead or lag i s most uncertain. Despite this lack of s t a b i l i t y the results have indicated that beta may be used e f f e c t i v e l y on a continuing basis in some market s i t u -ations. The results of the trading rules based on this market e q u i l i -brium concept indicate that weekly decisions are most p r o f i t a b l e i n a 43 44 declining market. The rules are able to i d e n t i f y those stocks which vary widely from t h e i r expected p r i c e s , allowing us to activate trading which i s p r o f i t a b l e for the p o r t f o l i o . The trading rules allow us to incorporate new stocks. The estab-lishment of a market trend ( f a l l i n g or r i s i n g ) indicates when the rules should be applied. We use the trading rules in l i g h t of decision making within the market trends. Once a trend has developed the rules may be applied to stocks that were never held in the p o r t f o l i o . Once the beta c o e f f i c i e n t has been established, the expected price of the stock can be determined. New stocks can thus be incorporated through the buy decisions in the trading r u l e s . I t seems that short term betas would be unstable because stock prices do not adjust instantaneously. However, a long term beta i s most useful f o r short term decisions in a declining market. In a r i s i n g market beta would be more useful f o r longer term decisions. I t seems that beta i s a better "loss" minimizing technique in the short run. In the d e c l i n i n g market there was a 50% curtailment in losses due to using a trading rule based on the beta c o e f f i c i e n t . The obvious question i s that could there not be rules devised that would provide s i m i l a r results in a r i s i n g market and even better results i n the d e c l i n i n g market. This could very well be the case. The findings would indicate that a technique based on these relationships may be most useful as a p o r t f o l i o revision t o o l . Port-f o l i o r e v i s i o n i s the central a c t i v i t y of an investment manager. The trading rules devised have the essential c h a r a c t e r i s t i c s of an e x i s t i n g 45 and ongoing p o r t f o l i o . They are e s s e n t i a l l y dynamic and adaptive. Furthermore, this practice allows us to look at the individual s e c u r i -t i e s in the p o r t f o l i o and make independent decisions. The trading rules based on this beta concept would be most useful as a p o r t f o l i o revision tool in l i g h t of a decline in the market. It i s a scheme that allows us to c u r t a i l losses. The rules would be much more useful i f we could forecast the market. The most obvious l i m i t a t i o n i s that the rules were not successful in a r i s i n g market. The number of transactions also involved in u t i l i z i n g the trading rules may also be too expensive. In the r i s i n g market the average transaction for each stock was 4.5 times. In the declining market there were 3.18 transactions for each stock on the average. However, since value weighted p o r t f o l i o s were not considered, i t was not p r a c t i c a l to compute the trading costs. Another l i m i t a t i o n i s in regards to the p o r t f o l i o beta. Any rules where we are buying and s e l l i n g stocks continuously w i l l a l t e r the p o r t f o l i o beta. An individual stock's beta contributes to the beta of the whole p o r t f o l i o . I t i s through the s e l e c t i o n of individual stocks that we a l t e r the value of the p o r t f o l i o ' s beta c o e f f i c i e n t . The trading rules devised do not take into consideration the p o r t f o l i o ' s beta. I t would almost be impossible to maintain a desired p o r t f o l i o beta. This value would depend e n t i r e l y on the trading done and i t would change almost continuously. However as was pointed out at the end of the l a s t chapter, the rules are able to i d e n t i f y those s e c u r i t i e s which vary widely from t h e i r expected prices. The main concern of this study was 46 with individual stocks where we could activate trading which would enhance the individual stock's p r o f i t and therefore the p r o f i t of the p o r t f o l i o . The p r o f i t of the whole p o r t f o l i o was looked at only as an a f t e r e f f e c t . However i t i s i n t e r e s t i n g to note that this may be a useful method of a l t e r i n g p o r t f o l i o beta given that this i s the purpose in mind. I t can be argued that through the use of computer technology, trading rules based on the beta c o e f f i c i e n t could be used e f f e c t i v e l y in the short run. Given the results of this study the trading rules may be improved upon considerably. Such trading rules should have the essential c h a r a c t e r i s t i c of being symmetric and therefore adaptive to a l l market s i t u a t i o n s . Furthermore the rules would have to be s c r u t i n i z e d p e r i o d i c a l l y in order to make adjustments so that the best results may be achieved. F i n a l l y i t seems that the conclusions of this study are too weak. The main d i f f i c u l t y i s in predicting the market. It'Hs most d i f f i c u l t to define a r i s i n g and a f a l l i n g market. Therefore confidence in the f i l t e r rules established would f a l l short of being strong. Naturally more confidence would r e s t with decisions made in a d e c l i n i n g market. BIBLIOGRAPHY Blume, Marshall. "On the Assessment of Risk," Journal of Finance, March 1971, 1-9. Fama, Eugene. " P o r t f o l i o Analysis in a Stable Paretion Market," Management  Science, January 1965, 404-419. Lintner, John. "The Valuation of Risk Assets and the Selection of Risky Investments in Stock P o r t f o l i o s and Capital Budgets," Review of  Economics and S t a t i s t i c s (1965), 13-37. Sharpe, William F. "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk," Journal of Finance, September 1964, 425-42. Thomas, Conrad. "Beta Mousetrap," Baron's, February 7, 1972. Treynor, Jack. "How to Rate Management of Investment Funds, Harvard  Business Review (1965), 63-75. 47 APPENDIX TABLES I to XII 48 49 TABLE I INDUSTRIAL STOCKS AND THEIR BETA COEFFICIENTS Beta Stock No. Stock Name Coe f f i c i e n t 1 A b i t i b i Paper 0.6283 2 Alberta Gas and Trunk 0.8870 3 Algoma Steel 1.2760 4 Alcan Aluminum 1.0450 5 Anthes Imperial A 1.3670 6 A t l a n t i c Sugar Refining Co. 1.0810 7 Asbestos Corp. 0.8746 8 Bank of Montreal 1.1980 9 Bank of Nova Scotia 1.1680 10 Bell Canada 0.5486 11 B. C. Forest Products 1.5240 12 B. C. Telephone 0.6364 13 14 Burns Foods 0.6750 15 Calgary Power 0.8765 16 Canada Cement 1.1680 17 Canada Iron Foundries - Canron 1.3100 18 Canada Malting A 1.1750 19 Canada Permanent Mortgage Corp. 1.0330 20 Canada Steamship Lines Ltd. 1.0300 21 Canadian B r i t i s h Aluminum 'A' 1.1780 22 Canadian Industries Ltd. 1.1900 23 Canadian P a c i f i c Railway 1.0320 24 Cassiar Asbestos Corp Ltd. 0.5023 25 Cominco (Consolidated Mining & Smelting) 1.2200 26 Consumer Gas Co. 0.8568 27 Craigmont Mines 0.8579 28 Canada Packers A 0.9049 continued . . . 50 TABLE I - continued Beta Stock No. Stock Name Co e f f i c i 29 Canada Packers B 0.9801 30a Canadian Chemical Co. chemcell 1.1520 30b Canadian Celanese 1.3780 31 Canadian Imperial Bank of Commerce 1.0430 32 Chrysler Corporation 1.0210 33 Distributors Corp. Seagrams 0.8567 34 Dome Mines -0.0792 35 Dominion Foundries and Steel (Dofasco) 1.6090 36 Dominion Glass Co. 0.7400 37 Dominion Stores 0.7542 38 Dominion Oil Cloth and Linoleum 0.9174 39 Dominion Te x t i l e s 1.2880 40 Domtar Ltd. 1.2120 41 Dupont of Canada 0.9104 42 Ford Motor Co. 1.0380 43 Fraser Co. Ltd. 0.8168 44 Falconbridge 0.9902 45 General Dynamics 1.2150 46 General Motors 0.8220 47 George Weston B 1.0920 48 Great Lakes Paper 1.1150 49 Great Lakes Power 0.6214 50 Great Plains Development 0.8650 51 Greater Winnipeg Gas 1.1790 52 Gunnar Mines 0.9714 53 Gulf Oil 0.8473 54 Greyhound Lines of Canada 0.6871 55 Corby D i s t i l l e r y A 0.7526 56 Hiram Walker Gooderham 1.1250 continued . . . 51 TABLE I - continued Beta Stock No. Stock Name Coe f f i c i e n t 57 Hoi l i n g e r Consolidated 0.5003 58 Hudson Bay Mining and Smelting 0.7702 59 Hudson Bay Oil and Gas 1.1020 60 Husky Oil 1.1550 61 Imperial O i l 0.9424 62 Imperial Tobacco (Imasco) 0.6933 63 Industrial Acceptance - I.A.C. 1.2730 64 Home Oil A 0.6136 65 Home Oil B 1.3650 66 International Nickel 0.9380 67 f Interprovincial Pipe 0.7687 68 Investor's Group 0.8276 69 Canadian International Paper 0.9043 70 Jefferson Lake Pet. Chem. (Canadian Occidental) 0.8458 71 Kerr Addison Gold Mines -0.1289 72 Labbatts - John 0.9512 73 Labrador Mining and Exploration 0.9937 74 Loblaw Grocery A 0.9317 75 Loblaw Grocery B 0.9626 76 Mclntyre Porcupine Mines 0.9636 77 Maple Leaf M i l l s 0.5246 78 National Drug and Chemical Co. 0.5475 79 North and Central Gas 1.2380 80 Molson's Brewery A 1.5070 81 Molson's Industries B 1.3370 82 Massey Ferguson 1.9180 83 Pembina Pipeline 1.0280 84 Placer Development 1.9045 continued . . . 52 TABLE I - continued Beta Stock No. Stock Name Co e f f i c i e n t 85 Price Co. Ltd. , 1.1760 86 P a c i f i c Petroleum Ltd. 1.1050 87 Royal Bank of Canada 1.0920 88 S h e r r i t t Gordon Mines 1.2160 89 Simpson's Ltd. 0.5976 90 Southam Press Co. 1.0310 91 Standard Broadcasting Corp. Ltd. 0.4611 92 Steel Company of Canada 1.2910 93 Steinberg 'A' 0.6751 94 Supertest Petroleum 0.5431 95 Texaco Canada 1.0810 96 Trader's Group Ltd. 1.105O 97 Trans Canada Pipeline Ltd. 1.3330 98 Trans Mountain Pip e l i n e 1.038(1 99 Union Gas of Canada 1.0810 100 Teledyne Ltd. 1.915C 101 Woodward Stores Ltd. 0.982Z 53 TABLE II STOCK'S RELATIONSHIP TO MARKET MOVEMENTS -EX POST DATA Stock No. 1 2 3 4 5 6 7 8 9 10 R i s i n g Lags Leads With 15 32 7 39 10 5 46 4 4 54 4 48 2 52 1 3 11 39 4 54 54 53 1 F a 1 1 i n Lags 21 5 6 53 55 54 7 18 12 1 Leads 23 42 45 - - - 35 27 37 47 With 11 8 4 2 - 1 13 10 6 7 g / X / / / Stock No. 11 12 14 15 16 17 18 19 20 21 R i Lags 5 2 - - 13 18 37 22 12 21 s i n g Leads 47 44 54 53 39 30 12 27 38 22 With 2 8 - 1 2 6 5 5 4 11 F a 1 1 i n g Lags Leads 53 19 28 2 50 42 7 1 53 54 0 1 53 4 49 48 5 38 15 With 2 8 3 6 1 1 1 2 2 2 • / / / / X continued . . . 54 TABLE II - continued R i s i n g F a 1 1 i n 9 R i s i n g F a 1 1 i n g Stock No. 22 23 24 25 26 27 28 29 30a 30b Lags 33 1 15 16 27 54 - 4 - -Leads 18 50 31 34 20 - 5J_ 45 54 54 With 3 3 8 4 7 - 3 5 - -Lags 10 9 47 19 45 31 6 4 2 2 Leads 42 42 6 36 8 20 37_ 36 50 49 With 3 4 2 - 2 4 12 15 3 4 / / X X / / / • Stock > No. 31 32 33 34 35 36 37 38 39 40 41 Lags - 36 5 1 14 3 32 10 2 3 -Leads 54 16 41 51 38 51 21 43 52 51 54 With •- 2 8 2 2 1 1 - - -Lags 3 13 - 40 2 1 - - 30 27 -Leads 43 32 50 8 46 47 54 55 21 13 55 With 9 10 5 7 7 7 1 -• 4 15 -/ / / • / • continued 55 TABLE II - continued Stock No. 42 43 44 45 46 47 48 49 50 51 52 53 R i s i n 9 Lags Leads 11 13 12 39 39 12 39 12 5J_ 1 33 18 13 38 15 37 7 42 17 36 2 52 4 50 With - 3 3 3 2 3 3 2 5 1 - -F a 1 1 i n g Lags Leads 6 43 3 47 16 30 55 12 39 19 22 33 21 2 5_1 43 7 55 11 4J_ 37 9 With 6 5 9 - 4 14 1 2 5 - 3 9 / X X / / Stock No. 54 55 56 57 58 59 60 61 62 63 64 65 R i c Lags 8 7 20 - 17 25 30 4 23 1 - -i n g Leads With 43 3 47 17 17 54 34 4 27 2 19 5 40 10 31 5J_ 2 54 54 F a 1 1 i n g Lags Leads 5J[ 1 10 37 1 50 54 55 44 10 33 18 30 8 8 33 14 37 36 11 22 30 With 3 8 4 1 - 1 4 17 14 4 8 3 / / / X X / / • continued . . . 56 TABLE II - continued a Stock No. 66 67 68 69 70 71 72 73 74 75 76 77 Lags 54 13 48 - 48 1 - 17 12 42 49 -Leads - 33 6 52 5 51 53 26 41 41 29 54 With - 8 - 2 1 2 1 11 1 1 11 -Lags 24 - 51 9 55 50 7 8 3 6 48 23 Leads 15 53 3 38 - 4 48 42 47 45 1 20 With 16 2 1 8 - 1 - 5 5 4 6 12 X / X / X • / / / X / Stock No. 78 79 80 81 82 83 84 85 86 87 88 89 R i Lags 1 - - - 22 1 42 2 3 - 10 12 s i Leads 5J_ 54 52 54 28 48 10 4 9 4 9 5 4 4 2 3 6 n g With 2 - 2 - 4 5 2 3 2 - 2 6 Lags 40 25 11 12 32 4 53 50 54 4 9 4_i Leads 11 23 42 37 17 44 1 3 - 46 40 8 With 4 7 2 6 6 7 1 2 1 5 6 6 • / / / X • • continued 57 TABLE II - continued Stock No. 90 91 92 93 94 95 96 97 98 99 100 101 Lags - - - 45 - 6 2 2 54 48 10 28 Leads 50 53 53 8 54 46 49 5J_ - 3 43 18 With 4 1 1 1 - 4 3 1 - 3 1 8 Lags 16 9 1 38 35 50 1 21 - 53 23 12 Leads 30 45 54 9 9 1 49 32 52 1 28 36 With 9 1 - 8 11 4 5 2 3 1 4 7 • / X / / X / 58 TABLE III EX POST RESULTS - TRADING RULES Rising Market Declining Market Stock No. Stock Rtn % (54 wks) Holding Period Rtn % Holding Period Weeks Stock Rtn % (55 wks) Holding Peri od Rtn % Holding Peri od Weeks 1 49.57 39.11 41 -9.60 -6.98 15 2 31.05 16.42 38 -19.48 -19.96 24 3 24.73 30.59 41 -31.98 -12.60 21 4 66.55 50.48 43 -1.93 11.23 26 5 58.05 53.58 26 -1.79 18.10 22 6 -9.66 -33.64 26 16.65 -2.62 25 7 29.11, 21.76 27 -18.46 -1.16 21 8 38.09 36.30 41 -10.82 -6.37 17 9 58.35 52.19 43 -14.53 -14.81 25 10 12.55 10.81 35 -24.31 -12.22 31 11 110.28 106.83 48 -33.86 4.07 24 12 29.04 21.84 46 -25.09 -3.31 30 14 40.88 26.26 33 -35.25 -30.40 21 15 31.20 24.35 46 -15.96 5.24 8 16 36.36 25.97 34 -29.84 -7.26 18 17 34.23 16.84 27 .53 2.97 33 18 21.21 -5.04 33 -34.14 -25.22 22 19 27.32 20.48 38 -29.97 -38.67 28 20 40.66 14.52 38 -4.19 4.95 25 21 36.07 -4.30 39 4.83 26.88 20 22 47.52 -33.76 40 -16.83 -14.59 25 23 58.80 58.80 54 -18.81 -14.56 24 24 30.41 8.22 40 11.88 -5.36 32 25 53.37 25.17 35 -32.42 -11.65 22 continued 59 TABLE III - continued Rising Market Declining Market Stock Holding Holding Stock Holding Holding Stock No. Rtn % (54 wks) Period Rtn % Period Weeks Rtn % (55 wks) Period Rtn % Period Weeks 26 5.20 -.88 21 -1.85 -2.99 21 27 14.36 13.66 31 3.78 6.22 19 28 39.49 15.19 43 -15.71 -1.06 15 29 33.80 11.95 42 -19.46 -4.64 23 30a 73.51 57.85 37 -9.64 12.89 28 30b 73.51 63.48 37 -9.64 26.79 26 31 54.72 29.27 44 -17.10 -8.02 20 32 -9.37, 4.03 25 -38.60 -35.43 28 33 26.13 4.57 41 -25.85 -14.04 21 34 31.87 19.20 24 6.49 -9.83 22 35 56.47 32.44 27 -26.63 -18.56 22 36 93.02 52.81 39 -12.31 -5.72 24 37 -6.87 -22.71 34 -32.39 -16.64 24 38 18.95 35.59 23 -79.08 -6.63 17 39 46.93 27.65 31 -25.77 7.24 28 40 62.51 16.32 32 5.34 5.05 18 41 48.13 35.45 41 -23.39 -8.74 26 42 18.70 -16.35 27 -29.03 -10.69 23 43 49.88 13.22 42 -27.95 -13.66 26 44 22.38 30.98 34 -21.20 -16.96 18 45 -14.35 -68.74 25 26.69 5.58 27 46 11.56 10.59 31 -32.79 -11.84 23 47 -16.83 42.08 29 24.38 4.99 20 48 77.63 22.67 37 -3.63 3.78 30 49 23.34 18.72 25 -34.42 -25.94 24 50 70.46 27.82 37 4.63 8.81 18 continued . . . 60 TABLE III - continued Rising Market Declining Market Stock No. Stock Rtn % (54 wks) Holding Period Rtn % Holding Period Weeks Stock Rtn % (55 wks) Holding Period Rtn % Holding Period Weeks 51 67.40 16.35 35 35.19 30.28 18 52 59.87 33.90 29 -28.71 10.79 15 53 26.79 12.15 45 -3.18 1.39 18 54 26.72 21.44 40 35.09 24.12 29 55 18.06 9.31 22 -15.10 -11.79 28 56 29.18 18.55 46 -27.16 -23.22 24 57 28.71 18.22 39 -27.95 -12.95 29 58 50.65' 43.81 43 2.74 13.31 28 59 10.13 -8.16 26 14.47 10.58 17 60 -.14 -6.64 35 -6.31 2.89 27 61 22.53 27.92 43 .49 -2.93 30 62 7.00 9.24 33 -5.89 -2.23 22 63 50.64 24.04 30 -15.20 -7.43 28 64 109.86 41.85 36 14.27 -3.31 21 65 107.00 70.73 30 8.72 19.51 24 66 -11.77 -8.63 20 -16.75 -2.20 25 67 8.97 7.04 26 -15.78 -16.06 26 68 35.24 -6.84 32 -17.66 13.76 23 69 50.15 36.01 33 -17.72 -3.20 27 70 -46.51 -6.89 22 29.27 15.65 23 71 8.96 .08 3 46.40 10.68 29 72 59.42 53.12 44 -10.79 -21.69 25 73 25.40 15.31 39 -20.36 -9.62 24 74 15.67 50.35 26 -23.94 -9.00 24 75 14.90 28.16 33 -20.64 -5.17 28 76 45.45 42.49 30 14.82 21.85 27 continued . . . 61 TABLE III - continued Rising Market Declining Market  Stock Holding Holding Stock Holding Holding Stock No. Rtn % (54 wks) Period Rtn % Period Weeks Rtn % (55 wks) Period Rtn % Period Weeks 77 45.06 21.24 36 2.48 5.69 19 78 21.09 3.95 32 -17.57 15.09 20 79 68.91 48.99 49 -10.29 4.17 26 80 48.24 37.16 25 -14.62 1.21 30 81 50.51 14.96 39 -13.08 -9.53 27 82 52.67 24.91 27 -33.23 3.39 33 83 34.78 3.49 26 -14.92 -14.63 31 84 30.14 16.59 43 8.53 -.18 20 85 65.36 38.89 36 1.98 8.34 23 86 70.28 32.56 43 1.08 -1.51 22 87 51.63 30.70 49 -13.89 -3.32 19 88 87.62 61.13 32 -25.15 -15.59 26 89 15.61 -3.80 39 -.55 1.75 27 90 44.69 29.68 38 -18.68 - -5.73 27 91 40.37 -4.46 23 9.66 12.14 32 92 48.21 39.77 35 -31.19 -32.38 26 93 -29.44 -29.49 30 -22.34 10.42 25 94 68.56 58.45 37 -1.94 -1.64 17 95 28.23 25.44 25 13.27 11.17 27 96 41.24 35.42 26 -22.19 -7.61 25 97 57.79 27.71 33 -22.83 -9.67 34 98 11.85 11.65 35 -21.32 -26.62 32 99 -5.20 -11.85 27 3.55 1.87 23 100 100.12 81.03 26 -5.34 .27 29 101 9.79 31.24 22 -9.59 -15.25 23 TABLE IV SUMMARY OF TABLE III Rising Market Declining Market Stock No D i f f Rtn % D i f f Weeks Extra Extra Less P r o f i t Loss P r o f i t Less Loss D i f f Rtn % D i f f Weeks Extra Extra P r o f i t Loss Less P r o f i t Less Loss 1 10.46 13 / -2.62 40 / 2 14.63 16 / .48 31 / 3 -5.86 13 • -18.98 34 / 4 15.77 11 / -13.17 29 / / 5 4.77 28 / -19.99 33 / / 6 23.98 28 / 19.27 30 / 7 6.35 27 / -17.30 34 / 8 5.30 2 / -4.45 38 / 9 6.16 11 / .28 30 / 10 2.81 19 / -12.09 24 / 11 9.45 6 / -37.93 31 / / 12 8.20 8 / -21.78 25 / 14 14.61 21 / -4.85 34 / 15 6.85 8 / -19.18 27 / / 16 10.39 20 / -22.58 37 / 17 17.30 27 / -2.35 22 / continued . . . TABLE IV - continued Rising Market Declining Market Stock No D i f f Rtn % D i f f Weeks Extra Extra Less P r o f i t Loss P r o f i t Less Loss D i f f Rtn % D i f f Weeks Extra Extra Less P r o f i t Loss P r o f i t Less Loss 18 26.20 21 / / -3.89 33 / 19 16.84 16 / 8.70 27 • 20 26.15 16 / -9.14 30 / / 21 40.39 15 / / -22.05 35 / / 22 13.76 15 / -2.24 30 / 23 0 0 Same -4.25 31 / 24 22.18 14 / 17.24 23 / / 25 26.20 19 / -17.77 33 / 26 6.08 33 / • 1.14 34 / 27 .60 23 / -2.44 36 28 24.31 11 / -14.65 40 / 29 21.85 12 / -15.32 32 / 30a 15.66 17 / -22.53 27 • / 30b 10.03 17 / 17.15 29 • 31 25.45 20 / -9.10 35 / 32 -13.40 29 / / -3.17 27 • 33 21.56 13 / -12.81 34 / 34 12.67 30 / 16.32 33 35 24.03 28 • -8.07 33 / 36 40.21 15 -6.59 29 / continued . . . TABLE IV - continued Rising Market Stock No D i f f Rtn % D i f f Weeks Extra Extra P r o f i t Loss Less P r o f i t 37 15.84 20 / 38 -16.64 31 • 39 19.28 23 / 40 46.19 22 • 41 12.68 13 / 42 35.05 27 • / 43 36.66 12 / 44 -8.60 20 45 54.39 29 / 46 .97 23 / 47 -17.70 25 / 48 54.96 17 / 49 4.62 29 / 50 42.64 17 / 51 51.05 19 / 52 25.97 25 • 53 14.14 9 / 54 5.28 14 / Declining Market D i f f Rtn % D i f f Weeks Extra Profi t Extra Loss Less P r o f i t Less Loss -16.35 29 / -72.45 38 / -33.01 27 • / -10.39 37 / -14.65 29 • -18.34 32 -14.29 29 • -4.24 37 / 21.11 28 / -20.95 32 / -21.82 35 / / -7.31 25 / • -8.48 31 / -4.18 37 / 4.91 37 / -39.90 39 • / -4.57 36 • / 10.97 26 • CD continued . . . TABLE IV - continued Rising Market D i f f Stock No Rtn % Di f f Weeks Extra Extra P r o f i t Loss Less P r o f i t 55 8.75 32 / 56 10.63 8 / 57 10.49 15 / 58 6.84 11 • 59 18.29 28 / / 60 6.50 19 / 61 -5.39 11 / 62 -2.24 21 / 63 26.60 24 / 64 68.01 18 / 65 36.27 24 / 66 -3.14 34 67 1.93 28 / 68 42.08 22 • / 69 14.14 21 / 70 -39.62 32 71 8.88 51 / Declining Market D i f f Rtn % D i f f Weeks Extra Extra Profi t Loss Less P r o f i t Less Loss -3.31 27 / -3.94 31 / 15.00 26 / 10.57 27 / 3.89 38 / -9.20 28 / / 3.42 25 / / -3.66 33 • -7.77 27 / 17.58 34 / / •10.79 31 / •14.55 30 / .28 29 / •31.42 32 / / •14.52 28 / 13.62 32 / 35.72 26 • continued . . . TABLE IV - continued Rising Market Declining Market Stock No. D i f f Rtn % D i f f Weeks Extra Extra Less P r o f i t Loss P r o f i t Less Loss D i f f Rtn % D i f f Weeks Extra Profi t Extra Loss Less Less P r o f i t Loss 72 6.30 10 / 10.90 30 • 73 10.09 15 / -10.74 31 / 74 -34.68 28 / -14.94 31 / 75 -13.26 21 • -15.47 27 • 76 3.16 24 • -7.03 28 77 23.82 18 / -3.21 36 • 78 17.14 22 / -32.66 35 / / 79 19.92 5 • -14.46 29 / / 80 11.08 29 • -15.83 25 • / 81 35.55 15 -3.55 28 / 82 27.76 27 • -36.62 22 / 83 31.29 28 / - .29 24 / 84 13.55 11 / 8.71 35 / 85 26.63 36 / -6.36 32 • 86 37.72 43 • 2.59 33 • / 87 20.93 49 -10.57 36 • 88 26.49 32 • -9.56 29 continued . . . TABLE IV - continued Rising Market Declining Market Stock No. Di f f Rtn % D i f f Weeks Extra P r o f i t Extra Loss Less P r o f i t Less Loss D i f f Rtn % Di f f Weeks Extra P r o f i t Extra Less Loss P r o f i t Less Loss 89 19.41 39 / / -2.30 28 / / 90 15.01 38 / -12.95 28 / 91 45.01 23 / / -2.48 23 / 92 8.44 35 / 1.19 29 93 .05 30 / -32.76 30 / / 94 10.11 37 / -.30 38 / 95 2.79 25 / 2.10 28 / 96 4.82 26 / -12.58 30 / 97 30.06 33 / -13.16 21 / 98 .20 35 / 5.30 23 / 99 6.65 27 / 1.68 32 100 19.09 26 / -6.61 36 / 101 -21.45 22 / 5.66 32 / TABLE V EX POST PORTFOLIO RETURNS Rising Market P o r t f o l i o Return Trade P o r t f o l i o 37.53% 22.74% 54 weeks 34.53 weeks Declining Market P o r t f o l i o Return Trade P o r t f o l i o -11.50% 55 weeks 23.97 weeks Difference between p o r t f o l i o s : Rising Market Declining Market 14.79% 7.92% 19.37 weeks 31.03 weeks 69 TABLE VI EX ANTE RESULTS - TRADING RULES Rising Market Declining Market Stock Holding Holding Stock Holding Holding Stock No. Rtn % (25 wks) Period Rtn % Period Weeks Rtn % (35 wks) Period Rtn % Period Weeks 1 42.24 34.95 19 -14.15 -9.04 16 2 10.32 9.06 28 -3.46 12.56 17 3 16.80 4.74 19 -24.72 -9.82 13 4 20.16 -2.86 14 -29.98 -21.38 9 5 2.32 1.90 16 13.19 7.90 16 6 8.20 -1.96 13 -21.08 -9.70 18 7 -.88, -36.37 13 -16.75 -10.97 26 8 22.92 26.36 17 3.74 5.79 23 9 21.42 3.68 17 14.67 13.37 24 10 2.59 -3.55 16 -8.13 -7.76 23 11 19.43 14.04 17 -31.74 -20.61 15 12 9.84 .79 15 -6.78 3.14 8 14 14.04 -1.37 18 7.94 6.98 24 15 -.85 -8.23 14 -8.05 -8.33 20 16 22.90 13.10 20 9.81 2.64 24 17 32.88 23.98 18 -4.57 -1.16 10 18 17.97 2.59 16 16.61 10.84 17 19 12.42 12.23 19 21.38 16.99 24 20 5.11 1.78 17 24.68 7.09 8 21 -27.68 -34.15 12 -14.83 4.55 15 22 35.81 35.81 25 -7.21 5.81 18 23 12.44 17.53 21 -14.24 -1.49 11 24 7.76 3.47 10 -23.33 13.88 19 25 31.63 18.98 19 -14.23 -1.94 21 26 -2.60 -9.33 5 -1.04 -9.84 16 continued . . . 70 TABLE VI - continued Rising Market Stock Holding Holding Stock No. Rtn % (25 wks) Period Rtn % Period Weeks 27 -12.73 -30.61 18 28 -3.31 -5.65 9 29 30a 24.72 -10.24 9 30b 24.72 -10.24 9 31 15.87 -3.06 13 32 10.83 .92 17 33 17.12 1.89 15 34 4.97, -5.02 11 35 23.56 19.85 19 36 32.80 3.56 14 37 18.31 18.31 25 38 77.78 106.13 19 39 35.79 21.39 17 40 28.73 -2.91 14 41 45.63 25.18 18 42 5.31 1.47 17 43 8.95 -10.30 14 44 15.81 13.31 19 45 8.18 0 12 46 -2.14 -9.56 10 47 10.31 2.13 21 48 15.64 13.34 13 49 7.34 -1.31 20 50 4.43 -2.83 13 51 52 -2.97 -24.08 6 Declining Market Stock Holding Holding Rtn % Period Period (35 wks) Rtn % Weeks -9.46 12.61 6 -14.14 3.89 7 -2.60 10.89 10 -2.60 10.89 10 3.27 9.16 17 -.31 10.19 12 .50 -8.12 13 -16.31 2.44 11 -16.09 -6.83 19 -40.23 -10.07 14 25.02 23.11 19 11.57 26.46 15 15.18 -2.73 17 -40.67 -24.37 18 14.45 25.64 25 13.78 3.54 21 -27.74 -14.40 10 -80.20 -31.16 14 8.47 9.40 15 -6.38 -5.59 20 -26.97 -2.10 14 -23.59 -14.89 13 -7.23 -1.90 27 -16.41 1.83 23 -27.19 10.23 9 continued . . . 71 TABLE VI - continued Rising Market Declining Market Stock Holding Holding Stock Holding Holding Stock No. Rtn % (25 wks) Period Rtn % Period Weeks Rtn % (35 wks) Period Rtn % Period Weeks 53 9.83 .23 16 11.09 5.89 17 54 23.87 17.67 20 -2.76 -6.59 18 55 12.15 3.79 23 -13.29 -15.21 11 56 23.68 13.91 23 5.03 -4.10 24 57 18.85 15.55 14 -9.88 7.22 11 58 18.05 2.96 12 -23.10 4.38 20 59 -2.70 3.45 9 -.30 7.67 22 60 -1.43 -13.19 14 -10.97 3.79 20 61 12.51, 7.20 18 35.13 26.60 30 62 19.00 10.40 18 .19 5.53 29 63 2.65 -8.21 10 5.34 6.16 23 64 2.51 5.23 14 5.88 15.83 14 65 -1.76 -.65 14 9.23 9.93 22 66 9.12 12.84 20 -50.85 -27.39 13 67 12.57 2.91 18 3.09 -.74 24 68 34.18 43.35 18 -37.59 -3.06 8 69 3.92 19.20 14 -4.40 -11.98 4 70 4.67 -8.93 15 -28.05 -16.63 8 71 30.60 19.03 20 -34.52 .95 7 72 1.56 -7.84 19 3.55 -6.13 18 73 26.48 4.37 10 -4.02 1.30 21 74 4.20 -13.60 15 -2.66 - .83 23 75 6.97 5.27 15 -6.91 -3.12 21 76 16.06 17.94 15 -70.66 -2.42 12 77 .66 7.15 13 -11.22 -11.64 19 78 20.42 -11.85 16 7.89 25.39 11 79 -3.18 -12.53 11 19.40 -5.27 18 continued . . . 72 TABLE VI - continued Rising Market Declining Market Stock Holding Holding Stock Holding Holding Stock No. Rtn % (25 wks) Period Rtn % Period Weeks Rtn % (35 wks) Period Rtn % Period Weeks 80 27.88 9.82 18 9.83 -.27 21 81 23.16 14.74 23 4.52 -4.59 20 82 21.32 16.08 15 -15.02 -10.80 14 83 7.38 1.27 16 4.94 4.45 10 84 42.69 27.11 16 -42.92 -10.17 14 85 16.96 -2.72 15 -28.21 -27.21 16 86 -3.55 -2.81 15 -8.46 -6.09 22 87 18.10 2.84 12 8.19 .42 20 88 20.40 8.07 15 -49.27 -17.49 17 89 16.74 -.12 18 5.63 -.22 23 90 30.42 10.13 19 14.46 -1.27 9 91 32.37 24.26 17 6.55 ,41 20 92 29.46 12.60 16 -17.76 -10.44 28 93 41.30 27.89 20 14.83 6.56 19 94 31.03 14.70 8 21.34 21.08 20 95 28.47 .01 18 8.76 6,05 22 96 19.13 .49 15 19.65 11.52 20 97 16.55 9.53 18 7.47 4.74 11 98 8.71 2.33 15 -14.34 -6.57 22 99 1.33 -6.90 14 -10.02 -5.86 23 100 24.81 4.23 12 -31.87 -.20 6 101 21.05 22.59 17 7.75 12.90 24 TABLE VII SUMMARY OF TABLE VI Rising Market Declining Market Stock No D i f f Rtn % D i f f Weeks Extra Extra P r o f i t Loss Less P r o f i t Less Loss D i f f Rtn % D i f f Weeks Extra Extra Less P r o f i t Loss P r o f i t Less Loss 1 7.29 6 / -5.11 19 / 2 1.26 7 • -16.02 18 • 3 12.06 6 -14.90 22 / 4 23.04 11 • • -7.74 26 / 5 .42 9 / 5.29 19 • • 6 10.23 12 / -11.38 17 / 7 35.49 12 • -5.78 9 8 -2.84 8 • -2.05 12 9 17.74 8 • 1.30 11 / 10 6.14 9 / -.47 12 • 11 5.39 8 • -11.13 20 • 12 9.05 10 • -9.92 27 • / 14 15.14 7 / • .96 11 / 15 7.38 11 / .28 15 / 16 4.74 5 7.17 11 / 17 8.90 7 • -3.14 25 / CO continued . . , / TABLE VII - continued Rising Market Stock No D i f f Rtn % D i f f Weeks Extra Extra P r o f i t Loss Less P r o f i t 18 14.38 9 • 19 .14 6 / 20 3.23 8 / 21 6.47 13 / / 22 0 0 Same 23 -5.09 4 • 24 4.29 15 • 25 12.65 6 / 26 6.73 20 27 17.88 7 • 28 2.34 16 / 29 30a 34.96 16 / / 30b 34.96 16 / • 31 18.93 12 / / 32 10.01 8 / 33 15.23 10 • 34 9.99 14 / Declining Market D i f f Rtn % D i f f Weeks Extra P r o f i t Extra Less Loss P r o f i t Less Loss 5.77 18 / 4.39 11 • 17.59 27 • •20.14 20 • • 13.02 17 • • 12.75 24 • 10.05 16 • 12.29 14 • 8.80 19 22.07 29 • • 18.03 28 • • 13.39 25 • • 13.39 25 • -5.89 18 • 10.50 23 / • 8.62 22 • / 18.75 24 / continued . . . TABLE VII - continued Rising Market Declining Market Stock No D i f f Rtn % D i f f Weeks Extra Extra P r o f i t Loss Less Profi t Less Loss Di f f Rtn % Di f f Weeks Extra Extra P r o f i t Loss Less P r o f i t Less Loss 35 3.71 6 / -9.26 16 / 36 29.34 11 / -30.16 21 / 37 0 0 Same 1.91 16 / 38 -28.35 6 / -14.91 20 • 39 14.40 8 • 17.91 18 / 40 31.64 11 / / -16.30 17 / 41 20.45 7 / -11.19 10 / 42 3.84 8 / 10.24 14 / 43 19.25 11 • / -13.34 25 / 44 2.50 6 / -49.04 21 / 45 8.18 13 • -.93 20 / 46 7.42 15 / -.79 15 / 47 8.18 4 / -24.81 21 / 48 2.34 12 / -8.70 22 / 49 9.65 3 / / -5.33 8 / 50 7.26 12 / / -18.24 12 / / 51 52 21.11 14 • -37.42 26 / • cn continued . . . TABLE VII - continued Rising Market Declining Market Stock No. D i f f Rtn % Di f f Weeks Extra Extra P r o f i t Loss Less P r o f i t Less Loss D i f f Rtn % D i f f Weeks Extra Extra P r o f i t Loss Less Less P r o f i t Loss 53 9.60 9 5.20 18 / 54 6.20 5 / 3.83 17 / 55 8.36 2 / 1.92 24 / 56 9.77 2 / 9.13 11 / / 57 3.40 11 / -17.10 24 / / 58 15.09 13 / -27.48 15 / / 59 -6.17 16 / / -7.97 13 • / 60 11.86 11 / -14.76 15 / / 61 5.31 7 / 8.53 5 / / 62 8.60 7 / -5.72 6 • 63 11.26 15 / / -.82 12 / 64 -2.72 11 / -10.75 21 / 65 -1.11 11 / -.70 13 / 66 -3.72 5 / -23.46 22 • 67 9.66 7 / 3.83 11 / 68 -9.17 7 / -34.53 27 / 69 -14.28 14 / 7.58 31 / 70 13.60 10 / / -11.44 27 / continued .. . TABLE VII - continued Rising Market Stock No D i f f Rtn % Di f f Weeks Extra Extra P r o f i t Loss Less P r o f i t 71 10.77 5 / 72 9.40 6 • / 73 22.01 15 • 74 17.80 10 • • 75 1.75 10 / 76 -1.88 10 • 77 -6.51 12 • 78 32.37 9 • / 79 9.35 14 • 80 18.06 7 / 81 8.42 2 / 82 5.24 10 / 83 5.71 9 / 84 15.58 9 • 85 19.68 10 / 86 -.74 10 87 15.26 13 / 88 12.33 10 • Declining Market D i f f Rtn % D i f f Weeks Extra P r o f i t Extra Loss Less P r o f i t Less Loss •35.47 28 • / • 9.68 17 / / -5.32 14 / / -1.83 12 / -3.79 14 / •68.24 23 / .42 16 / •17.50 24 / •14.19 17 / 10.10 14 / / 9.07 15 / / -4.22 21 / .49 25 • 32.75 21 / -1.00 19 • -2.37 13 / 7.77 15 31.78 18 / continued , . . TABLE VII - continued Rising Market Stock No Di f f Rtn % D i f f Weeks Extra Extra Profi t Loss Less Profi t 89 16.86 7 / / 90 21.47 5 / 91 7.11 8 / 92 16.86 9 • 93 13.41 5 / 94 16.33 4 / 95 28.46 7 / 96 18.54 10 / 97 7.02 7 • 98 6.38 10 / 99 8.23 11 / / 100 20.58 13 / 101 -1.54 8 / Declining Market Di f f Rtn % D i f f Weeks Extra P r o f i t Extra Loss Less P r o f i t Less Loss 5.85 12 / / 15.73 26 • / 6.14 15 / -7.32 7 / 8.27 16 / .26 15 / 2.71 13 / 8.13 15 V 2.73 24 -7.77 13 / -4.16 12 / -31.67 29 / -5.15 11 / TABLE VIII EX ANTE PORTFOLIO RETURNS Rising Market P o r t f o l i o Return Trade P o r t f o l i o 15.48% 5.79% 25 weeks 17.46 weeks Declining Market P o r t f o l i o Return -7.55% 35 weeks Trade P o r t f o l i o .82% 16.99 weeks Difference i n Rising Market between P o r t f o l i o s 9.69% 6..86 weeks Difference i n Declining Market between P o r t f o l i o s 8.37% 18.01 80 TABLE IX WEEKLY STOCK HOLDING POSITION (Ex Ante) Week Rising Market Declining Market 1 99 99 2 99 99 3 84 95 4 10 83 5 6 83 6 24 82 7 26 78 8 36 71 9 45 5 10 53 2 11 78 0 12 75 0 13 69 22 14 69 57 15 79 54 16 82 48 17 74 52 18 70 51 19 68 50 20 64 52 21 63 51 22 72 50 23 69 47 24 67 43 25 62 41 26 64 27 63 28 56 continued . . . 81 TABLE IX - continued Week Rising Market Declining Market 29 4 30 0 31 0 32 11 33 11 34 10 35 26 82 TABLE X STOCK RELATIONSHIP TO MARKET MOVEMENT EX ANTE Stock No 1 2 3 4 5 6 7 8 9 10 11 12 R i Lags - I i - 6 I i 20 23 - - 10 12 I i s i Leads 24 7 16_ 14 11 - 3 25 23 5 10 6 n g With 1 2 9 5 1 4 1 - 2 5 3 6 F Lags 24 11 6 12 27 2 2± 35 35 7 7 14 a 1 i Leads 8 15 25 I i 4 25 14 - - 23 27 13 i i With 3 '1 4 4 4 8 4 - - 5 1 8 n g X / • / X / / X Stock No 14 15 16 17 18 19 20 21 22 23 24 25 26 R i Lags 3 10 1 1 9 9 11 1_6 - 24 18 7 18 s i Leads 20 7 I i 24 11 12 10 8 24 - 4 I i 6 n g With 2 8 5 - 5 5 1 1 1 1 3 5 1 F Lags 35 19 35 31 35 35 34 13 13 7 4 32 33 a 1 i Leads - 12 - 2 - - - 11 14 22 20 3 -i i n With - 4 - 2 - - 1 1 8 6 11 1 2 II g x x x X / X continued . . . 83 TABLE X - continued Stock No 27 28 29 30a 30b 31 32 33 34 35 36 37 R i Lags 20 24 5 7 6 19. - 16 18_ 11 5 s i Leads 2 - 20 18_ 11 6 24 9 1 13. 14 n g With 3 1 — ~ 6 — 1 6 1 6 F Lags 31 16 34 35 35 35 34 18 22 - 32 a 1 i Leads 4 17 - - - - - 15 7 32 2 i i in With - 2 1 - - - 1 2 6 3 1 i l g X x X X X / Stock No 38 39 40 41 42 43 44 45 46 47 48 49 R i Lags - 1 1 - 18 24 22 9 24 12 9 8 s i Leads 25 24 2J_ 25 7 - - 15 - 8 14. 11 n g With — — 3 - - 1 3 1 1- 5 2 6 F Lags 12 34 1 34 35 21 8 35 26 4 5 6 a 1 i Leads 22 - 31 - - 14 27 - 2 30 30 21 i i With 1 1 3 1 - - - •- 7 1 - 8 n g / • X X X / / continued . . . 84 TABLE X - continued Stock No 50 51 52 53 54 55 56 57 58 59 60 61 62 Lags 24 23 I i 8 1 - 3 17. 22 25 10 4 Leads - - 7 13. 23 25 17 5 - - 8 15. With 1 2 4 4 1 - 5 3 3 - 7 6 Lags 15 31 35 26 8 32 28 22 35 16 35 35 Leads 15 4 - 1 23 1 6 12 - 15 -With 5 - - 8 4 2 1 1 - 4 - -X X X / X X X X Stock No 63 64 65 66 67 68 69 70 71 72 73 74 Lags 10 24 21 25 1 7 19 23 11 l i 4 16 Leads 15 - 2 - 21 18 6 2 l i 4 18 5 With - 1 2 - 3 - - - - 2 3 4 Lags 35 35 33 1 35 9 17 19 8 32 30 33 Leads - - - 30 - 23 15 13 22 3 1 1 With - - 2 4 - 3 3 3 5 - 4 1 X X • / / / X X continued . . TABLE X - continued Stock No 75 76 77 78 79 80 81 82 83 R i Lags 9 16 15 U 19 3 7 23 20 s i Leads 11 8 7 12 2 20 14 1 2 n g With 5 1 3 — 4 2 4 1 3 F Lags 31 12 16 35 12 35 35 35 35 a 1 i Leads - 22 14 - 15 - - - -i i With 4 1 5 _ 8 _ _ - -n g X X X X X X Stock No 84 85 86 87 88 89 90 91 92 R i Lags 18 9 23 7 17. 1 - - 3 s i Leads 6 i i 1 11 4 20 25. 25 I i n g With 1 1 1 7 4 4 ™ 3 F Lags 9 15 28 35 6 29 34 32 15 a 1 i Leads 24 13 3 - 27 2 - - 16 i i With 2 8 4 _ 2 4 1 3 4 n g / X X • continued TABLE X - continued Stock No 93 94 95 96 97 98 99 100 101 Lags - 1 3 3 I i 20 I i 5 -Leads 25 12 19 £1 6 3 7 I i 25 With - - 3 1 3 2 4 4 -Lags 35 18 35 35 35 17 27 11 35 Leads - 12 - - - 14 2 23 -With - 5 - - - 4 6 1 -X X X • TABLE XI COMPARISON EX POST AND EX ANTE RETURNS XP - Extra XL - Extra P r o f i t Loss LP -LL - Less P r o f i t Less Loss Rising Market Declining Market stock No. Ex Post Ex Ante Ex Post Ex Ante 1 LP LP LL LL 2 LP LP XL XP, LL 3 XP LP LL LL 4 LP XL, LP XP, LL LL 5 , LP LP XP, LL LP 6 XL XL, LP XL, LP LL 7 LP XL LL LL 8 LP XP LL XP 9 LP LP XL LP 10 LP XL, LP LL LL 11 LP LP XP, LL LL 12 LP LP LL LL 14 LP XL, LP LL XP, LL 15 LP XL XP, LL LP 16 LP LP LL XL 17 LP LP XP LP 18 XL, LP LP LL LL 19 LP LP XL LP 20 LP LP XP, LL LP 21 XL, LP XL, LP XP, LL LP 22 LP Same LL XP, LL 23 Same XP LL XP, LL 24 LP LP XL, LP LL continued . . . TABLE XI - continued Rising Market Declining Market Stock No. Ex Post Ex Ante Ex Post Ex Ante 25 LP LP LL LL 26 XL, LP XL XL LL 27 LP XL XP XP, LL 28 LP XL LL XP, LL 29 LP LL 30a LP XL, LP XP, LL XP, LL 30b LP XL, LP XL XP, LL 31 LP XL, LP LL XP 32 XP, LL LP LL XP, LL 33 , LP LP LL XL, LP 34 LP XL, LP XL, LP XP, LL 35 LP LP LL LL 36 LP LP LL LL 37 XL Same LL LP 38 XP XP LL XP 39 LP LP XP, LL XL, LP 40 LP XL, LP LP LL 41 LP LP LL XP 42 XL, LP LP LL LP 43 LP XL, LP LL LL 44 XP LP LL LL 45 XL LP LP XP 46 LP XL LL LL 47 XP LP XP, LL LL 48 LP LP XP, LL LL 49 LP XL, LP LL LL 50 LP XL, LP XP XP, LL 51 LP LP continued TABLE XI - continued Rising Market Stock No Ex Post Ex Ante 52 LP XL 53 LP LP 54 LP LP 55 LP LP 56 LP LP 57 LP LP 58 LP LP 59 XL, LP XP, LL 60 XL XL 61 'XP LP 62 XP LP 63 LP XL, LP 64 LP XP 65 LP LL 66 LL XP 67 LP LP 68 XL, LP XP 69 LP XP 70 LL XL, LP 71 LP LP 72 LP XL, LP 73 LP LP 74 XP XL, LP 75 XP LP 76 LP XP 77 LP XP 78 LP XL, LP 79 LP XL Declining Market Ex Post Ex Ante XP,LL XP, LL XP, LL LP LP XL LL XL LL XL, LP LL XP, LL XP XP, LL LP XP, LL XP, LL XP, LL XL, LP LP LL XP LL XP XL, LP XP XP XP LL LL XL XL, LP XP, LL LL LL XL LP LL LP XP, LL XL XL, LP LL XP, LL LL LL LL LL XP LL XP XL XP, LL XP XP, LL LL continued TABLE XI - continued Rising Market Declining Market Stock No. Ex Post Ex Ante Ex Post Ex Ante 80 LP LP XP, LL XL, 81 LP LP LL XL, 82 LP LP XP, LL LL 83 LP LP LL LP 84 LP LP XL, LP LL 85 LP XL, LP XP LL 86 LP LL XL, LP LL 87 LP LP LL LP 88 LP LP LL LL 89 ' XL, LP XL, LP XP, LL XL, 90 LP LP LL XL, 91 XL, LP LP XP LL 92 LP LP XL LL 93 XL LP XP, LL LP 94 LP LP LL LP 95 LP LP LP LP 96 LP LP LL LP 97 LP LP LL LP 98 LP LP XL LL 99 XL XL, LP LP LL 100 LP LP XP, LL LL 101 XP XP XL XP TABLE XII COMPARISON OF LEADS AND LAGS - EX POST TO EX ANTE Rising Market Stock No Ex Post Ex Ante 1 Lead Lead 2 Lag Lag 3 Lag Lead 4 Lead x Lead 5 Lead Lag 6 Lag Lag 7 Lead Lag 8 Lead x Lead x 9 Lead x Lead 10 Lag x Lead 11 Lead Lead 12 Lead Lag 14 Lead x Lead 15 Lead Lag 16 Lead Lead 17 Lead Lead x 18 Lag Lag 19 Lag Lag 20 Lead Lag 21 Lag Lag 22 Lag Lead 23 Lead Lag 24 Lead Lag 25 Lead Lead 26 Lead Lag 27 Lag x Lag Declining Market Ex Post Ex Ante Lead Lag Lead Lag Lead Lead Lag Lead Lag x Lag Lag Lead Lead Lag Lead Lag x Lead Lag x Lead Lead Lead Lead Lead Lag Lead Lag x Lag Lag Lead Lag x Lag Lag Lead Lag x Lead Lag x Lag Lag Lag Lead Lead Lead Lead Lead Lag Lead Lead x Lag Lag Lag Lag Lag x continued . . TABLE XII - continued Rising Market Declining Market ;ock No Ex Post Ex Ante Ex Post Ex Ante 28 Lead Lag Lead Lag 29 Lead Lead 30a Lead X Lead x Lead Lag 30b Lead X Lead x Lead Lag x 31 Lead X Lead Lead Lag x 32 Lag Lag x Lead Lag x 33 Lead Lead Lead Lag 34 Lead Lag x Lag Lag 35 Lead Lag Lead Lag 36 •' Lead X Lead Lead Lead 37 Lag Lead Lead Lag 38 Lead Lead x Lead x Lead 39 Lead X Lead x Lag Lag 40 Lead X Lead Lead Lead 41 Lead X Lead x Lead x Lag 42 Lag X Lag x Lead Lag x 43 Lead Lag Lead Lag x 44 Lag Lag Lead Lead : 45 Lag Lead Lag x Lag x 46 Lag Lag Lead Lag 47 Lag Lead Lag Lead 48 Lag Lead Lag Lead ; 49 Lag Lead Lead Lead 50 Lag Lag Lag Lag 51 Lag Lag x 52 Lag X Lag Lead Lag x 53 Lead X Lag Lead Lag x 54 Lead Lead Lag Lag continued . . TABLE XII - continued Rising Market Declining Market Stock No Ex Post Ex Ante Ex Post Ex Ante 55 Lead X Lead Lead Lead 56 Lead Lead x Lead Lag 57 Lead X Lead Lead Lag 58 Lead Lag Lag x Lag 59 Lag Lag Lag Lag 60 Lag Lag x Lag Lag 61 Lead Lag Lag Lag x 62 Lead X Lead Lead Lag x 63 Lead Lead x Lead Lag x 64 'Lead X Lag Lag Lag x 65 Lead X Lag Lead Lag 66 Lag X Lag x Lag Lead 67 Lead Lead Lead Lag x 68 Lag X Lead x Lag Lead 69 Lead Lag x Lead Lag 70 Lag Lag x Lag x Lag 71 Lead Lead x Lag Lead 72 Lead Lag Lead Lag 73 Lead Lead Lead Lag 74 Lead Lag Lead Lag 75 Lead Lag Lead Lag 76 Lag Lag Lag Lead 77 Lead X Lag Lead Lag 78 Lead Lag x Lag Lag x 79 Lead X Lag Lead Lag 80 Lead Lead Lead Lag x 81 Lead X Lead Lead Lag x 82 Lead Lag Lag Lag x TABLE XII - continued Rising Market Declining Market Stock No Ex Post Ex Ante Ex Post Ex Ante 83 Lead Lag Lead Lag x 84 Lag Lag Lag Lead 85 Lead Lead Lag Lead 86 Lead Lag Lag Lag 87 Lead x Lag Lead Lag x 88 Lead Lag Lead Lead 89 Lead Lead Lag Lag 90 Lead Lead x Lead Lag 91 Lead Lead x Lead Lag 92 ' Lead Lead Lead Lead 93 Lag Lead x Lag Lag x 94 Lead x Lead x Lag x Lag 95 Lead Lead Lag Lag x 96 Lead Lead Lead Lag x 97 Lead Lag Lead Lag x 98 Lag x Lag Lead x Lag 99 Lag Lag Lag Lag 100 Lead Lead Lead Lead 101 Lag Lead x Lag Lag x x - indicates no movement with the market. 

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