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A re-examination of stock-market risk Gardiner, Daniel Francis 1972-12-31

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A RE-EXAMINATION OF STOCK-MARKET RISK by DANIEL FRANCIS GARDINER B.A., University of Western Ontario, 1967 M.A., Queen's University, 1969 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION in the Department of COMMERCE AND BUSINESS ADMINISTRATION We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA June, 1972  In presenting this thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h 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.  I t i s understood that copying or publication  of this thesis for financial gain shall not be allowed without my written permission.  Daniel F. Gardiner  Department of Commerce and Business Administration The University of B r i t i s h Columbia Vancouver 8, Canada  Date: June, 1972  ABSTRACT The purpose of the research undertaken in this thesis i s twofold:  a) to test the relationship between a security analyst's percep-  tion of risk based upon f i n a n c i a l statement data and overall market return and  b) to determine the relationship between the practitioners  concept of risk and risk as outlined in the l i t e r a t u r e . The main data sources for the thesis were the Financial Post computer tape from which "accounting" measures of risk were derived and stock exchange price quotations from which "economic" or " t r a d i t i o n a l " risk measures were determined.  "Accounting" measures of risk considered included the co-  e f f i c i e n t of variation, standard deviation and mean-absolute deviation of the earnings stream variables, net operating income, net income and net income plus depreciation.  The " t r a d i t i o n a l " or "economic"  measures computed were the standard deviation of return and the beta c o e f f i c i e n t or v o l a t i l i t y index. Arguments were then presented for the relevance of each measure in describing stock market r i s k . To determine any relationship among various risk measures, a correlation and sectoral analysis was undertaken. The correlation analysis indicated a s i g n i f i c a n t relationship existed among certain "accounting" and "economic" risk measures and in general, this r e l a t i o n ship was supported by the sectoral  analyses.  - ii -  To indicate the relationship among the risk measures and overall return, a graphical analysis was undertaken. Mixed results were obtained in this analysis, with certain measures of r i s k displaying a more s i g n i ficant risk/return relationship than did others. Thus, i t appears that there does e x i s t some degree of association between "accounting" and " t r a d i t i o n a l " measures of risk as indicated by the analyses undertaken in this thesis. What the l i t e r a t u r e i s measuring as r i s k could possibly then be a r e f l e c t i o n of what the security analyst views as stock market r i s k . However, there may be other factors which play an important role in the practitioners formation of r i s k estimates, factors which are, as of yet,  non-quantifiable.  F. J . Brooks-Hill, Chairman  ACKNOWLEDGEMENTS This thesis would not have been attempted nor completed were i t not f o r the i n s p i r a t i o n , guidance and encouragement given me by my thesis advisor, Professor F. J . Brooks-Hill. His counsel and advice were, at times, badly needed. In addition, the assistance of Mr. Koit Teng, Senior Analyst at the U.B.C. Computing Centre i n helping to develop the necessary computer programmes applicable i n this research, i s not to be underestimated.  Further, Miss Catherine Giles worked patiently and consis  tently over one summer i n the most tedious task of c o l l e c t i n g stock price data. To a l l of the above, I owe a considerable debt of gratitude and l a s t , but c e r t a i n l y not least, I wish to thank a most favourite "school teacher" from Penticton who I'm sure, would prefer to remain anonymous at this stage.  Her unfathomable d i l i g e n c e , encouragement  and optimism provided me with much of the moral support necessary to complete this t h e s i s , e s p e c i a l l y during the l a t t e r stages. To quote good f r i e n d , she also "deserves a l l the happiness the world can hold. D.F.G. Vancouver, B. C.  TABLE OF CONTENTS Page ABSTRACT  ii  ACKNOWLEDGEMENTS  iv  LIST OF FIGURES  vii  CHAPTER I.  II.  INTRODUCTION AND BACKGROUND  1  Focus of Research  1  Background  2  Format  6  DATA AND METHODOLOGY  8  Data  8  Accounting Data  8  Stock Price Data  9  Methodology  12  "Traditional" Measures of Risk .... '  13  Standard Deviation of Return  13  The Beta Coefficient  15  Accounting Measures of Risk  19  Standard Deviation  20  Coefficient of Variation  20  Mean-Absolute Deviation  21  v  - vi CHAPTER III.  Page RELATIONSHIPS AMONG RISK MEASURES . . The Tests  24  Correlation Analyses  24  Sectoral Analyses  25  The Results  IV  24  27  Correlation Analyses  27  Sectoral Analyses  30  RELATIONSHIPS AMONG RISK AND RETURN  33  The Tests  33  The Results  34  V. CONCLUSIONS AND FURTHER RESEARCH IMPLICATIONS  37  Conclusions and Implications  37  Areas of Future Research  41  BIBLIOGRAPHY  43  APPENDIX A - Market Returns, Risk-Free Returns and Correlation Matrices  44  APPENDIX B - Average Annual Return and Traditional Risk Measures . . 50 APPENDIX C - Accounting Measures of Risk  56  APPENDIX D - Graphical Analyses of Risk/Return Relationships . . . .  72  APPENDIX E - L i s t o f Firms Contained i n Sample  84  LIST OF FIGURES FIGURE 1. 2.  Page Risk/Return Relationships and Interrelationships Between Economic and Accounting Measures Movement of T.S.E. Index, Actual and Return, By Quarter, 1958 to 2nd Quarter 1967  - vi i -  5 11  CHAPTER I INTRODUCTION AND BACKGROUND  A. Focus of Research This thesis reviews and tests the hypothesis that security analysts or practitioners perceive r i s k associated with an individual security i n the stock market by reference to accounting or financial statement data. The traditional measure of risk i n the l i t e r a t u r e has been the variance or dispersion of individual security returns around the mean. A more recent concept of risk i s the beta c o e f f i c i e n t or v o l a t i l i t y index. (These measures w i l l be discussed more f u l l y l a t e r in this and the following chapters.) The purpose of this thesis i s then two-fold: a) to test the relationship between the analyst's perception of risk from accounting data and overall market return - i . e . the risk/return tradeoff, and b) to determine the relationship between the practitioner's concept of risk and r i s k as outlined i n the l i t e r a t u r e - i.e. a comparison of risk measures. I f a relationship i s found between accounting and economic measures of r i s k , this thesis postulates that the traditional measures of risk are merely reflections of the impact of security analyst or practitioner perceptions upon the actions of investors i n the stock market. - 1 -  - 2 -  B.  Background The research undertaken in e f f e c t constitutes a  re-examination  of the concept of stock-market r i s k , with reference to the actions of the participants themselves. When one talks to these p r a c t i t i o n e r s , they appear very reluctant to discuss r i s k in terms that the l i t e r a t u r e seems to suggest - i . e . they disclaim any knowledge of a conscious e f f o r t to consider r i s k by reference to the dispersion or variance of security returns about the mean. Nor for that matter, do they consider any other measure of return dispersion. The question then becomes: What, in fact, dp_ they consider in t h e i r asset selection procedures?  On the  other hand, i t did seem evident that they were at least aware of r i s k in that they w i l l not accept extremely risky investments but w i l l accept some degree of r i s k or uncertainty inherent in p a r t i c u l a r investments. The best evidence of r i s k averse investment behavior i s that p o r t f o l i o managers tend to hold more s e c u r i t i e s than would be defensible in l i g h t of capital market imperfections.  Therefore, one may conclude that  they turn to d i v e r s i f i c a t i o n as a means of reducing r i s k . Thus i t seems that at least inherently the practitioners by t h e i r actions consider some degree of r i s k associated with a p a r t i c u l a r asset. i) Questions  Raised  How do practitioners or fund managers estimate the r i s k associated with p a r t i c u l a r s e c u r i t i e s comprising t h e i r p o r t f o l i o ? Upon what do portf o l i o managers base t h e i r decisions as to the certainty of return for an individual security? How confident are they in t h e i r estimates once they are formed?  - 3 -  In order to estimate a confidence level for a p a r t i c u l a r secur i t y ' s expected return, i t may be worthwhile to examine the underlying components of the informational process upon which fund managers base t h e i r decisions. three sources:  It appears that this information i s derived from the reports of security analysts; what the p o r t f o l i o  managers hear from other people on the street or in the market place (for convenience "street t a l k " ) ; and f i n a l l y , t h e i r own personal biases. Assuming that "street t a l k " i s influenced by analysts' findings and randomly generated rumors and that personal biases are randomly distributed across the market, the focus of this study i s limited s o l e l y to the accounting information available to the analyst. Thus, the problem e s s e n t i a l l y becomes one of determining what the analyst considers in forming his estimate of the value of the security which he is currently analysing.  F i r s t of a l l , an analysis of the firms past  financial history i s undertaken by reference to company f i n a n c i a l statements. Based upon this information, the analyst then forms expectations as to the future f i n a n c i a l conditions of the p a r t i c u l a r enterprise in the l i g h t of expectations of the overall economy, the industry in which the firm i s situated and the future management of the company. From his analyses, the security analyst i s able to form expectations as to the future earnings power of the business and attaches, either consciously or unconsciously, a degree of certainty to his predictions. E s s e n t i a l l y , the question becomes two-fold:  how does the analyst  form a measure of r i s k and upon what bases does he generate a degree of confidence in his forecast?  It appears that one of these bases  concerns the management of the company and the analyst's in-depth  - 4 -  interviews with them. This, of course, i s not quantifiable. Another base mentioned previously may be that the analyst in some way i n t u i t s estimates of the future f i n a n c i a l position of the firm when he investigates i t s f i n a n c i a l h i s t o r y . In this case, i t appears reasonable that one of the variables that the analyst may consider i s the variance or fluctuations of the earnings stream since ultimately i t is the net income that accrues to the owners (equity shareholders). The s t a b i l i t y (or v o l a t i l i t y ) of the earnings stream of a part i c u l a r company may be conceptualized in a variety of ways, a l l by reference to the firms f i n a n c i a l statement data. (NI) i s one way.  Reported net income  However, this figure may not be that relevant due,  i n t e r a l i a , to the fluctuations caused by debt repayment, extraordinary gains and losses and so f o r t h . Net operating income (NOI) may be more appropriate.  In addition, as a proxy f o r cash flows, net income plus  depreciation (NI + D) may be considered.  From a s t a t i s t i c a l point of  view, measures of dispersion such as the standard deviation(or variance) of individual returns about t h e i r mean, the mean-absolute deviation and c o e f f i c i e n t of variation for each of these earnings-stream  variables  may be e a s i l y computed. It may be that i f a security analyst were to u t i l i z e these measures that he could form an estimate of the r i s k associated with the return of an individual security. Asset selection procedures can be greatly s i m p l i f i e d by this technique.  Figure 1 i l l u s -  trates diagrammatically the informational flow upon which practitioners may base t h e i r decisions and in addition, outlines possible i n t e r r e l a t i o n ships between "accounting" and " t r a d i t i o n a l " measures of r i s k . f a i r l y straightforward and no explanation i s required.  It i s  Portfolio Implications  Market Efficiency Implications  I  X  Literature Risk/Return Concepts  r  i  Pension Fund Managers or Practitioner's Risk/Return Concepts  \ \  \  F  0  RM VA T\ I 0  i  Bias \ \  Talk • Reports  N  I i  I  I  Management Interviews, Economi c, Industrial Forecasts, etc.  A.  >A Financial x5 Statements ' NI, NOI, NI + D, Risk Bases  Y Effect of what Practitioners do with Respect to Security Reports may be what Literature Measures as Risk-Return Concepts.  FIGURE 1. RISK/RETURN RELATIONSHIPS AND INTERRELATIONSHIPS BETWEEN ECONOMIC AND ACCOUNTING MEASURES  I I  I J  i  - 6 -  In summary, the central hypothesis underlying this thesis i s that risk i s perceived by practitioners in the market place in a very d i f f e r e n t manner than i s suggested by the l i t e r a t u r e .  It i s the dual  purpose of this thesis to examine the risk/return tradeoff u t i l i z i n g the "new" measures of risk (based on the v a r i a b i l i t y of a firms earnings stream over time) as well as to compare these "new" measures with the t r a d i t i o n a l concepts of risk as outlined in the l i t e r a t u r e . relationship  I f the  i s f a i r l y close, i t may well be that what the l i t e r a t u r e  is viewing as risk i s r e a l l y the effect of what the practitioners i n t u i t as r i s k . This point w i l l be more f u l l y developed l a t e r in this thesis.  C.  Format of Thesis The layout of a thesis i s largely a matter of personal choice.  This thesis shall take the following form:  Chapter I dealt mainly with  the purpose(s) of the proposed research along with a b r i e f background as to how the research came to mind. Hypotheses w i l l be explained and relationships to be tested outlined.  Chapter II describes the data  sources f o r the project and in addition, discusses the methodology to be undertaken.  Computational equations are developed with respect to  calculating the various "accounting" and " t r a d i t i o n a l " measures of stock-market r i s k .  In Chapter I I I , tests and results of relationships  among the various risk measures developed i n the previous chapter are outlined and Chapter IV deals with an analysis of the risk/return r e l a t i o n ships f o r the various risk measures previously discussed. F i n a l l y ,  - 7 -  Chapter V presents the conclusions and results of analyses undertaken and suggests areas of future research. Appendix tables follow the final chapter and are referred to extensively throughout the thesis. *  *  *  *  *  *  CHAPTER II DATA AND METHODOLOGY  This chapter i s divided into two main sections: 1) the data, and 2) methodology. The f i r s t section deals with sources of data, relevance of the time period and the development of the ultimate sample to be u t i l i z e d i n the analyses. The second section, methodology, presents the actual computational equations f o r each of the " t r a d i t i o n a l " as well as "accounting" measures o f risk plus relevant assumptions underlying each measure.  A. The Data Data sources u t i l i z e d f o r this research can be subdivided into two components: the data necessary f o r determining the "accounting" measures o f risk and the data necessary f o r calculating the " t r a d i t i o n a l " risk measures. i ) Accounting Data In determining the "accounting" measures o f risk the Financial Post Computer Services Library tape was u t i l i z e d for three reasons: 1) ease o f access, 2) readily a v a i l a b l e financial statement f i g u r e s , and 3) a f a i r l y representative time period (1958-67) over which financial statement figures were available.  Essentially this " l i b r a r y " consists - 8-  - 9 of 68 data items on an annual basis f o r 279 Canadian firms, ranging from standard balance sheet and income statement figures to various adjustments for accounting changes, tax losses, stock s p l i t s and sharevolume outstanding. For the purposes of this thesis, of p a r t i c u l a r interest were the annual figures of net operating income, net income and depreciation for each firm. As mentioned previously, the net income figure may not be that accurate since i t might r e f l e c t extraordinary items and the l i k e . Accordingly, this figure was adjusted f o r non-recurring items as well as changes i n accounting practice to allow for relevant comparisons with other measures. Since i t i s desirable to compute the "accounting" measures of risk with the most complete information a v a i l a b l e , those firms having quite sparse financial data ( i . e . less than seven annual figures f o r NOI, NI, and NI + D) were eliminated from the i n i t i a l sample.  The  sample was now reduced to 224 upon which to carry out analyses of price and dividend behavior over the ten-year period. The financial figures of the companies remaining in the sample given by the Financial Post tape were then checked, on a random basis against the actual annual reports and no s i g n i f i c a n t deviations were noted in the comparisons. Hence, the remaining sample of 224 firms was then considered in order to develop the " t r a d i t i o n a l " measures of risk as outlined i n the l i t e r a ture. i i ) Stock Price Data As the " t r a d i t i o n a l " risk measures are based upon both i n d i v i dual and market returns (of which p r i c e and dividend figures are the  - 10 two components), quarterly prices and dividends were c o l l e c t e d over the period December, 1957 to December, 1967.  Most of this data was  obtained  from various issues of the Toronto Stock Exchange (TSE) Review, although some firm quotations were found in the Montreal and Vancouver Exchange periodicals. Also computed were the quarterly "market" rate of return figures based upon the TSE composite i n d u s t r i a l index and quarterly " r i s k - f r e e " rates of return based on 90-day Treasury B i l l y i e l d s . Tables 1 and 2, Appendix A present these values, the s i g n i f i c a n c e of which shall become apparent l a t e r in this chapter.  Figure 2 following,  graphs the quarterly rates of market return over the ten-year period and as can be seen, the time span is s u f f i c i e n t l y long to eliminate any bias that may r e s u l t when the stock market i s in either a " b u l l " or "bear" position. Also any firms having less than seven complete years of price and dividend data were eliminated from the sample.  In  addition where data was lacking f o r only two or three consecutive quarters and could not be extrapolated based upon previous months figures, these firms also were dropped out of the sample. Based upon this screening procedure, the ultimate sample used throughout this research f e l l to 114 companies which represented firms l i s t e d upon the Toronto,  Montreal  or Vancouver Stock Exchanges. A complete l i s t i n g of firms represented in the sample i s contained in'Table; 1, Appendix E. In summary then, the data for the proposed research encompassed the period 1958-1967 and consisted of a sample of 114 firms, complete with respect to NOI, NI and NI + D data as well as quarterly prices and d i v i dends. "Market" and " r i s k - f r e e " rates of return were also computed. In the following section of this chapter, the discussion focuses upon the methodology involved in the actual analysis of the data.  - 11 -  1 0 X IO T O T H E I N C H 7  X  IH  INCHES KCUFFtL  46 0 7 8 0 UAOt IN U . S . « .  0. t S S E I I  CO.  - 12 B. The Methodology The f i r s t step undertaken was to calculate both the " t r a d i t i o n a l " and "accounting" measures of r i s k .  The computational equations u t i l i z e d  in the determination of these measures as well as some of the relevant assumptions inherent in t h e i r derivation are described below. However, before discussing these measures i t is useful to outl i n e the methodology involved in computing the return per quarter f o r an individual stock as these figures play a crucial role in the development of the two t r a d i t i o n a l measures. Formula 1 defines return (expressed as a percentage) as consisting primarily of capital appreciation plus dividends:^ R  jt  =  P  c " o Po P  jt Po  +  D  (1)  j = 1 ... 114 stocks t = 1 ... 40 quarters  where: R.. = return on j ^ * stock f o r t^* quarter, 1  1  J t  D. = dividend on j +  stock f o r t  quarter,  P = c l o s i n g price of stock at end of quarter, c  P = opening price of stock at beginning of quarter Q  or previous quarter's closing price. From a total of 41 prices and dividends per firm over the ten-year period, 40 quarterly returns were calculated using Formula 1.  These  40 returns are then used in c a l c u l a t i n g the variance or standard deviation of return upon which attention shall now be focused. ^For the purposes of this t h e s i s , a l l prices and dividends have been adjusted f o r stock s p l i t s and stock dividends.  - 13 i ) "Traditional" Measures o f Risk In the l i t e r a t u r e , the two most common measures of risk associated with an individual security are the variance or standard deviation or return and the beta c o e f f i c i e n t or v o l a t i l i t y index. a) Standard Deviation of Return The standard deviation or variance of return about the mean is calculated i n accordance with Formula 2: 40  40 E  Rij'  z Rij  r  2  i =1 n  or  Srj  i  i/2  . -  i = 1 ....  (2) 40 quarters,  j = 1 . . . .114 stocks where: V . = variance of return of j D  stock over entire period,  KJ J.L-  Rij = return on j  J.L.  stock i n the i  quarter,  n = sample s i z e , i . e . 40 quarters, and s . = standard deviation of return of j D  stock over entire period.  The greater the standard deviation or variance of return about the mean value, the greater the risk associated with that p a r t i c u l a r security. Table 1, Appendix B shows the various standard deviations per coded stock over the ten-year period.  Variance of return i s not reported  as i t i s simply the square of the standard deviation and such a small number i s not that meaningful i n this context. Considering the appropriateness of the standard deviation as a measure of r i s k , several disadvantages may be pointed out:  a) returns  - 14 and underlying stock prices are assumed to be normally d i s t r i b u t e d ; b) a measure of downside risk instead of both the upside and downside l i a b i l i t y as variance measures may be more relevant - in other words, semi variance i s more appropriate; and c) variance i s an absolute amount when a r e l a t i v e figure may be more desirable. However, these arguments against the use of variance or standard deviation may be countered as follows. With respect to the f i r s t c r i t i c i s m , that of non-normality of underlying d i s t r i b u t i o n s , i f a d i s t r i b u t i o n is "normal," only the f i r s t two moments - the mean and variance - are needed to completely describe the d i s t r i b u t i o n .  Higher moments such as skewness and kurtosis (third  and fourth moments respectively) are not of use since the normal dist r i b u t i o n i s neither skewed nor abnormally peaked. Even when the underlying d i s t r i b u t i o n i s not normal, evidence has shown that the d i s t r i b u t i o n of returns i s a special type of stable Paretian d i s t r i b u t i o n which has 2  the important property of s t a b i l i t y under addition. In addition, Fama and Roll have pointed out that in assuming normality, no serious 3  aberrations i n the results w i l l appear. See f o r example, Eugene F. Fama, " P o r t f o l i o Analysis i n a Stable Paretian Market," Management Science, Vol. 11, January 1965, pp. 404-419; and Benoit Mandlebrot, "The Variation of Speculative Prices," Journal of Business, Vol. 36, October 1963, pp. 394-419. 3  Eugene Fama, "The Behavior of Stock-Market Prices, Journal of Business, Vol. XXXVIII (January 1965), pp. 34-105; and Richard R o l l , "The E f f i c i e n t Market Model Applied to U. S. Treasury B i l l Rates," Unpublished Ph.D. t h e s i s , Graduate School of Business, University of Chicago, 1968. See also E. F. Fama and R. R o l l , "Some Properties of Symmetric Stable D i s t r i b u t i o n s , " Journal of the American S t a t i s t i c a l Association, Vol. 63, September 1968, pp. 817-36.  - 15 The argument f o r the use of semi-variance and not variance, raises three points: a) in developing an appropriate risk measure, i t seems natural to consider both the deviations above and below the mean return rather than simply the ones below (the negative deviations) compare a capital budgeting problem where only the "costs" are considered instead of both costs and benefits; b) there i s a greater s t a t i s t i c a l " f a m i l i a r i t y " with the standard deviation measure; and c) although not necessarily the case, there are additional costs involved in calculating the semi-variance and from a practical standpoint at least, these may be prohibitive.  Further, i t i s unclear, at least to this author that most  d i s t r i b u t i o n s , given a large enough sample, are s u f f i c i e n t l y d i f f e r e n t from symmetrical to warrant the use of the semi-variance technique. The t h i r d c r i t i c i s m suggesting that a r e l a t i v e concept as opposed to the absolute variance or standard deviation figure i s desirable, emphasizes use of the c o e f f i c i e n t of variation (standard deviation divided by the mean) to eliminate the magnitude problem. However, i n this case, since return i s measured in price r e l a t i v e s , the same effect is achieved and there i s no need to consider the c o e f f i c i e n t of variation. Thus, one of the " t r a d i t i o n a l " measures of risk associated with a p a r t i c u l a r security employed i n this thesis i s the standard deviation (or variance) of security returns. Evidence was presented why this i s not an unwise choice. b) The Beta Coefficient In addition to the standard deviation or variance of return, another " t r a d i t i o n a l " measure of the risk associated with a p a r t i c u l a r  - 16 security i s the "beta c o e f f i c i e n t " or " v o l a t i l i t y index," developed most 4  notably by Markowitz and Sharpe.  B a s i c a l l y , this model asserts that the  return of an individual security can be broken down into two elements, a market or systematic component, r e f l e c t i n g a comovement of the i n d i vidual security's return with that of the average return of a l l other securities in the market and an i n d i v i d u a l i s t i c or unsystematic element which moves independently of the market return and i s unique to the individual security.  Examples of the l a t t e r component affecting a  security's return might well include a cut in dividends, a s t r i k e , worker attitudes, management a b i l i t i e s and other factors unique to the firm or the industry.  In a p o r t f o l i o context, i t i s argued that the  risk associated with this i n d i v i d u a l i s t i c component of security return can be d i v e r s i f i e d away with the result that a l l the covariance between security returns i s due to a single common market factor.  Algebrai-  c a l l y , this market model may be presented as Formula 3 below: *jt  =  +  B  j  *mt  +  ht  (3)  j = 1 ....  114 stocks  t = 1 ....  40 quarters  where: E (5) = 0 r (R ,  ij)  =  r  l)  = 0  m  4  (L,  k  0 3 f k  Harry M. Markowitz, P o r t f o l i o Selection: E f f i c i e n t D i v e r s i f i cation of Investments (New York: John Wiley and Sons Inc., 1959); and William F. Sharpe, P o r t f o l i o Theory and Capital Markets (New York: McGraw-Hill Inc., 1970T  - 17 -  R.-f. = return on security j , in t  quarter,  R = quarterly return on all other securities in the m market (hereafter called "market return"), ?.  t  = the individualistic component of security j ' s return in the t  quarter (supposedly diversified  away in a portfolio context), a., B • = intercept and slope associated with the linear J  J  relationship, and r  =  partial correlation coefficient  The particular equation utilized in this thesis is a form of the above equation but is adjusted by a "risk-free" rate of return in order to examine the risk premium of the market and the individual securities. This equation is outlined in Formula 4 and has the same assumptions and symbols as does Formula 3 with the exception that R  f t  refers to the  quarterly risk-free rate:  ~ jt " ~ ft R  R  =  a  j  +  6  j  (~mt " f t R  R  }  +  ht  ( 4 )  j = 1 . . . . t = 1 . . . . where:  114 stocks 40 quarters  R.., R . = security and market rates of return as jt mt specified in Formula 3 above, R  f t  = quarterly risk-free rate of return in the market place, and  a-,  3 -j  J  J  - parameters and residual as specified  n  J  also in Formula 3 above.  - 18 At this point i t i s desirable to explain the derivation of the " r i s k - f r e e " rate of return (R^) and the "market" rate of return (P^) as u t i l i z e d in Formulae 3 and 4.  As a proxy for a "risk-free" rate of  return on the market, a reasonable measure i s the average y i e l d on 3-month Treasury B i l l s .  This quarterly y i e l d may be calculated by d i v i -  ding by four the annualized y i e l d (per cent) on 3-month Treasury B i l l s at the end of each quarter (weekly tender on Thursdays following Wednesday date shown). These quarterly rates are shown in Table 1, Appendix A. The market rate of return i s calculated in a s l i g h t l y different manner. In this case, the TSE industrial index can be u t i l i z e d as a reasonable proxy to calculate the quarterly market rate. Added to 5 this rate w i l l be a quarterly market dividend adjustment of .009. Formula 5 shows the computation of the market rate of return in algebraic terms: R  mj  =  R  mjc " mjo mjo R  +  .009  (5)  R  114 stocks where:  = quarterly market return of j * ' stock, 1  over 40 quarters, R . = closing market return of j  stock at  end of quarter, R mjo  =  opening • market return of j beginning of quarter, and  stock at  .009 = quarterly market dividend adjustment (constant per quarter). 5 The annual dividend given by the TSE index i s in the order of 4% over the time period considered or about .009% per quarter u t i l i z i n g a geometric average.  - 19 Table 2, Appendix A outlines the various quarterly market returns (percentages) f o r the period 1958-1967. Regressions of the form of Equation 4 were run f o r each stock over the ten-year period and the resulting beta coefficients (the e. s 1  in Equation 4) indicating the r e l a t i o n s h i p between the actual stock "risk premium" (R^ - R ) and market "risk premium" (R t  ft  fnt  - R ) are ft  l i s t e d by firm code in Table 1, Appendix B along with the standard deviation of return. In summary, the purpose of this section of the chapter was to develop the two " t r a d i t i o n a l " measures of security r i s k . i i ) Accounting Measures of Risk This thesis postulates that practitioners or fund managers view risk in a different manner than does the l i t e r a t u r e . Security analysts may generate t h e i r estimates of the risk associated with a unique security, i n t e r a l i a , upon financial statement figures. Of part i c u l a r importance i s the h i s t o r i c a l earnings stream of the individual firm.  This earnings stream of a firm may be viewed as net operating  income (NOI), net income (NI) and net income plus depreciation over the ten-year period. S t a t i s t i c a l methods can be undertaken to calculate the degree of risk associated with each of these flows. Three such measures of risk f o r each earnings stream are the standard deviation, meanabsolute deviation and the c o e f f i c i e n t of variation. These measures were u t i l i z e d in this thesis and w i l l be discussed in turn.  - 20 a) Standard Deviation The standard deviation of each earnings stream flow was calculated according to Formula 6 which i s e s s e n t i a l l y the same as Formula 2 but with s l i g h t symbolic modification: 10  10 E  Eij  2  n  E  i = 1 Eij n  2  1/2 or  'Ej  (6)  'Ej  i =1  10 years  j =1  114 stocks  where: V^j = variance of earnings stream of jth stock over entire period, E i j = earnings stream o f j * * stock per i 1  n s  tn  year,  = sample s i z e , i . e . 10 years, and  Ej  =  standard deviation of the earnings stream of j "th stock over 1 :  1  entire period. Accordingly, given Formula 6, the standard deviation for each earnings stream variable (NOI, NI, and NI + D) was computed and the resulting magnitudes noted i n column 1 of Tables 1, 2 and 3, Appendix C. With respect to the appropriateness of such a measure, much of what has been said already i n the previous section under "Standard Deviation of Return" i s applicable here and w i l l not be repeated. b) Coefficient o f Variation Since the standard deviation of return i s already a measure of r e l a t i v e dispersion based upon price r e l a t i v e s , the standard deviations of earnings stream variables, on the other hand represent absolute magnitudes.  To overcome this problem of magnitude d i f f e r e n t i a l ,  the coefficients of variation of the various earnings stream variables  - 21 were computed per Formula 7 below: C 0 V  (7)  Ej • j = 1 . . . 114 stocks  where: COV^. = c o e f f i c i e n t of variation of earnings stream variable of j  stock over 10 year period,  s,-. = standard deviation of earnings stream variable of j** stock over 10 years, (see Formula ( 6 ) ) , and 1  Ej = mean value of earnings stream variable of j  stock  over 10 year period. In column 2 of Tables 1, 2 and 3, Appendix C are l i s t e d the various c o e f f i c i e n t s of variation f o r each stock over the period 1958-67. c) Mean-Absolute Deviation A t h i r d measure of risk and one that offers direct support to the standard deviation of the earnings stream variables i s the meanabsolute deviation s t a t i s t i c .  Formula 8 shows the algebraic derivation  of this measure: 10 M.A.D. . = z lEj - E.l n  (8)  C  i = 1 ....  10 years  j = 1 ....  114 stocks.  where: M.A.D.^. = mean-absolute deviation of the earnings stream variable of the j ten-year period,  stock, over the  - 22 Ej = earnings stream value per annum of the j  stock, "th  Ej = mean value of earnings stream variable of j  stock  over 10 years, and n = sample s i z e , i . e . 10 years. This s t a t i s t i c was calculated f o r each earnings stream variable (NOI, NI, and NI + D) over the entire sample 114 stocks and the results noted in column 3 o f Tables 1, 2 and 3 of Appendix C. In summary then, three accounting measures of risk were calculated based upon f i n a n c i a l statement figures.  To this author, the most meaning-  ful measure f o r comparison with the " t r a d i t i o n a l " measures of security risk i s the measure of r e l a t i v e dispersion, the c o e f f i c i e n t of variation for each earnings stream variable.  Further tests shall be undertaken  u t i l i z i n g only this measure of security r i s k . In conclusion, this chapter has focused upon a discussion o f the sources of data f o r this thesis and the development of the " t r a d i t i o n a l " and "accounting" measures or risk associated with a p a r t i c u l a r security. The " t r a d i t i o n a l " measures to be u t i l i z e d i n further analyses are the standard deviation of return and the beta c o e f f i c i e n t or v o l a t i l i t y index. Only one accounting measure of r i s k , the c o e f f i c i e n t of variation s t a t i s t i c for each earnings stream variable (NOI, NI, and NI + D) i s to be considered. Given the above measures, tests were carried out i n order t o : a) determine i f any s i g n i f i c a n t relationship exists among these various risk measures, and to b) report any s i g n i f i c a n t relationships between the r i s k measures and the p a r t i c u l a r returns of a stock over time. Chapter IV discusses the results o f tests involving risk measures alone  - 23 -  ((a) above) while Chapter V describes the results when the risk/return tradeoffs were analysed.  CHAPTER III RELATIONSHIPS AMONG RISK MEASURES  An examination of the relationships among both the "accounting" and " t r a d i t i o n a l " measures of security risk i s the purpose of this chapter and discussion shall now focus upon the development of s p e c i f i c tests to indicate i f any relationship does indeed exist among the various risk measures. A correlation analysis was performed on the risk measures and the movement of two variables are noted.  Further tests were carried  out to support the results obtained from this correlation analysis.  A.  The Tests i ) Correlation Analyses Often a bivariate population may be non-normal and when this  is so, calculation of a correlation c o e f f i c i e n t by the usual method i s not v a l i d . Even though the distributions underlying the t r a d i t i o n a l risk measure may be considered normal, there i s no guarantee that the distributions of accounting risk measures w i l l be normal.  Nevertheless,  one may s t i l l wish to examine whether these two variables are independent or whether they vary i n the same or opposite directions.  One of the  best-known procedures i n which a correlation c o e f f i c i e n t may be computed - 24  -  - 25  -  between two variables where neither variable may be normal, involves ranking both variables and then calculating the Spearman rank correlation c o e f f i c i e n t , given by Formula 9: r  = 1 - 6  n z  d.  2 c  H^TT-  H < r , < „  i = 1 ....  <> 9  114  where: rs = rank correlation c o e f f i c i e n t between two risk measures, d = differences in ranks between the two measures, and n = sample s i z e , i . e . 114 stocks. As indicated above, the range of values of r , may be from -1 (complete discordance) to +1 (complete concordance). A total of ten Spearman rank correlation c o e f f i c i e n t s were calculated involving both the " t r a d i t i o n a l " and "accounting" measures of security risk in pairs. To test f o r s t a t i s t i c a l s i g n i f i c a n c e , Ttests were performed on each of these rank c o e f f i c i e n t s and the r e s u l t s , along with the actual c o e f f i c i e n t s themselves are summarized in matrix form i n Table 3, Appendix A. i i ) Sectoral Analyses To further support these rank correlation c o e f f i c i e n t s , additional s t a t i s t i c s were computed.  In the f i r s t place, the range of each measure  of risk was divided into thirds and each corresponding t e r t i a r y sector was compared to see how many pairs of firms changed sectors over the ten-year period.  The number of firms (pairs) that did in fact change  - 26  -  sectors i s also noted i n each c e l l of the matrix i n Table 3, Appendix A, just below the magnitudes of the Spearman correlation c o e f f i c i e n t s . Secondly, and again to further substantiate the rank correlation c o e f f i c i e n t s , a "mean" and "median" analysis was carried out i n order to indicate the number of stocks common to two p a r t i c u l a r measures of risk. With reference to the "mean" a n a l y s i s , the number of stocks above the mean of one risk measure was expressed as a percentage of the number of stocks above the mean of the other measure. These percentages are shown i n Table 4, Appendix A. In addition, the number of companies common to both measures above the mean was compared to the number of companies above the mean f o r the other measure. The resulting percentages are also shown i n Table 4, Appendix A. A "median" analysis was also undertaken i n a s i m i l a r fashion to the "mean" analysis except that the r a t i o of the number of stocks above the median of one measure to the number of stocks above the median of the other measure was omitted. less and constant at 1.0.  Obviously, this r a t i o would be meaning-  The results of this analysis are portrayed  in Table 5, Appendix A. In summary, a correlation analysis was undertaken as well as other related tests to determine i f any s i g n i f i c a n t r e l a t i o n s h i p exists between "accounting" and " t r a d i t i o n a l " measures of risk as developed i n the previous chapter.  -  B.  27  -  The Results i ) The Correlation Analysis Based upon the results shown in Table 3, Appendix A, several  conclusions were drawn with respect to the significance of the r e l a t i o n ships between risk measures. Noted was a lack of s t a t i s t i c a l s i g n i ficance (at both the .05 and .01 l e v e l s ) and low magnitudes of a l l rank correlation c o e f f i c i e n t s involving the accounting measures of risk (COV) based upon NOI, NI and NI + D and the beta c o e f f i c i e n t . This result indicates acceptance of the null hypothesis that there i s no s i g n i f i c a n t correlation betweeen these measures - in other words, s t a t i s t i c a l independence.  But the question may now be raised: Should  one expect any s i g n i f i c a n t r e l a t i o n s h i p to exist in this case?  In the  opinion of this author, since individual stocks and not portfolios are being analysed, no relationships ought to be expected.  The beta co-  e f f i c i e n t analysis eliminates the stochastic or unique element of i n dividual asset return which may have a great e f f e c t upon the risk of a p a r t i c u l a r asset. U t i l i z i n g the beta c o e f f i c i e n t concept involves assuming away a l l stochastic or residual elements of individual asset return through d i v e r s i f i c a t i o n .  This assumption i s i n v a l i d when one looks at  the return of an individual stock. With respect to the other measures, the i n d i v i d u a l i s t i c element is not assumed away and i t s presence may very well result i n higher rank correlation c o e f f i c i e n t s (as well as s t a t i s t i c a l s i g n i f i c a n c e ) being obtained when measures other than those involving the beta coe f f i c i e n t are considered. This hypothesis i s borne out in Table 3, Appendix A.  - 28 The two " t r a d i t i o n a l " measures of risk (standard deviation  and  the beta coefficient) when correlated together do show s t a t i s t i c a l signi ficance with a r e l a t i v e l y high rank c o e f f i c i e n t (.593). J u s t i f i c a t i o n of this observation may be derived from the fact that each measure i s based upon an underlying distribution of security returns.  Thus,  correlation i s to be expected. It i s also important in Table 3, Appendix A, to note the s t a t i s t i c a l significance of the correlation coefficients between the standard deviation of return and the coefficients of variation for each of the earnings stream variables.  It is disappointing  to find a moderate lack  of power in the c o e f f i c i e n t which describes the degree of  association  between the pairs of measures, i . e . correlation coefficients of only .425,  .454 and .474.  The highest c o e f f i c i e n t (.474  above) for "accoun-  ting" and " t r a d i t i o n a l " measures of risk was obtained when the standard deviation of return and the c o e f f i c i e n t of variation for NI + D were correlated.  This was expected for two reasons: a) NI + D is more of a  "cash flow" concept and perhaps a higher c o e f f i c i e n t r e f l e c t s i t s importance in estimating the risk associated with an individual and  security,  b) NI + D r e f l e c t s both "business" and " f i n a n c i a l " risk whereas  NOI r e f l e c t s only "business" r i s k . Beaver, Kettler and Scholes in t h e i r paper "Market and Accounti Determined Risks," The Accounting Review, Vol. XLV, No. 4, October 1970, pp. 654-82, show a rank correlation c o e f f i c i e n t of .45 between a market determined measure of risk and an earnings stream variable over the period 1957-65. Their market risk measure was the beta c o e f f i c i e n t but evidence does indicate the range of .42 to .47 for the rank coe f f i c i e n t i s reasonable.  - 29 One further observation may be made before concluding this section and this concerns the high degree of correlation indicated between the various accounting measures. A p r i o r i reasoning would expect this to be the case and this i s borne out with the rank correlation c o e f f i c i e n t s approximately .86 i n a l l cases. The results of this section may now be summarized: 1) no s i g n i f i c a n t relationships were indicated between the accounting measures and the beta c o e f f i c i e n t , with the correlation c o e f f i c i e n t s of r e l a t i v e l y low magnitudes (.192 to .218); 2) when the two " t r a d i t i o n a l " measures of security risk were correlated together, a s i g n i f i c a n t relationship was observed with a correlation c o e f f i c i e n t of .593; 3)  the correlation c o e f f i c i e n t s obtained when comparing the standard  deviation of return and the other accounting measures, although of only moderate power (.425 to .474) were s t a t i s t i c a l l y s i g n i f i c a n t ; 4) the "best" correlation c o e f f i c i e n t (.474) between an "accounting" and " t r a d i t i o n a l " measure of risk which was s t a t i s t i c a l l y s i g n i f i c a n t occurred when the standard deviation of return and the c o e f f i c i e n t of variation of net income plus depreciation were compared; and 5) as expected, when correlated among themselves, the accounting measures generally displayed high rank correlation c o e f f i c i e n t s (.764 to .867). More w i l l be said about these results i n the f i n a l chapter but now, discussion w i l l s h i f t to the results obtained by sectoral analyses of the various risk measures.  - 30 i i ) Sectoral Analyses As was mentioned before, to further substantiate the results of the correlation analysis, a sectoral analysis was undertaken. The range of values f o r each risk measure (beta,  COV^QJ  COV^J  S  COV^J  +  D  ,  and s.d.p) was subdivided into thirds and the number of firms (pairs) that changed sectors was noted in Table 3, Appendix A.  As expected, a  high number of "switches" indicated a r e l a t i v e l y low correlation coefficient. Upon analysis of the median and mean matrices i n Tables 4 and 5, Appendix A, additional support i s given to the v a l i d i t y or reasonableness of the rank correlation c o e f f i c i e n t s .  In the "median" matrix of  Table 5, i t i s generally observed that the greater the percentage of "common" elements or stocks above the median when comparing two measures of r i s k , the higher the correlation c o e f f i c i e n t .  Even including comparisons  involving the beta c o e f f i c i e n t and accounting measures, this i s the case although t h e o r e t i c a l l y , this comparison may be rejected f o r reasons previously stated. Thus, from the "median" a n a l y s i s , further support i s given to the v a l i d i t y of the rank correlation c o e f f i c i e n t s .  However, when one  scrutinizes the "mean" matrix of Table 4, Appendix A, somewhat c o n f l i c t i n g results appear.  To repeat, the "bracketed" percentage figures in each  c e l l represent the number of stocks common to both measures above the mean divided by the number of stocks common to one measure above the mean. Again, some support f o r the calculated correlation c o e f f i c i e n t s is indicated in that generally a greater percentage of common elements above the mean were associated with higher rank c o e f f i c i e n t s .  - 31 However, when one looks at the number of stocks above the mean of one risk measure over the number of stocks above the mean of the other, inconclusive results are obtained.  Referring to Table 4 i f one disregards  a l l comparisons involving the beta c o e f f i c i e n t ( f o r reasons previously explained), absolute deviations range from approximately -36 to +54 or a range o f 90 percentage points. This result i s i n d i c a t i v e of quite substantial f l u c t u a t i o n s . However, this may be due to the fact that extreme COV values are not included i n the computation of the mean NI figure (see Table 2, Appendix C). As a consequence, a fewer number of stocks may be above the mean than the analysis i n d i c a t e s , the high figures would be readjusted s u b s t a n t i a l l y downward and this would bring the NI figures more i n line with the NOI and NI + D figures. Summarizing this section, the following results are relevant: 1) when the range f o r each measure of risk was subdivided into t h i r d s , the greater the number of "switches" occurring outside of corresponding sectors, the lower the c o r r e l a t i o n c o e f f i c i e n t (this lent support to the values o f the c o e f f i c i e n t s obtained under section B i ) o f this chapter); 2) with respect to the "median" a n a l y s i s , further support was given to the previously computed values of the c o r r e l a t i o n c o e f f i c i e n t as i t was observed that the greater the percentage of "common" stocks above the median when comparing two risk measures, the higher the c o e f f i c i e n t ; 3)  inconclusive results were noted when the "mean" analysis was under-  taken and complete support f o r the values of the c o r r e l a t i o n c o e f f i c i e n t s was not indicated by the results.  - 32  -  This completes the discussion concerning relationships among the various risk measures. The two " t r a d i t i o n a l " measures of risk show s t a t i s t i c a l significance when correlated with each other (as expected), but when correlated with the various "accounting" measures of security r i s k , only one (the standard deviation of return) displays any s t a t i s t i c a l significance. When a sectoral analysis was undertaken, i n general, the values of the rank correlation c o e f f i c i e n t s were supported, inconclusive evidence being observed i n only one instance. However, one important point to be discussed l a t e r , concerns the "lack of power" of the correlation c o e f f i c i e n t s obtained when the "accounting" measures of risk and the standard deviation of return were considered. This observation shall be made more relevant i n the final chapter, Chapter V, when a l l previous results are summarized and integrated into a more meaningful whole. Having dealt with a comparison of the various risk measures, attention shall now focus upon the second purpose of this thesis:  to  determine any existing r e l a t i o n s h i p between the various measures of risk and overall return in the market. * * * * * *  CHAPTER IV RELATIONSHIPS AMONG RISK AND RETURN  A second purpose of the research undertaken in this thesis i s to test the strength of the relationship between the analysts perception of r i s k based upon accounting data and overall security return in the market. A s p e c i f i c test designed to show any e x i s t i n g r e l a t i o n ship between risk and overall market return was devised and w i l l be described in the next section.  Following that, the results in the  next section obtained in applying the t e s t shall be discussed.  A.  The Test To test the relationship outlined in the previous section be-  tween r i s k and overall market return, a graphical analysis was undertaken in which the risk/return tradeoff was described.  Figures 1  through 11, Appendix D present, in graphical form, the various measures of r i s k , beginning with the two " t r a d i t i o n a l " measures (Figures 1 and 2) plotted against average annual return (per cent) over the ten-year period, 1958-67. For each earnings stream variable, three measures of r i s k are plotted against return:  standard deviation, mean-absolute deviation and  the c o e f f i c i e n t of v a r i a t i o n . "Risk" i s measured upon the v e r t i c a l axis, - 33  -  - 34 "return" along the horizontal. From the theory of " e f f i c i e n t capital markets," one would expect higher returns associated with higher degrees of r i s k .  Whether this relationship exists or not i s discussed i n the  following section.  B.  Results When one considers the standard deviation and beta c o e f f i c i e n t  measures of risk plotted against average annual rates of return in Figures 1 and 2 respectively i n Appendix D, marked upward-sloping  trend  lines can readily be distinguished. The slope of the trend line i n v o l ving the beta c o e f f i c i e n t i s s l i g h t l y less steep than that involving the standard deviation/return tradeoff. This i s to be expected since the former measure should produce a lower return per unit of risk on account of the i n d i v i d u a l i s t i c or unique element of risk of the i n dividual security being d i v e r s i f i e d away. However, these are the " t r a d i t i o n a l " measures of risk - what about the "accounting" measures? How well do they perform i n a risk/return tradeoff? As can be seen from the graphs in Appendix D, the standard deviation and mean-absolute deviation of al 1 the accounting measures display no_ s i g n i f i c a n t trend when plotted against average annual return over the ten-year period, (see Figures 3, 4, 6, 7, 9 and 10.)  In addition, in each case, there  are generally consistent o u t l i e r s occurring at high extreme values which would tend to pull a trend l i n e up and lead to a somewhat more positive risk/return tradeoff than normal.  - 35 Nevertheless, when Figures 5, 8 and 11 of Appendix D are considered (COV for NOI, NI and NI + D r e s p e c t i v e l y ) , s l i g h t upward trends may be distinguished, e s p e c i a l l y with respect to the COV f o r NOI and NI + D (Figures 8 and 11). 1)  For two reasons this may be expected:  the c o r r e l a t i o n c o e f f i c i e n t s for these two measures, as previously  noted, were highly s i g n i f i c a n t i n the order of about .42 to .47 and 2)  the NOI and NI + D earnings stream variables are more "cash-flow"  concepts than i s the NI variable. Further, i t may be s i g n i f i c a n t that NOI r e f l e c t s only "business" risk and NI + D considers both "business" and " f i n a n c i a l " risk although this relationship i s unclear. when one compares  COV^QJ  and COV^j  +  In addition,  ^ (Figures 8 and 11) with Figure 1  of Appendix D involving the standard deviation of return, the slopes are not s i g n i f i c a n t l y d i f f e r e n t . This observation lends further support for s i g n i f i c a n t , but not that high, ranked c o r r e l a t i o n c o e f f i c i e n t s (.425 to .474). Comparing Figure 1 with the other accounting risk measures (standard deviation and mean-absolute deviation of each earnings stream variable), no real s i m i l a r i t i e s i n trend can be distinguished. Thus, generally speaking, the risk/return tradeoff or r e l a t i o n ship i s shown to e x h i b i t a moderate upward-sloping trend when one considers the COV measures of accounting risk plotted against overall market return. This was not the case when the standard deviation and mean-absolute deviation o f NOI, N I , and NI + D was examined, for i n these cases, magnitude d i f f e r e n t i a l s may greatly d i s t o r t any underlying trends. In other words, an increase i n risk i s accompanied by additional return, which i s what one would expect based upon a p r i o r i reasoning.  When the  - 36 -  " t r a d i t i o n a l " measures of risk were plotted as in Figures 1 and 2, Appendix D, much more s i g n i f i c a n t , positive sloping trend lines were distinguished.  7  This also supports what would be expected of the r i s k /  return tradeoff. This completes the discussion of the relationships existing between, the two " t r a d i t i o n a l " measures of security r i s k and the various accounting measures when compared to overall market return over the years 1958 to 1967.  In the next and f i n a l chapter, conclusions shall  be drawn based upon the results of this and the previous chapters  and  also implications and possible areas for future research s h a l l be outlined. * * * * * *  The mean value of the beta c o e f f i c i e n t i n c i d e n t a l l y was found to be about .9354 over the ten-year period. This i s consistent with other independent empirical evidence.  CHAPTER V CONCLUSIONS AND FURTHER RESEARCH IMPLICATIONS  It has been the purpose of this thesis to investigate d i f f e r e n t measures of risk associated with individual s e c u r i t i e s in the stock market. In p a r t i c u l a r , this thesis set about to do two things: a)  to test any correspondence between What security analysts perceive 1  as risk (based upon accounting information and s p e c i f i c a l l y , earnings stream v a r i a b i l i t y ) , and two " t r a d i t i o n a l " or economic measures of r i s k , the variance or standard deviation of return and the beta c o e f f i cient, and  b) to show any e x i s t i n g relationship between the various  "accounting" measures (as well as " t r a d i t i o n a l " measures) and overall market returns. As a proxy for risk based upon "accounting" i n f o r mation, the c o e f f i c i e n t s of variation of net operating income, net income and net income plus depreciation were u t i l i z e d .  A.  Conclusions and Implications Given the two-fold purpose of this t h e s i s , and the analyses  outlined in previous chapters, general conclusions may be drawn with respect to each "dual" purpose.  Concerning the relationship among v a r i -  ous risk measures, a c o r r e l a t i o n analysis was undertaken, the results of - 37  -  -  38  -  which are b r i e f l y summarized below: i)  there does indeed exist a s t a t i s t i c a l l y s i g n i f i c a n t corres-  pondence but moderate lack of power to explain the variation between certain measures of accounting risk (namely, coefficients of variation for the earnings stream variables) and one " t r a d i t i o n a l " measure of r i s k , the standard deviation of return; ii)  since the beta c o e f f i c i e n t i s more d i r e c t l y and aptly con-  cerned with p o r t f o l i o analysis, no s i g n i f i c a n t correspondence was expected nor found when the beta c o e f f i c i e n t and the "accounting" measures were compared; iii)  the low magnitudes o f the correlation c o e f f i c i e n t s obtained  in i i ) above were generally suspected to be due to the elimination of the i n d i v i d u a l i s t i c risk component of a security return; iv) when risk measures were correlated amongst themselves, i . e . " t r a d i t i o n a l " versus " t r a d i t i o n a l , " "accounting" versus "accounting," as expected, s i g n i f i c a n t relationships having higher magnitude c o e f f i cients were noted; and v) the "best" correlation c o e f f i c i e n t  (.474)  between an "accounting"  and " t r a d i t i o n a l " measure o f risk was observed to occur when the standard deviation o f return and c o e f f i c i e n t of variation of net income plus depreciation (NI + D) were compared. Further support f o r the values of these correlation coefficients was obtained through a sectoral analysis of each risk measure involved. These conclusions can be stated below: i)  by analysing the movement of stocks among various sectors and  - 39 the communality  (or lack of i t ) of elements between the various measures,  the results lent further support to the v a l i d i t y of the magnitude of the correlation c o e f f i c i e n t s ; and ii)  further support was forthcoming by way of a "median" and  "mean" analysis, although not e n t i r e l y conclusive support. With respect to existing relationships between various measures of risk and overall return i n the market, several relevant conclusions may also be noted, based upon a graphical analysis to test f o r any dominant or s i g n i f i c a n t relationship. These conclusions may also be b r i e f l y summarized: i)  both the "accounting" measures of risk (coefficients of variation  for each earnings stream variable) and the " t r a d i t i o n a l " measures d i s played upward or p o s i t i v e trend lines (the " t r a d i t i o n a l " measures to a more marked degree), when plotted against overall return i n the market; and ii)  no_ dominant trends were ascertainable when the other measures  of "accounting" r i s k , standard deviation and mean-absolute  deviation of  NOI, NI, and NI + D, were examined i n the context of a r i s k / r e t u r n tradeoff. Accordingly, given these results what can be implied with respect to the original purposes of this thesis as outlined i n Chapter I? It was noted i n the f i r s t chapter that, besides testing f o r s i g n i f i c a n t relationships between various risk measures and determining i f there exists any s i g n i f i c a n t r i s k / r e t u r n tradeoff f o r each measure of security r i s k , a further postulate of the thesis emphasized that the "traditional  -  40  -  measures of risk are merely reflections of the impact of a security analyst or p r a c t i t i o n e r perceptions  upon the actions of investors in  the stock market" (Chapter I, p. 1). Based upon the above correlation and sectoral analyses,  there  appears to be some degree of association between the "accounting" measures of risk and at l e a s t , one " t r a d i t i o n a l " measure, the standard deviation of return.  However, correlation analysis in no way, indicates direction  of causality.  In other words, what the l i t e r a t u r e may be measuring as  risk could just as e a s i l y as not be a r e f l e c t i o n of what the practitioners or security analysts view as r i s k . Other factors such as "street talk" and management interviews play perhaps an even more important role than the t r a d i t i o n a l measures in the formation of risk estimates by a security analyst.  The above point appears relevant, given the lack  of power of the low correlation c o e f f i c i e n t s observed when the "accounting" measures were compared to the standard deviation of return. To be sure, the informational process of the security analyst obviously does play a major role in the formation of risk estimates for a p a r t i c u l a r security.  An indication of the importance of financial  statement data has been outlined in this thesis but there are other variables in this informational process that defy quantification. As to whether the " t r a d i t i o n a l " measures r e f l e c t the actions of the participants in the market place, they may or may not based upon the correlation and sectoral analyses undertaken in this thesis.  On the  other hand, a f a i r l y good relationship evolved when the "accounting" and " t r a d i t i o n a l " risk measures were compared to overall return on the market. Therefore, the significance of this thesis l i e s in the fact  - 41 that risk measures based upon financial or accounting information may not be t o t a l l y i r r e l e v a n t in determining the future value of a security. Further research and more rigorous testing may be needed. The results in t h i s thesis may only "whet the appetite."  B.  Areas of Future Research Based upon analyses undertaken i n this t h e s i s , several areas  of future research may be enumerated. The f i r s t and somewhat most obvious i s to u t i l i z e the same methodology as outlined above but develop additional " t r a d i t i o n a l " measures of security risk - such as semi-variance, covariance and so on - along with further accounting variables such as Q  those u t i l i z e d by Beaver, K e t t l e r and Scholes.  Perhaps also extend  the time period and compare the results obtained from using d i f f e r e n t time period bases. A further area of proposed research may involve an analysis s i m i l a r to the above, only for data c l a s s i f i e d according to asset s i z e . In the opinion of this author, risks associated with s e c u r i t i e s such as IBM, or General E l e c t r i c or General Motors may not be s t r i c t l y comparable to those risks inherent in the stocks of much smaller companies.  This  would be quite an i n t e r e s t i n g project and may lead to very s i g n i f i c a n t results. In addition, the q u a n t i f i c a t i o n of such nebulous concepts as "street t a l k " and "in-depth management interviews" would go a long way o  Beaver, K e t t l e r , and Scholes, op. c i t . , pp. 659-63 and p. 666.  - 42  -  in incorporating these estimates into both the theory of security analysis and i t s logical extension into p o r t f o l i o theory. A related problem occurs i n that even i f they are "quantified" or "quantifiable," are these concepts comparable to other variables? As more and more new research i s carried out, no doubt procedures w i l l be developed f o r the accurate refinement of such terms.  A further area of proposed enquiry,  and perhaps the most readily achieved, concerns a methodological problem that arose during the c o l l e c t i o n of data f o r this thesis. I t would be most helpful to future researchers i n the area of security and p o r t f o l i o analysis to have at t h e i r disposal a magnetic tape or some other computer storage device of h i s t o r i c a l price and dividend data say per quarter and beginning i n the early f i f t i e s and updated constantly. The Financial Post has already put on tape annual selected financial statement data. Combine this tape with the price and dividend one already proposed and the result would be invaluable tools f o r anyone who desired to undertake future research i n this area. Obviously, there are other areas of proposed research but, to this author at least, the ones l i s t e d above are some of the more important. The f i e l d of security analysis and i t s extension into p o r t f o l i o theory is of quite recent origin and there e x i s t many areas where new, original research can be undertaken which may have the potential to y i e l d f r u i t f u l benefits to both the researcher and the whole body of associated knowledge.  BIBLIOGRAPHY Books Croxton, F. E. and Cowden, D. J . Applied General S t a t i s t i c s . Second Edition. Englewood C l i f f s , New Jersey: Prentice-Hall Inc., 1955. Latane, H. A. and T u t t l e , D. L. Security Analysis and P o r t f o l i o Management. New York: The Ronald Press Company, 1970. Markowitz, Harry M. P o r t f o l i o Selection: E f f i c i e n t D i v e r s i f i c a t i o n of Investments. New York: John Wiley and Sons Inc., 1959. Sharpe, William F. P o r t f o l i o Theory and Capital Markets. McGraw-Hill Inc., 1970.  New York:  Smith, Keith V. P o r t f o l i o Management. Theoretical and Empirical Studies of P o r t f o l i o Decision-Making. New York: Holt, Rinehart and Winston Inc., 1971.  Articles Beaver, W. H., Kettler, P., and Scholes, M. "Market and Accounting Determined Risks," The Accounting Review, Volume XLV, No. 4, October, 1970, pp. 654-82. Fama, Eugene F. " P o r t f o l i o Analysis in a Stable Paretian Market," Management Science, Volume I I , January, 1965, pp. 404-419. . "The Behavior of Stock-Market Prices," Journal of Business, Volume XXVIII, January, 1965, pp. 34-105. , and R o l l , Richard. "Some Properties of Symmetric Stable Distributions," Journal of the American S t a t i s t i c a l Association, Volume 63, September, 1968, pp. 817-36. Mandlebrot, Benoit. "The Variation of Speculative Prices," Journal of Business, Volume XXXVI, October, 1963, pp. 394-419. R o l l , Richard, "The E f f i c i e n t Market Model Applied to U. S. Treasury B i l l Rates." Unpublished PH.D. thesis, Graduate School of Business, University of Chicago, 1968. - 43 -  APPENDIX A  MARKET, RISK-FREE RETURNS AND CORRELATION MATRICES  - 44 -  APPENDIX A, TABLE 1 RISK-FREE RATES OF RETURN ( R ) , BY QUARTER, f  1958-1967* Year  1st Quarter  2nd Quarter  3rd Quarter  4th Quarter  (Percentages) 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967  .0090 .0081 .0128 .0083 .0077 .0098 .0094 .0093 .0115 .0117  .0045 .0108 .0081 .0081 .0077 .0090 .0092 .0094 .0127 .0100  .0040 .0125 .0079 .0065 .0135 .0081 .0091 .0099 .0125 .0108  .0059 .0131 .0055 .0064 .0123 .0090 .0092 .0103 .0129 .0123  Source: Bank of Canada S t a t i s t i c a l Summaries and Supplements, various issues from 1959. For method of c a l c u l a t i o n , see Chapter I I , Subsection B i ) .  - 45 -  APPENDIX A, TABLE 2 MARKET RATES OF RETURN ( R j , BY QUARTER 1958-1967*  Year  1st Quarter  2nd Quarter  3rd Quarter  4 th Quarter  (Percentages) 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967  .0669 .0410 -.0657 .1163 -.0163 .0385 .0661 .0437 .0063 .1272  Source:  .0665 .0350 .0086 .0821 -.1570 .0407 .0870 -.0399 -.0274 .0057  .1201 - -.0415 .0056 .0242 .0095 .0121 .0637 .0350 -.1157 .0344  .0439 .0410 .1156 .0657 .1159 .0480 .0132 .0152 .0504 -.0291  TSE Indices, 4th Edition, February 1, 1968, Toronto Stock Exchange, Toronto, Ontario. See also Figure 2 of this thesis f o r a graphical representation of the above rates.  For method of c a l c u l a t i o n , see footnote 1, Table 1, Appendix A. - 46 -  APPENDIX A, TABLE 3 RANK CORRELATION COEFFICIENTS AND TERTIARY SECTOR COMPARISONS BETA BETA  COV (NOI)  COV (NI)  COV (NI + D)  s.d.  r = .218  r = .192 s 82  r s = .210  r = .593*  s  85 COV (NOI)  r = .218 s  85 0  COV (NI)  rs  = .192  N  S  N  S  n  \  37  88  r s = .867*  r = .454* s 61  0SSSS  \  r s = .474*  s.d.  r = .425* r = .454* r = .474*  r = .593* s  53  26 s  74  31 $  72  72  31  r s = .866* r s = .867*  R  53 r s = .425*  r = .210 COV (NI + D) 88 s  s  r = .764* r s = .866* s 26 37  r s = .764*  82  c  R  \  s  61  74  0 X N  \  r = Spearman rank correlated c o e f f i c i e n t . g  * = s i g n i f i c a n t at .05 and .01 levels of confidence. Tertiary Comparison Method: For each measure above, data divided into thirds and each number below r i n matrix c e l l s represents pairs of firms that have changed sectors when comparing two measures. - 47 -  APPENDIX A, TABLE 4 MEAN ANALYSIS (PERCENTAGE FIGURES)  NUMERATOR BETA BETA  COV (NOI)  \  COV (NOI)  COV (NI)  COV (NI + D)  s .d.p  76.2 (45.7) r s = .218  96.7 (61.0) r = .192  62.7 (45.7) r = .210  76.2 (61.0) r = .593 s  126.6 (91.1) r = .764  82.2 (73.3) r s = .866  100.0 (60.0) r s = .425  103.5 (63.1) r = .192  78.9 \ 100.0^^ (71.9) r = .764 s  64.9 (68.4) r = .867  78.9 (54.3) r = .454  159.4 (72.9)  121.6 (89.1) r = .866  154.0 (105.4) r s = .867  100.0^^  121.6 (67.5) r = .474 s  100.0 (60.0) r = .425  126.6 (82.2) r =.454  82.2 (55.5) r = .474 s  100.0  \  p  131.1 (60.0) r s = .218  \  100.0  r  COV (NI)  s  COV (NI + D)  \  s  c  s  s.d.  R  131.1 (80.0) r = .593 s  s  s  s  p  s  s  N  JOO.O  \  Number of Stocks above Mean of one Measure .100 Number of Stocks above Mean of Another Measure Number of Stocks Common to both Measures above Mean Number o f Stocks Common o f one Measure above Mean Spearman rank correlation c o e f f i c i e n t ( r ) - 48 -  APPENDIX A, TABLE 5 MEDIAN ANALYSIS (PERCENTAGE FIGURES) COV (NOI)  BETA BETA  NUMERATOR COV (NI)  56.1 r = .218  ^^lOO.O  s  COV (NI + D)  s.d.  56.1 r s = .192  57.8 r = .210 s  70.1 r = .593  o  c  R  s  COV (NOI)  56.1 r s = .218 ^100.0  78.9 r = .764  84.2 r = .866 s  57.8 r = .425 s  COV (NI)  56.1 r = .192  78.9 r = .764  100.0  84.2 r = .867  63.1 r = .454  COV (NI + D)  57.8 r„ = .210 s  84.2 r s = .866  84.2 r = .867  100.0  59.6 r = .474  s.d.  70.1 r s = .593  57.8 r s = .425  63.1 r = .454 s  R  s  s  s  ^  s  s  s  s  59.6 r = .474 s  Number of stocks common to both Measures above Median Number of stocks common to one Measure above Median  .100  Spearman rank correlation c o e f f i c i e n t r  - 49 -  p  X  |oo.o ^ x  APPENDIX B  AVERAGE ANNUAL RETURN AND TRADITIONAL MEASURES OF RISK  - 50  APPENDIX B, TABLE 1 RETURN AND TRADITIONAL RISK MEASURES SELECTED STOCKS, 1958-67  Stock 001 018 021 030 033 037 051 078 087 102 104 105 108 111 117 135 141 144 150 156 159 165 171  Average Annual Return {%)  8.36 11.32 10.68 1.44 -0.80 32.40 30.72 16.48 6.56 18.92 13.24 5.52 13.80 10.36 8.72 10.20 7.76 19.80 13.96 11.84 13.56 9.48 9.96  Beta Coefficient  Standard Deviation  Magnitude  Rank  Magnitude  .676398 .646171 1.365533 .310174 .411987 1.163869 .915839 .762435 .601491 1.003545 .475746 .807566 1.256283 .520163 .669440 .728880 1.285816 1.128401 1.270107 .796914 .679163 1.013409 .905270  24 21 107 3 5 92 55 34 17 66 71 39 98 12 22 29 103 86 101 38 25 71 52  .0775 .1082 .1088 .0355 .0756 .1436 .1318 .1240 .0700 .1223 .0560 .0860 .1364 .0815 .0727 .0950 .1157 .1637 .1311 .0960 .0712 .0941 .0917  Rank 15 58 59 2 14 92 86 81 6 78 4 25 89 18 11 41 72 104 85 44 8 38 33  Continued . . . - 51 -  - 52 Appendix B, Table 1 - Continued  Stock 177 195 204 207 213 219 231 243 252 279 282 285 288 294 300 315 318 319 336 339 348 354 357 360 361 363 366 369  Average Annual Return  Beta Coefficient  Standard Deviation  (%)  Magnitude  Rank  Magni tude  4.28 17.76 5.92 13.40 18.44 5.04 4.20 7.88 13.44 4.20 47.92 18.52 13.28 12.96 8.08 13.64 6.80 12.88 16.84 3.24 21.68 17.18 2.76 8.52 -0.36 9.60 7.04 18.64  .506481 1.101863 1.142513 .810219 1.201669 .864392 .197390 1.108533 .701946 .896671 .365081 .824488 .586956 .767248 .563894 .291657 1.036773 .739119 1.164382 1.075374 1.522138 1.555255 .509156 .840186 .974302 1.008755 1.178676 1.030428  9 79 89 41 96 45 1 80 27 49 4 42 15 35 14 2 75 32 93 78 no 111 10 43 60 69 94 72  .0561 .1443 .1094 .1287 .2009 .1230 .0316 .1482 .0926 .0932 .2375 .0820 .0983 .0875 .0710 .0914 .0834 .1347 .0820 .1158 .2340 .1121 .0781 .1031 .1413 .1033 .1021 .1573  Rank 5 95 60 84 111 79 1 96 34 35 114 19 47 27 7 32 21 88 20 73 113 67 16 52 91 53 51 98  Continued . . .  - 53 Appendix B, Table 1 - Continued  Stock  Average Annual Return (%)  372 375 381 389 393 402 407 411 413 414 417 423 426 447 450 457 463 464 466 468 471 479 481 485 489 492 495  13.80 9.16 7.00 21.44 16.00 16.64 4.60 20.24 2.52 8.60 9.24 12.52 16.76 35.36 -7.64 12.88 9.68 14.80 15.80 9.92 6.76 21.80 8.08 14.32 17.80 7.16 19.36  Beta Coefficient  Standard Deviation  Magnitude  . Rank  Magnitude  Rank  .998227 .891119 .760502 1.121094 .945385 1.109638 .900370 1.073937 .554052 1.151289 1.136112 1.149905 .869241 1.240491 1.337089 .986881 .771754 1.004304 1.030503 .732043 .728483 1.007211 1.265937 .499373 1.126773 1.059292 .803549  64 48 33 83 56 81 50 77 13 91 87 90 46 97 105 63 36 67 73 31 28 68 99 8 85 76 40  .1010 .1147 .0799 .1058 .1189 .1213 .0845 .1243 .0965 .1637 .1062 .1100 .1106 .2188 .1545 .1615 .0745 .1439 .1979 .0721 .0725 .1954 .1286 .0910 .0945 .0993 .0906  50 71 17 56 76 77 22 82 47 103 57 61 64 112 97 101 12 93 110 9 10 109 83 12 31 40 30 Continued . . .  - 54 Appendix B, Table 1 - Continued  Beta Coefficient  Standard Deviation  Stock  Average Annual Return (%)  Magnitude  Rank  Magnitude  Rank  496 510 513 519 522 525 546 573 579 603 612 628 633 647 657 663 676 678 687 691 702 741 753 756 777 786 789 798 804  16.08 13.72 8.68 9.52 19.16 12.32 7.60 11.56 18.48 15.84 6.16 12.16 3.16 16.12 9.24 14.40 4.44 16.04 12.84 3.84 7.82 21.76 6.92 16.04 14.40 9.12 17.72 20.64 1.84  .699342 1.123003 .954575 .882598 .962815 1.435808 1.114440 .842380 1.977755 1.267186 .628245 .721727 .518170 .908779 .984296 .625862 .952071 .790374 .609331 1.035398 1.002339 1.462731 1.180282 1.655674 1.548835 .443465 .670069 1.012344 .906806  27 84 58 47 59 108 82 44 114 100 20 29 11 54 61 19 57 37 18 74 65 109 95 113 110 6 23 70 53  .0746 .1231 .1117 .1672 .1057 .1938 .1121 .1113 .1624 .1101 .0938 .1103 .0942 .0855 .1125 .0888 .1442 .1379 .0953 .0854 .0956 .1703 .1575 .1674 .1586 .0495 .0933 .1008 .0963  13 80 66 105 55 108 68 65 102 62 37 63 39 24 69 28 94 90 42 23 43 107 99 106 100 3 36 49 45  Continued . . .  - 55 Appendix B, Table 1 - Continued  Stock 813 831 855 858 909 940 949  Average Annual Return  Beta Coefficient  Standard Deviation  (%)  Magnitude  Rank  Magnitude  10.04 9.56 5.04 12.60 10.00 12.92 18.04  1.139135 .598421 1.354916 .986021 .903329 1.285555 1.283032  88 6 106 62 51 103 102  .0863 .0897 .1339 .1140 .1056 .1182 .1175  Rank 26 29 87 70 54 75 74  For computation of measures and return, see Chapter I I , Subsection B i ) .  APPENDIX C  ACCOUNTING MEASURES OF RISK  - 56 -  APPENDIX C, TABLE 1 ACCOUNTING RISK MEASURES BASED ON NET OPERATING INCOME SELECTED STOCKS, 1958-67 Standard Devi ati on (OOO's)  Coefficient of Variation  Stock  Magni tude  Rank  001 018 021 030 033 037 051 078 087 102 104 105 108 111 117 135 141 144 150 156 159 165 171 177  4,601 2,563 12,516 48,580 2,337 3,976 2,045 814 72,996 277 153 16,982 5,286 1,038 14,790 3,900 2,302 323 3,567 328 3,117 3,406 4,282 1,278  78 59 96 112 56 70 52 25 114 9 6 103 82 32 100 68 55 12 65 13 62 64 73 41  Magnitude .11 .89 .27 .28 .15 .66 .34 .15 .29 .16 .14 .21 .34 .26 .35 .18 .11 .26 .39 .09 .20 .19 .12 .44  Mean-Absolute Deviation (OOO's)  Rank  Magnitude  Rank  6 114 58 62 14 108 70 15 67 16 13 35 71 52 75 21 5 56 85 3 33 25 10 90  3,840 2,380 10,900 43,400 2,070 3,740 1,790 656 61,800 228 120 15,300 4,750 832 12,600 3,230 1,790 272 3,280 224 2,520 2,950 3,670 1,180  77 61 97 113 57 75 52 24 114 9 6 104 84 31 100 68 53 13 69 8 62 65 74 45  Continued . . . - 57 -  - 58 Appendix C, Table 1 - Continued Coefficient of Variation  Standard Devi ati on (000's) Stock  Magnitude  Rank  195 204 207 213 219 231 243 252 279 282 285 288 294 300 315 318 319 336 339 348 354 357 360 361 363 366 369  1,368 4,954 2,578 1,971 4,797 1,154 3,799 100 4,097 448 9,328 1,346 977 91 690 7,558 355 15,514 4,993 234 14,196 1,228 1,141 3,708 4,354 14,138 6,293  44 80 60 51 79 37 67 3 71 16 92 43 30 2 23 89 14 101 81 7 99 39 36 66 75 98 85  Magnitude .59 .19 •17 .50 .35 .22 .56 .14 .11 .88 .48 .50 .32 .11 .36 .23 .18 .20 .72 .19 .28 .22 .46 .36 .19 .27 .46  Mean-Absolute Deviation (000's)  Rank  Magnitude  Rank  104 26 20 96 76 40 103 12 8 113 94 97 68 4 83 45 23 30 109 27 63 42 93 79 28 59 92  1,060 4,260 2,090 1,830 3,800 980 3,120 80 3,030 392 8,000 1,030 676 80 632 6,790 290 12,900 4,610 192 13,000 940 944 2,750 3,980 12,000 4,660  42 80 59 54 76 38 67 3 66 16 92 41 26 2 23 89 15 101 81 7 102 35 36 63 79 98 82 Continued . . .  - 59 Appendix C, Table 1 - Continued Coefficient of Variation  Standard Deviation (OOO's) Stock  Magnitude  Rank  372 375 381 389 393 402 407 411 413 414 417 423 426 447 450 457 463 464 466 468 471 479 481 485 489 492 495  652 8,533 564 4,427 1,498 16,314 2,099 272 416 784 2,346 3,241 952 1,008 6,835 3,903 5,430 10,237 7,275 20,855 1,466 1,040 1,246 110 49,529 21,870 18,643  21 90 19 77 47 102 53 8 15 24 57 63 29 31 86 69 83 94 87 107 45 33 40 4 113 110 106  Magnitude .18 .28 .20 .17 .36 .24 .18 .22 .41 .50 .26 .25 .20 .45 .36 .48 .25 .43 .76 .13 .05 .81 .40 .21 .27 .11 .63  Mean-Absolute Devi ati on (OOO's)  Rank  Magni tude  Rank  22 66 34 17 84 48 24 41 88 98 57 50 31 91 80 95 51 89 111 11 1 112 86 39 61 9 107  584 7,610 500 3,570 966 12,100 1,510 232 282 658 1,950 2,780 812 910 5,460 3,660 4,740 9,220 6,250 15,900 1,280 848 1,030 90 40,300 17,800 14,100  21 91 19 72 37 99 50 10 14 25 56 64 30 34 86 73 83 94 87 105 47 32 40 4 112 108 103 Continued . . .  - 60 -  Appendix C, Table 1 - Continued Coefficient of Variation  Standard Deviation (000's)  Mean-Absolute Deviati on (000's)  Stock  Magnitude  Rank  Magnitude  Rank  Magnitude  Rank  496 510 513 519 522 525 546 573 579 603 612 628 633 647 657 663 676 678 687 691 702 741 753 756 777 786 789 798  8,763 863 1,051 293 4,372 1,108 17,490 1,511 22,664 4,223 1,315 151 508 20,890 1,479 1,696 9,939 521 64 5,906 2,403 892 2,713 1,205 638 855 4,352 1,577  91 27 34 10 76 35 104 48 111 72 42 5 17 108 46 51 93 18 1 84 58 28 61 38 20 26 74 49  .17 .21 .26 .27 .33 .51 .35 .20 .34 .22 .73 .22 .55 .55 .35 .36 .59 .11 .08 .28 .34 .28 .36 .23 .50 .19 .26 .17  18 36 53 60 69 100 77 32 72 43 no 44 102 101 78 81 105 7 2 64 73 65 82 46 99 29 54 19  7,540 790 908 236 3,480 1,000 16,700 1,370 20,700 3,560 1,070 114 430 19,100 1,220 1,630 8,400 420 56 4,980 2,070 736 2,310 1,100 540 680 3,870 1,390  90 29 33 11 70 39 106 48 111 71 43 5 18 109 46 51 93 17 1 85 58 28 60 44 20 27 78 49 Continued  - 61 Appendix C, Table 1 - Continued Mean-Absolute Devi ati on (OOO's)  Coefficient of Vari ati on  Standard Deviation (OOO's) Stock  Magnitude  Rank  804 813 831 855 858 909 940 949  687 21,599 314 18,525 7,399 13,010 11,491 2,266  22 109 11 105 88 97 95 54  Magnitude .24 .26 .21 .60 .34 .21 .40 .23  Rank  Magnitude  Rank  49 55 37 106 74 38 87 47  610 19,100 270 16,900 6,260 10,900 9,690 1,890  22 110 12 107 88 96 95 55  For computation of measures, see-Chapter I I , Subsection B i i ) .  APPENDIX C, TABLE 2 ACCOUNTING RISK MEASURES BASED ON NET INCOME SELECTED STOCKS, 1958-67 Standard Deviation (000's)  Coefficient of Variation  Stock  Magnitude  Rank  Magnitude  Rank  001 018 021 030 033 037 051 078 087 102 104 105 108 111 117 135 141 144 150 156 159 165 171 177  4,953 784 8,458 21,245 1,379 1,583 1,789 471 26,742 90 163 6,288 3,318 692 4,703 1,694 2,645 171 1,969 155 1,771 2,116 1,974 700  94 43 101 111 56 59 64 27 113 3 10 97 76 36 92 61 73 11 68 9 63 70 69 38  .30 .42 .32 .45 .26 .70 .53 .21 .38 .14 .31 .19 .50 .75 .46 .20 .32 .35 .57 .11 .29 .24 .15 .60  42 61 46 62 32 92 78 18 57 4 45 9 73 93 66 11 47 52 80 3 41 25 5 83  Mean-Absolute Deviation (000's) Magnitude  Rank  4,120 703 7,480 18,700 1,230 1,450 1,520 380 20,600 76 113 5,200 3,110 578 3,590 1 ,530 2,140 152 1,620 122 1,530 1,770 1,450 665  95 47 101 112 58 60 63 26 113 3 7 97 84 38 90 64 75 11 67 9 65 72 61 45  Continued . . . - 62 -  - 63 Appendix C, Table 2 - Continued Coefficient of Vari ati on  Standard Deviation (OOO's)  Mean-Absolute Devi ati on (OOO's)  Stock  Magnitude  Rank  Magnitude  Rank  Magnitude  Rank  195 204 207 213 219 231 243 252 279 282 285 288 294 300 315 318 319 336 339 348 354 357 360 361 363 366 369 372  846 1,865 902 996 3,372 421 2,453 62 4,533 269 3,913 815 656 104 534 3,420 268 8,733 3,434 140 12,112 490 663 4,072 1,595 9,509 4,313 297  48 65 49 52 77 24 72 2 91 18 86 46 33 7 29 79 17 102 80 8 106 28 34 87 60 104 88 19  .63 .25 .09 1.05 .60 .23 .99 .21 .24 1.75 .47 .75 .36 .27 .50 .28 .35 .25 .99 .27 .45 .21 .56 2.74 .18 .47 1.41 .22  86 28 2 101 84 23 99 16 27 107 68 94 56 37 75 39 53 29 100 34 63 19 79 112 8 69 106 20  706 1,650 764 952 2,820 382 1,940 43 3,730 217 3,290 569 454 75 492 3,080 214 7,790 3,000 119 11,300 352 560 3,030 1,490 7,740 3,220 260  48 70 50 55 76 27 73 2 91 17 87 36 29 2 31 83 16 103 79 9 108 24 35 80 62 102 85 18 Continued . . .  - 64 -  Appendix C, Table 2 - Continued Standard Deviation (000's)  Stock  Magnitude  Mean-Absolute Deviation  Coefficient of Variation  (000's)  Rank  Magnitude  Rank  Magnitude  Rank  375  4,409  89  .35  54  4,010  94  381  307  20  .27  38  267  20  389  12,518  108  .50  74  10,900  107  393  714  40  .45  65  475  30  402  7,050  100  .39  58  5,500  99  407  2,893  74  .69  90  1,670  71  411  173  12  .46  67  145  11  413  209  13  .52  77  180  14  414  696  37  5.95  114  592  40  417  1,424  57  .41  60  1,170  57  423  3,681  83  .64  87  3,030  81  426  444  25  .27  35  396  28  447  684  35  .60  85  610  42  450  4,863  93  3.44  113  3,970  93  457  3,491  81  1.27  104  3,260  86  463  3,401  78  .26  33  2,840  77  464  6,819  98  .65  88  5,930  100  466  3,259  75  1.96  108  3,030  82  468  17,114  110  .22  21  15,500  no  471  952  51  .08  1  850  52  479  1,172  54  2.61  920  54  481  837  47  485  47  1  489  33,146  492  no  .89  97  607  41  .23  24  33  1  114  .30  44  27,600  114  11,755  105  .15  6  9,560  105  495  6,996  99  .67  89  507  33  496  3,876  85  .20  12  3,300  88  510  234  14  .17  7  197  15  513  337  21  .25  30  284  21  ;  Continued  - 65 -  Appendix C, Table 2 - Continued Coefficient of Variation  Standard Deviation (OOO's) Stock  Magnitude  Rank  Magnitude  519  256  15  1.23  522  1,887  66  525  808  546  Mean-Absolute Deviation (OOO's) Magnitude  Rank  102  173  13  .35  51  1,620  68  45  1.23  103  732  49  1,763  62  .19  10  1,550  66  573  783  42  .27  36  631  43  579  12,325  107  .49  72  10,300  106  603  1,930  67  .22  22  1,630  69  612  785  44  .95  98  637  44  628  98  4  .82  95  86  45  633  389  23  1.38  105  322  23  647  16,911  109  .59  82  15,200  109  657  925  50  .58  81  840  51  663  632  32  .25  31  576  37  676  5,339  95  2.70  111  4,560  96  678  701  39  .34  50  682  46  687  104  6  .36  55  90  6  691  4,452  90  .41  59  3,860  92  702  630  31  .24  26  524  34  741  734  41  .45  64  579  39  753  1,475  58  .69  91  1,240  59  756  547  30  .29  40  504  32  777  268  16  .48  71  240  18  786  354  22  .20  13  303  22  789  2,219  71  .32  48  1,990  74  798  1,016  53  .21  17  900  53  804  456  26  .52  96  361  25  813  21,308  112  .51  76  18,000  Rank  in  Continued . . .  - 66 Appendix C, Table 2 - Continued Standard Deviation (000's) Stock 831 855 858 909 940 949  Magnitude 104 9,020 3,510 6,185 3,794 1,200  Coefficient of Variation Rank  Magnitude  Rank  5 103 82 96 84 55  .20 1.98 .48 .20 .33 .30  14 109 70 15 49 43  For computation of measures, see Chapter I I , SubsectioniB i i ) .  Mean-Absolute Deviation (000's) Magnitude 91 7,930 2,930 5,360 3,450 1,060  Rank 7 104 78 98 89 56  APPENDIX C, TABLE 3 ACCOUNTING RISK MEASURES BASED ON NET INCOME PLUS DEPRECIATION , SELECTED STOCKS, 1958-67 1  Standard Deviation (OOO's)  Coefficient of Variation  Mean-Absolute Deviation (OOO's)  Stock  Magnitude  Rank  Magnitude  Rank  Magnitude  Rank  001 018 021 030 033 037 051 078 087 102 104 105 108 111 117 135 141 144 150 156 159 165 171  5,413 1,033 10,183 31,994 1,391 2,243 1,845 525 52,141 173 196 10,445 5,172 682 10,787 2,862 2,310 227 2,490 167 2,373 3,156 2,984  85 43 97 112 51 59 56 25 114 8 9 98 84 29 99 69 61 11 66 7 63 73 72  .20 .29 .26 .30 .14 .62 .43 .18 .31 .19 .26 .14 .41 .34 .42 .21 .17 .26 .40 .07 .23 .21 .13  22 48 42 57 7 101 89 18 58 19 44 8 80 65 84 25 13 45 79 2 37 26 5  4,660 951 9,030 28,500 1,230 2,120 1,590 410 42,700 136 141 9,270 4,910 582 8,970 2,510 1,870 208 2,120 136 2,040 2,650 2,390  85 46 100 112 52 64 57 24 114 7 9 101 87 31 99 71 58 13 65 8 63 73 70  ?  Conti nued  - 68 Appendix C, Table 3 - Continued Coefficient of Variation  Standard Devi ati on (000's)  Mean-Absolute Devi ati on (000's)  Stock  Magnitude  Rank  Magnitude  Rank  Magnitude  Rank  177 195 204 207 213 219 231 243 252 279 282 285 288 294 300 315 318 319 336 339 348 354 357 360 361 363 366  869 1,447 2,888 1,859 1,339 4,769 739 2,681 69 6,388 286 5,737 1,104 726 111 675 5,071 360 13,036 3,590 265 15,836 439 560 4,061 2,567 13,469  36 53 70 57 50 81 33 68 2 89 15 87 47 32 5 28 83 16 102 75 14 . 106 20 26 78 61 103  .42 .58 .17 .15 .57 .35 .23 .54 .19 .26 .89 .44 .56 .37 .17 .48 .23 .23 .29 .65 .33 .41 .11 .29 .51 .19 .35  85 100 14 9 99 70 34 95 20 46 112 90 98 75 15 92 35 38 49 103 63 81 3 56 94 21 71  845 1,180 2,580 1,570 1,200 4,100 630 2,130 47 5,320 241 4,880 809 521 90 628 4,640 312 11,600 3,150 209 14,700 338 476 3,000 2,350 10,700  41 50 72 56 51 81 34 66 2 89 15 86 38 27 4 33 84 17 104 77 14 106 18 26 75 69 103 Continued . . .  - 69 Appendix C, Table 3 - Continued Standard Deviation (OOO's)  Coefficient of Variation  Mean-Absolute Devi ati on (OOO's)  Stock  Magnitude  Rank  Magnitude  Rank  Magnitude  Rank  369 372 375 381 389 393 402 407 411 413 414 417 423 426 447 450 457 463 464 466 468 471 479 481 485 489 492  4,050 440 6,919 397 10,891 993 12,032 2,966 225 242 699 2,335 4,265 482 801 5,527 4,129 3,769 9,484 5,803 19,464 942 1,056 1,085 47 37,502 19,290  77 21 90 18 100 41 101 71 10 12 31 62 80 23 34 86 79 76 96 88 109 39 44 45 1 113 108  .42 .21 .32 .22 .35 .34 .24 .33 .24 .34 .77 .34 .45 .18 .54 .41 .74 .22 .42 .81 .16 .06 .99 .73 .15 .28 .13  86 27 62 31 72 66 40 64 39 67 109 68 91 16 96 82 107 32 87 110 11 1 113 105 10 47 6  3,270 392 6,360 357 8,950 579 8,910 2,140 201 190 588 1,940 3,800 426 698 4,190 3,890 3,110 8,460 5,190 17,600 860 824 888 30 31,400 16,900  78 22 93 19 98 30 97 67 12 11 32 60 79 25 36 83 80 76 96 88 109 42 39 43 1 113 108 Continued . . .  - 70 Appendix C, Table 3 - Continued Standard Devi ati on  Coefficient o f Variation  (000's)  Mean-Absolute Deviation  (000's)  Stock  Magnitude  Rank  Magnitude  Rank  Magnitude  Rank  495 496 510 513 519 522 525 546 573 579 603 612 628 633 647 657 663 676 678 687 691 702 741 753 756 777 786  14,259 4,852 455 629 243 2,300 973 8,270 1,093 17,294 2,418 803 138 361 19,589 1,148 1,210 8,649 1,006 101 7,141 1,465 910 2,168 889 421 687  105 82 22 27 13 60 40 94 46 107 64 35 6 17 no 48 49 95 42 3 93 54 38 58 37 19 30  .74 .16 .20 .26 .35 .29 .65 .32 .22 .37 .21 .65 .22 .82 .54 .34 .31 .73 .29 .18 .41 .31 .39 .42 .29 .49 .22  108 12 23 43 73 50 102 61 29 74 28 104 33 111 97 69 59 106 51 17 83 60 78 88 52 93 30  10,600 4,170 407 550 171 1,960 892 7,830 921 15,800 2,030 657 116 290 17,700 1,020 1,170 7,320 966 84 6,350 1,250 767 1,870 834 370 573  102 82 23 28 10 61 44 95 45 107 62 35 6 16 110 48 49 94 47 3 92 53 37 59 40 20 29  Continued . . .  - 71 Appendix C, Table 3 - Continued Coefficient of Vari ati on  Standard Deviation (OOO's)  Mean-Absolute Deviation (OOO's)  Stock  Magnitude  Rank  Magni tude  Rank  Magni tude  Rank  789 798 804 813 831 855 858 909 940 949  2,467 1,442 521 24,818 108 13,518 3,552 7,109 7,019 1,631  65 52 24 111 4 104 74 92 91 55  .29 .23 .25 .38 .12 1.01 .29 .20 .38 .29  53 36 41 76 4 114 54 24 77 55  2,210 1,280 381 21,700 99 12,000 2,970 6,090 6,110 1,430  68 54 21 111 5 105 74 90 91 55  For computation of measures, see Chapter I I , Subsection B i i ) .  APPENDIX D  GRAPHICAL ANALYSES OF RISK/RETURN RELATIONSHIPS  - 72 -  1 11  ]  1!  1  1  _1_H  1 1 ! ! 1  _] j I I  1 1i . 1 !  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Return , 1 i 1 1! 1i !! • 1 i j I | ! 1 I 1 1 !1 | 1i 1  AW  -Mean^ ^bs^Ttite  f'EA™S£)  10  Mm  mm  -V-S  REFURfv  F3R-  -SAM3-L-E  T  +358-67-  5*  x^ ±x  1* S_0L(rice  Appendi x  Tab-le_i3  1  •i1 I  1  I  I  1 ffi  t nt -i D  |  r I,QEF  |  atic )r —(-N- 4• m !  —y cwp. f.QQ  f I1 ,Pp w -X 0 J GU T \f ENr1 Ac u f Vi l l -TI- r \N1  11 R H ,N P Df3_sA  /  •fl  >  i  /  o  1  i1 1  ?  u  ri  1  67/  .-E l  i  i i1 I i|  X  X  I  A  I t 4  <  r r\  i»  I  1  1  <  i  >i  / /  r  1 .  i  a ni  XV  y >  /  t  /  Y  \  1  ?  >  |  i  s  t  ><  >  .  *r  /  >  >  i;  H  f  >I  /  7. t  #  A  "3\  /  >  k.  A  s  >  r s >  X  fx  >  kA  ><  <  t  \ #  <•  7f  /  :  4 V /V  •  1  r 4  I  >  5\  <  l i1  / >  <•  5  (v.  X  f K  C  <  >  /  )  1  i  ji iI  I  1  1 <>  i  £< ?  >  •  i -- - ...  -  5c ur -i— -r-  -- D.).cjr c i  ).1 4 i —, a  roj  i '«  1 <  r  >  >  ii !  Kean_  n' • t1 D o t 11 v.n ! Ir i 1i I t 1 1  i  I  -  APPENDIX E  LIST OF FIRMS IN SAMPLE  - 84 -  APPENDIX E, TABLE 1 LIST OF FIRMS CONTAINED IN SAMPLE BY CODE, 1958-67  1 18 21 30 33 37 51 54  Abi t i bi Paper Algoma Central Railway Algoma Steel Corp. Alcan Aluminium Anglo-Canadian P. & P. Anthes Imperial A t l a n t i c Sugar Auto E l e c t r i c  78 87 102 104 105 108 111 117  Beaver Lumber Bell Canada Bright T. G. B. A. Bank Note B. A. Oil B. C. Forest Products B. C. Packers B. C. Telephone  135 141 144 150 156 159 165 171 177 195 204 207 213 219 231 243 252 279 282 285 288 294 300  Calgary Power Can. Cement Can C. & Cut Stone Canron Can. Malting Can. Packers Can. Steamship Lines Cdn. Breweries Cdn. Canners Cdn. Hydrocarbons Cdn. Industries Cdn. Int. Power Cdn. Marconi Cdn. Petrofina Cdn. U t i l i t i e s Cdn. Westinghouse Chateau-Gai Wines Consolidated-Bathurst Consolidated T e x t i l e Consumers' Gas Consumers Glass H. Corby Cosmos Imperial  315 318 319  Crown Cork & Seal Crown Zellerbach Crows Nest Industries  336 Distillers-Seagram 339 Dom. Bridge 348 Electrohome 354 Dom. Foundaries & Steel 357 Dom Glass 360 Domco Industries 361 Dom. Steel 363 Dom. Stores 366 Domtar 369 Dom. Textile 372 Donohue Bros. 375 Du Pont of Canada 381  Eddy Match  389 393 402 407  Falconbridge Nickel Federal Grain Ford Canada Fraser Companies  411 413 414 417 423 426  General Bakeries General Products General Steel Wares Goodyear Tire Great Lakes Paper Great Lakes Power  447 Harding Carpet 450 Hawker Siddeley 457 Home O i l 463 Hudson Bay Mining 464 H. B. Oil & Gas 466 Husky Oil  - 85 -  - 86 Appendix E, Table 1 - Continued 468 471 479 481 485 489 492 495 496  Imperial Oil Imperial Tobacco Inglis Inland Natural Gas Interior Breweries International Nickel International Paper International U t i l i t i e s Interprov. Pipelines  510 Jockey Club 513 Kelly, Douglas 519 Kelvinator 522 Labatt, John 525 Lafarge cement 546 Loblaw Cos. 573 579 603 612  Maple Leaf Mills Massey-Ferguson Molson Breweries MLW Worthington  628 Nabors D r i l l i n g 647 Noranda 657 Ocean Cement 663 Ogilvie Flour 676 678 687 691  P a c i f i c Petroleum Pembina Pipe Photo Engravers Price Co.  702 Quebec Telephone 741  Roll and Paper  753 756 777 786 789 798 804 813  St. Lawrence Cement Salada Foods Shop & Save Silverwood Dairies Simpsons Southam Press Standard Paving Steel Co. of Canada  831 Tamblyn 855 Trans-Canada Pipelines 858 Trans-Mt. O i l Pipe Line 909 Walker-G. & W. 904 Weston, Geo. 949 Woodward Stores  

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