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A re-examination of stock-market risk 1972

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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 in p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library 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 f i n a n c i a l 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 two- f o l d : 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 " r i s k 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. - i i - 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 - f i c a n t risk/return relationship than did others. Thus, i t appears that there does ex 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 for 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 in helping to develop the necessary computer programmes applicable in this research, i s not to be under- estimated. Further, Miss Catherine Giles worked patiently and consis tently over one summer in 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 cert 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 diligence, encouragement and optimism provided me with much of the moral support necessary to complete this thesis, especially 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. Vancouver, B. C. D.F.G. TABLE OF CONTENTS Page ABSTRACT i i ACKNOWLEDGEMENTS i v LIST OF FIGURES v i i CHAPTER I. INTRODUCTION AND BACKGROUND 1 Focus of Research 1 Background 2 Format 6 II. DATA AND METHODOLOGY 8 Data 8 Accounting Data 8 Stock Price Data 9 Methodology 12 "Trad i t i o n a l " 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 Page III. RELATIONSHIPS AMONG RISK MEASURES . . 24 The Tests 24 Correlation Analyses 24 Sectoral Analyses 25 The Results 27 Correlation Analyses 27 Sectoral Analyses 30 IV 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 of Firms Contained in Sample 84 LIST OF FIGURES FIGURE Page 1. Risk/Return Relationships and Interrelationships Between Economic and Accounting Measures 5 2. Movement of T.S.E. Index, Actual and Return, By Quarter, 1958 to 2nd Quarter 1967 11 - vi i - 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 in the stock market by reference to accounting or fi n a n c i a l statement data. The t r a d i t i o n a l measure of r i s k in 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 r i s k is 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 is then two-fold: a) to test the relationship between the analyst's perception of r i s k 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 ri s k and r i s k as outlined in the l i t e r a t u r e - i . e . a comparison of r i s k measures. If a relationship is found between accounting and economic measures of r i s k , this thesis postulates that the t r a d i t i o n a l measures of r i s k are merely ref l e c t i o n s of the impact of security analyst or prac t i t i o n e r perceptions upon the actions of investors in 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 con- sider 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 port- f 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 secu- r 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. It appears that this information i s derived from three sources: 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 dist r i b u t e d 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 con- siders 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 fi n a n c i a l history i s undertaken by reference to company f i n a n c i a l state- ments. 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 con- sciously 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 inves- tigates i t s f i n a n c i a l history. 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 par- t 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. Reported net income (NI) i s one way. 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 forth. Net operating income (NOI) may be more appropriate. In addition, as a proxy for 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 asso- ciated with the return of an individual security. Asset selection pro- cedures 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 . It i s f a i r l y straightforward and no explanation i s required. Market Ef f i c i e n c y Implications X Literature Risk/Return Concepts r i i I i I I P o r t f o l i o Implications \ \ \ Pension Fund Managers or Practitioner's Risk/Return Concepts I F 0 R-M V A T \ I 0 N Bias Talk • Reports \ \ Management Interviews, Economi c, Industrial Forecasts, etc. A . >A Financial x5 Statements ' NI, NOI, NI + D, Risk Bases Effect of what Practitioners do with Respect to Security Reports may be what Literature Measures as Risk-Return Con- cepts. Y I I I J i FIGURE 1. RISK/RETURN RELATIONSHIPS AND INTERRELATIONSHIPS BETWEEN ECONOMIC AND ACCOUNTING MEASURES - 6 - In summary, the central hypothesis underlying this thesis i s that r i s k 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 ri s k (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 ri s k as outlined in the l i t e r a t u r e . If the relationship 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 i s viewing as ri s k i s r e a l l y the e f f e c t 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 s h a l l 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 for 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 in 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 for the various ri s k 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 f i n a l 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 in the analyses. The second section, methodology, pre- sents the actual computational equations for each of the " t r a d i t i o n a l " as well as "accounting" measures of r i s k 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 for determining the "accounting" measures of ris k and the data necessary for calculating the " t r a d i t i o n a l " r i s k measures. i ) Accounting Data In determining the "accounting" measures of r i s k the Financial Post Computer Services Library tape was u t i l i z e d for three reasons: 1) ease of access, 2) readily available fi n a n c i a l statement figures, and 3) a f a i r l y representative time period (1958-67) over which fi n a n c i a l statement figures were available. E s s e n t i a l l y this " l i b r a r y " consists - 8 - - 9 - of 68 data items on an annual basis for 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 share- volume 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 for non-recurring items as well as changes in accounting practice to allow for relevant comparisons with other measures. Since i t i s desirable to compute the "accounting" measures of r i s k with the most complete information available, those firms having quite sparse f i n a n c i a l data ( i . e . less than seven annual figures for 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 fi n a n c i a l 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 ri s k as outlined in 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 " r i s k measures are based upon both i n d i v i - dual and market returns (of which price and dividend figures are the - 10 - two components), quarterly prices and dividends were collected 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 perio d i c a l s . 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 46 0780 7 X IH I N C H E S UAOt IN U. S . « . K C U F F t L 0. t S S E I I C O . - 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 out- l i n e the methodology involved in computing the return per quarter for an individual stock as these figures play a crucial role in the develop- ment 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 j t = P c " Po + D j t (1) j = 1 ... 114 stocks P P- t = 1 ... 40 quarters o o where: R.. = return on j ^ * 1 stock for t^* 1 quarter, J t D.+ = dividend on j stock for t quarter, P c = closing price of stock at end of quarter, P Q = opening price of stock at beginning of quarter 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 calculating the variance or standard de- viation of return upon which attention shall now be focused. ^For the purposes of this t h esis, a l l prices and dividends have been adjusted for stock s p l i t s and stock dividends. - 13 - i ) " T r a d i t i o n a l " Measures of Risk In the l i t e r a t u r e , the two most common measures of ris k asso- ciated 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 in accordance with Formula 2: 2 r i i/2 or Srj. - (2) i = 1 .... 40 quarters, j = 1 . . . .114 stocks where: V D. = variance of return of j stock over entire period, KJ J . L - J . L . Rij = return on j stock in the i quarter, n = sample s i z e , i . e . 40 quarters, and s D . = standard deviation of return of j 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 in 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 40 E Rij' 40 z Rij i = 1 n - 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 ri s k 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 ( t h i r d and fourth moments respectively) are not of use since the normal dis - t r i b u t i o n i s neither skewed nor abnormally peaked. Even when the under- lying 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 in the results w i l l appear. See fo r example, Eugene F. Fama, "P o r t f o l i o Analysis in 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. thesis, Graduate School of Business, University of Chicago, 1968. See also E. F. Fama and R. R o l l , "Some Properties of Symmetric Stable Distributions," 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 for the use of semi-variance and not variance, raises three points: a) in developing an appropriate ri s k 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 pr a c t i c a l standpoint at le a s t , these may be p r o h i b i t i v e . 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, in this case, since return is measured in price r e l a t i v e s , the same ef f e c t i s achieved and there i s no need to consider the c o e f f i c i e n t of v a r i a t i o n . Thus, one of the " t r a d i t i o n a l " measures of r i s k associated with a p a r t i c u l a r security employed i n this thesis is 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 s e c u r i t i e s 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 aff e c t i n g 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: * j t = + B j *mt + ht ( 3 ) j = 1 .... 114 stocks t = 1 .... 40 quarters where: E (5) = 0 r (R m, i j ) = 0 r (L, lk) = 0 3 f k 4 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: ~Rjt " ~Rft = a j + 6 j (~Rmt " R f t } + ht ( 4 ) j = 1 . . . . 114 stocks t = 1 . . . . 40 quarters where: 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 - , 3n-j - parameters and residual as specified J J J also in Formula 3 above. - 18 - At t h i s 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 " r i s k - f r e e " 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 Wed- nesday date shown). These quarterly rates are shown in Table 1, Appen- dix A. The market rate of return i s calculated in a s l i g h t l y d i f f e r e n t manner. In this case, the TSE i n d u s t r i a l 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: Rmj = Rmjc " Rmjo + .009 (5) Rmjo 114 stocks where: = quarterly market return of j * ' 1 stock, over 40 quarters, R . = closing market return of j stock at end of quarter, R = opening market return of j stock at mjo • beginning of quarter, and .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 (per- centages) for the period 1958-1967. Regressions of the form of Equation 4 were run for each stock over the ten-year period and the resulting beta c o e f f i c i e n t s (the e. 1s in Equation 4) indicating the relationship between the actual stock "risk premium" (R^ t - R f t) and market "risk premium" (R f n t - R f t) are 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 d i f f e r e n t 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 f i n a n c i a l statement figures. Of par- t 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 ri s k associated with each of these flows. Three such measures of ri s k for each earnings stream are the standard deviation, mean- absolute 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 calcu- lated 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: 2 10 E E i j 2 n 10 E i = 1 E i j n or i = 1 j = 1 'Ej 'Ej 1/2 (6) 10 years 114 stocks th where: V^j = variance of earnings stream of j stock over entire period, E i j = earnings stream of j * * 1 stock per i t n year, :th n = sample s i z e , i . e . 10 years, and s E j = standard deviation of the earnings stream of j 1 " 1 stock over 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 in 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 in the previous section under "Standard Deviation of Return" i s applicable here and w i l l not be repeated. b) Coefficient of 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 de- viations 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 c o e f f i c i e n t s of variation of the various earnings stream variables - 21 - were computed per Formula 7 below: C 0 V E j • (7) 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**1 stock over 10 years, (see Formula (6)), and 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 for 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 mean- absolute deviation s t a t i s t i c . Formula 8 shows the algebraic derivation of this measure: 10 M.A.D.C. = z lEj - E.l (8) n i = 1 .... 10 years j = 1 .... 114 stocks. where: M.A.D.^. = mean-absolute deviation of the earnings stream variable of the j stock, over the ten-year period, - 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 of Tables 1, 2 and 3 of Appendix C. In summary then, three accounting measures of risk were calculated based upon fi n a n c i a l statement figures. To this author, the most meaning- ful measure for 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 of the sources of data for 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 in 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 in order to: 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 of 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 r i s k 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 e x i s t among the various risk measures. A correlation analysis was performed on the ris k 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 in the same or opposite directions. One of the best-known procedures in 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: n 2 r = 1 - 6 z d. c H ^ T T - H < r , < „ <9> i = 1 .... 114 where: r = rank correlation c o e f f i c i e n t between two ri s k s 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 r i s k in pairs. To test for s t a t i s t i c a l s i g n i f i c a n c e , T- tests 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 in 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 in each c e l l of the matrix in 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 in order to indicate the number of stocks common to two p a r t i c u l a r measures of ri s k . With reference to the "mean" analysis, the number of stocks above the mean of one ris k measure was expressed as a percentage of the number of stocks above the mean of the other measure. These percentages are shown in 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 for the other measure. The resulting percen- tages are also shown in Table 4, Appendix A. A "median" analysis was also undertaken in 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. Obviously, this r a t i o would be meaning- less and constant at 1.0. 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 relationship exists between "accounting" and " t r a d i t i o n a l " measures of ris k as developed in the previous chapter. - 27 - B. 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 ris k 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 levels) 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 relationship to exist in this case? In the opinion of this author, since individual stocks and not p o r t f o l i o s 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 r e s u l t in 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 significance) being obtained when measures other than those involving the beta co- e 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 c o e f f i c i e n t ) 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 d i s t r i b u t i o n 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 s ignificance of the correlation c o e f f i c i e n t s between the standard deviation of return and the c o e f f i c i e n t s of variation for each of the earnings stream variables. It is disappointing to f i n d 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 c o e f f i c i e n t s of only .425, .454 and .474. The highest c o e f f i c i e n t (.474 above) for "accoun- tin g " and " t r a d i t i o n a l " measures of r i s k was obtained when the standard deviation of return and the c o e f f i c i e n t of variation f o r NI + D were correlated. This was expected for two reasons: a) NI + D i s 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 impor- tance in estimating the risk associated with an individual security, and b) NI + D r e f l e c t s both "business" and " f i n a n c i a l " r i s k 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 r i s k and an earnings stream variable over the period 1957-65. Their market ri s k 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 co-e f f i c i e n t i s reasonable. - 29 - One further observation may be made before concluding this section and thi s 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 in 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 r i s k 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 in 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 for 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 co- e f f i c i e n t . Upon analysis of the median and mean matrices in Tables 4 and 5, Appendix A, additional support i s given to the v a l i d i t y or reasonable- ness 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 for reasons pre- viously stated. Thus, from the "median" analysis, 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 for 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 (for reasons previously explained), absolute deviations range from approximately -36 to +54 or a range of 90 percentage points. This result i s indicative of quite substantial fluctuations. However, this may be due to the fact that extreme COV values are not included in 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 indicates, the high figures would be readjusted substantially downward and this would bring the NI figures more in l i n e with the NOI and NI + D figures. Summarizing this section, the following results are relevant: 1) when the range for each measure of ris k was subdivided into t h i r d s , the greater the number of "switches" occurring outside of corresponding sectors, the lower the correlation c o e f f i c i e n t (this lent support to the values of the c o e f f i c i e n t s obtained under section B i ) of this chapter); 2) with respect to the "median" analysis, further support was given to the previously computed values of the correlation 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 ris k 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 for the values of the correlation c o e f f i c i e n t s was not indicated by the resu l t s . - 32 - This completes the discussion concerning relationships among the various ri s k 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 s ignificance 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 s i g n i f i c a n c e . When a sectoral analysis was undertaken, in general, the values of the rank correlation c o e f f i c i e n t s were supported, incon- clusive evidence being observed in 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 s h a l l be made more relevant in the f i n a l 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 s h a l l now focus upon the second purpose of this t hesis: to determine any e x i s t i n g relationship between the various measures of ri s k 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 percep- tion 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 test shall be discussed. A. The Test To test the relationship outlined in the previous section be- tween ri s k and overall market return, a graphical analysis was under- taken 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 variation. "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 in 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 r i s k plotted against average annual rates of return in Figures 1 and 2 respectively in Appendix D, marked upward-sloping trend lines can readily be distinguished. The slope of the trend l i n e 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 r i s k 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 r i s k - what about the "accounting" measures? How well do they perform in 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 con- sidered (COV for NOI, NI and NI + D respectively), s l i g h t upward trends may be distinguished, especially with respect to the COV for NOI and NI + D (Figures 8 and 11). For two reasons this may be expected: 1) the correlation 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. In addition, when one compares COV^QJ and COV^j + ^ (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 correlation c o e f f i c i e n t s (.425 to .474). Comparing Figure 1 with the other accounting r i s k measures (standard deviation and mean-absolute deviation of each earnings stream v a r i a b l e ) , no real s i m i l a r i t i e s in 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 exhibit a moderate upward-sloping trend when one considers the COV measures of accounting r i s k plotted against overall market return. This was not the case when the standard deviation and mean-absolute deviation of NOI, NI, and NI + D was examined, for in 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 in ris k 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 out- l i n e d . * * * * * * 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 between1 What security analysts perceive 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 existing 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 r i s k 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 thesis, 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 r i s k measures, a correlation analysis was undertaken, the results of - 37 - - 3 8 - 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 ri s k (namely, co e f f i c i e n t s 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; i i ) 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; i i i ) the low magnitudes of 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 r i s k 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 of risk was observed to occur when the standard deviation of 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 for the values of these correlation c o e f f i c i e n t s was obtained through a sectoral analysis of each ris k 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 i i ) 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 ri s k and overall return in the market, several relevant conclusions may also be noted, based upon a graphical analysis to test for 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 ( c o e f f i c i e n t s 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 positive 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 in the market; and i i ) 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 in the context of a risk/return tradeoff. Accordingly, given these results what can be implied with respect to the o r i g i n a l purposes of this thesis as outlined in Chapter I? It was noted in 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 risk/return tradeoff f o r each measure of security r i s k , a further postulate of the thesis emphasized that the "t r a d i t i o n a l - 4 0 - measures of risk are merely re f l e c t i o n s 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 j u s t 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 r i s k 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 f i n a n c i a l statement data has been outlined in this thesis but there are other variables in t h i s informational process that defy q u a n t i f i c a t i o n . 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 fin a n c i a l 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 this thesis may only "whet the appetite." B. Areas of Future Research Based upon analyses undertaken in this thesis, 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 r i s k - 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, Kettler 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 re s u l t s . In addition, the quantification of such nebulous concepts as "street t a l k " and "in-depth management interviews" would go a long way o Beaver, Ke 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 l o g i c a l extension into p o r t f o l i o theory. A related problem occurs in 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 for 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 for this thesis. It would be most helpful to future researchers in 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 in the early f i f t i e s and updated constantly. The Financial Post has already put on tape annual selected f i n a n c i a l statement data. Combine this tape with the price and dividend one already proposed and the result would be invaluable tools for anyone who desired to undertake future research in this area. Obviously, there are other areas of proposed research but, to this author at l e a s t , 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 i s of quite recent or i g i n and there e x i s t many areas where new, orig i n a l 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 Manage- ment. 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. New York: McGraw-Hill Inc., 1970. 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. A r t i c l e s 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 f ) , BY QUARTER, 1958-1967* 1st 2nd 3rd 4th Year Quarter Quarter Quarter Quarter (Percentages) 1958 .0090 .0045 .0040 .0059 1959 .0081 .0108 .0125 .0131 1960 .0128 .0081 .0079 .0055 1961 .0083 .0081 .0065 .0064 1962 .0077 .0077 .0135 .0123 1963 .0098 .0090 .0081 .0090 1964 .0094 .0092 .0091 .0092 1965 .0093 .0094 .0099 .0103 1966 .0115 .0127 .0125 .0129 1967 .0117 .0100 .0108 .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* 1st 2nd 3rd 4 th Year Quarter Quarter Quarter Quarter (Percentages) 1958 .0669 .0665 .1201 .0439 1959 .0410 .0350 - -.0415 .0410 1960 -.0657 .0086 .0056 .1156 1961 .1163 .0821 .0242 .0657 1962 -.0163 -.1570 .0095 .1159 1963 .0385 .0407 .0121 .0480 1964 .0661 .0870 .0637 .0132 1965 .0437 -.0399 .0350 .0152 1966 .0063 -.0274 -.1157 .0504 1967 .1272 .0057 .0344 -.0291 Source: TSE Indices, 4th Edition, February 1, 1968, Toronto Stock Exchange, Toronto, Ontario. See also Figure 2 of this thesis for 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 COV (NOI) COV (NI) COV (NI + D) s.d. R BETA r s = .218 85 r = .192 s 82 r c = .210 s 88 r s = .593* 53 COV (NOI) r s = .218 85 0 N S N S n \ r = .764* s 37 r = .866* s 26 r = .425* s 72 COV (NI) r s = .192 82 r s = .764* 37 0 S S S S \ r = .867* s 31 r = .454* s 61 COV (NI + D) r s = .210 88 r = .866* s 26 r s = .867* 31 r s = .474* 74 s.d. R r s = .593* 53 r s = .425* 72 r $ = .454* 61 r s = .474* 74 \ 0 X N \ r g = Spearman rank correlated c o e f f i c i e n t . * = 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 in 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 COV (NOI) COV ( N I ) COV (NI + D) s .d.p BETA \ 100.0 \ 76.2 (45.7) r p = .218 s 96.7 (61.0) r s = .192 62.7 (45.7) r s = .210 76.2 (61.0) r = .593 s COV (NOI) 131.1 (60.0) r r = .218 s \ 100.0 \ 126.6 (91.1) r s = .764 82.2 (73.3) r = .866 s 100.0 (60.0) rp = .425 s COV ( N I ) 103.5 (63.1) r s = .192 78.9 (71.9) rc = .764 s \ 1 0 0 . 0 ^ ^ 64.9 (68.4) r s = .867 78.9 (54.3) r s = .454 COV (NI + D) 159.4 (72.9) 121.6 (89.1) r s = .866 154.0 (105.4) r = .867 s 1 0 0 . 0 ^ ^ 121.6 (67.5) r = .474 s s . d . R 131.1 (80.0) r s = .593 100.0 (60.0) r s = .425 126.6 (82.2) r =.454 82.2 (55.5) r = .474 s N J O O . 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 of Stocks Common of 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) NUMERATOR BETA COV (NOI) COV (NI) COV (NI + D) s.d. R BETA ^^lOO.O 56.1 r s = .218 56.1 r o = .192 s 57.8 rc = .210 s 70.1 r s = .593 COV (NOI) 56.1 r = .218 s ^100.0 78.9 r s = .764 84.2 r = .866 s 57.8 rp = .425 s COV (NI) 56.1 r s = .192 78.9 r s = .764 100.0 ^ 84.2 r s = .867 63.1 r s = .454 COV (NI + D) 57.8 r„ = .210 s 84.2 r = .866 s 84.2 r s = .867 100.0 59.6 r s = .474 s . d . R 70.1 r = .593 s 57.8 r = .425 s 63.1 r = .454 s 59.6 r s = .474 X | o o . o x ^ 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 - 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 Average Annual Return {%) Beta Coefficient Standard Deviation Magnitude Rank Magnitude Rank 001 8.36 .676398 24 .0775 15 018 11.32 .646171 21 .1082 58 021 10.68 1.365533 107 .1088 59 030 1.44 .310174 3 .0355 2 033 -0.80 .411987 5 .0756 14 037 32.40 1.163869 92 .1436 92 051 30.72 .915839 55 .1318 86 078 16.48 .762435 34 .1240 81 087 6.56 .601491 17 .0700 6 102 18.92 1.003545 66 .1223 78 104 13.24 .475746 71 .0560 4 105 5.52 .807566 39 .0860 25 108 13.80 1.256283 98 .1364 89 111 10.36 .520163 12 .0815 18 117 8.72 .669440 22 .0727 11 135 10.20 .728880 29 .0950 41 141 7.76 1.285816 103 .1157 72 144 19.80 1.128401 86 .1637 104 150 13.96 1.270107 101 .1311 85 156 11.84 .796914 38 .0960 44 159 13.56 .679163 25 .0712 8 165 9.48 1.013409 71 .0941 38 171 9.96 .905270 52 .0917 33 Continued . . . - 51 - - 52 - Appendix B, Table 1 - Continued Stock Average Annual Return (%) Beta Coefficient Standard Deviation Magnitude Rank Magni tude Rank 177 4.28 .506481 9 .0561 5 195 17.76 1.101863 79 .1443 95 204 5.92 1.142513 89 .1094 60 207 13.40 .810219 41 .1287 84 213 18.44 1.201669 96 .2009 111 219 5.04 .864392 45 .1230 79 231 4.20 .197390 1 .0316 1 243 7.88 1.108533 80 .1482 96 252 13.44 .701946 27 .0926 34 279 4.20 .896671 49 .0932 35 282 47.92 .365081 4 .2375 114 285 18.52 .824488 42 .0820 19 288 13.28 .586956 15 .0983 47 294 12.96 .767248 35 .0875 27 300 8.08 .563894 14 .0710 7 315 13.64 .291657 2 .0914 32 318 6.80 1.036773 75 .0834 21 319 12.88 .739119 32 .1347 88 336 16.84 1.164382 93 .0820 20 339 3.24 1.075374 78 .1158 73 348 21.68 1.522138 n o .2340 113 354 17.18 1.555255 111 .1121 67 357 2.76 .509156 10 .0781 16 360 8.52 .840186 43 .1031 52 361 -0.36 .974302 60 .1413 91 363 9.60 1.008755 69 .1033 53 366 7.04 1.178676 94 .1021 51 369 18.64 1.030428 72 .1573 98 Continued . . . - 53 - Appendix B, Table 1 - Continued Stock Average Annual Return (%) Beta Coefficient Standard Deviation Magnitude . Rank Magnitude Rank 372 13.80 .998227 64 .1010 50 375 9.16 .891119 48 .1147 71 381 7.00 .760502 33 .0799 17 389 21.44 1.121094 83 .1058 56 393 16.00 .945385 56 .1189 76 402 16.64 1.109638 81 .1213 77 407 4.60 .900370 50 .0845 22 411 20.24 1.073937 77 .1243 82 413 2.52 .554052 13 .0965 47 414 8.60 1.151289 91 .1637 103 417 9.24 1.136112 87 .1062 57 423 12.52 1.149905 90 .1100 61 426 16.76 .869241 46 .1106 64 447 35.36 1.240491 97 .2188 112 450 -7.64 1.337089 105 .1545 97 457 12.88 .986881 63 .1615 101 463 9.68 .771754 36 .0745 12 464 14.80 1.004304 67 .1439 93 466 15.80 1.030503 73 .1979 110 468 9.92 .732043 31 .0721 9 471 6.76 .728483 28 .0725 10 479 21.80 1.007211 68 .1954 109 481 8.08 1.265937 99 .1286 83 485 14.32 .499373 8 .0910 12 489 17.80 1.126773 85 .0945 31 492 7.16 1.059292 76 .0993 40 495 19.36 .803549 40 .0906 30 Continued . . . - 54 - Appendix B, Table 1 - Continued Stock Average Annual Return (%) Beta Coefficient Standard Deviation Magnitude Rank Magnitude Rank 496 16.08 .699342 27 .0746 13 510 13.72 1.123003 84 .1231 80 513 8.68 .954575 58 .1117 66 519 9.52 .882598 47 .1672 105 522 19.16 .962815 59 .1057 55 525 12.32 1.435808 108 .1938 108 546 7.60 1.114440 82 .1121 68 573 11.56 .842380 44 .1113 65 579 18.48 1.977755 114 .1624 102 603 15.84 1.267186 100 .1101 62 612 6.16 .628245 20 .0938 37 628 12.16 .721727 29 .1103 63 633 3.16 .518170 11 .0942 39 647 16.12 .908779 54 .0855 24 657 9.24 .984296 61 .1125 69 663 14.40 .625862 19 .0888 28 676 4.44 .952071 57 .1442 94 678 16.04 .790374 37 .1379 90 687 12.84 .609331 18 .0953 42 691 3.84 1.035398 74 .0854 23 702 7.82 1.002339 65 .0956 43 741 21.76 1.462731 109 .1703 107 753 6.92 1.180282 95 .1575 99 756 16.04 1.655674 113 .1674 106 777 14.40 1.548835 110 .1586 100 786 9.12 .443465 6 .0495 3 789 17.72 .670069 23 .0933 36 798 20.64 1.012344 70 .1008 49 804 1.84 .906806 53 .0963 45 Continued . . . - 55 - Appendix B, Table 1 - Continued Stock Average Annual Return (%) Beta Coefficient Standard Deviation Magnitude Rank Magnitude Rank 813 10.04 1.139135 88 .0863 26 831 9.56 .598421 6 .0897 29 855 5.04 1.354916 106 .1339 87 858 12.60 .986021 62 .1140 70 909 10.00 .903329 51 .1056 54 940 12.92 1.285555 103 .1182 75 949 18.04 1.283032 102 .1175 74 For computation of measures and return, see Chapter II, 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 Mean-Absolute Deviation (OOO's) Stock Magni tude Rank Magnitude Rank Magnitude Rank 001 4,601 78 .11 6 3,840 77 018 2,563 59 .89 114 2,380 61 021 12,516 96 .27 58 10,900 97 030 48,580 112 .28 62 43,400 113 033 2,337 56 .15 14 2,070 57 037 3,976 70 .66 108 3,740 75 051 2,045 52 .34 70 1,790 52 078 814 25 .15 15 656 24 087 72,996 114 .29 67 61,800 114 102 277 9 .16 16 228 9 104 153 6 .14 13 120 6 105 16,982 103 .21 35 15,300 104 108 5,286 82 .34 71 4,750 84 111 1,038 32 .26 52 832 31 117 14,790 100 .35 75 12,600 100 135 3,900 68 .18 21 3,230 68 141 2,302 55 .11 5 1,790 53 144 323 12 .26 56 272 13 150 3,567 65 .39 85 3,280 69 156 328 13 .09 3 224 8 159 3,117 62 .20 33 2,520 62 165 3,406 64 .19 25 2,950 65 171 4,282 73 .12 10 3,670 74 177 1,278 41 .44 90 1,180 45 Continued . . . - 57 - - 58 - Appendix C, Table 1 - Continued Standard Coefficient of Mean-Absolute Devi a t i on Variation Deviation (000's) (000's) Stock Magnitude Rank Magnitude Rank Magnitude Rank 195 1,368 44 .59 104 1,060 42 204 4,954 80 .19 26 4,260 80 207 2,578 60 •17 20 2,090 59 213 1,971 51 .50 96 1,830 54 219 4,797 79 .35 76 3,800 76 231 1,154 37 .22 40 980 38 243 3,799 67 .56 103 3,120 67 252 100 3 .14 12 80 3 279 4,097 71 .11 8 3,030 66 282 448 16 .88 113 392 16 285 9,328 92 .48 94 8,000 92 288 1,346 43 .50 97 1,030 41 294 977 30 .32 68 676 26 300 91 2 .11 4 80 2 315 690 23 .36 83 632 23 318 7,558 89 .23 45 6,790 89 319 355 14 .18 23 290 15 336 15,514 101 .20 30 12,900 101 339 4,993 81 .72 109 4,610 81 348 234 7 .19 27 192 7 354 14,196 99 .28 63 13,000 102 357 1,228 39 .22 42 940 35 360 1,141 36 .46 93 944 36 361 3,708 66 .36 79 2,750 63 363 4,354 75 .19 28 3,980 79 366 14,138 98 .27 59 12,000 98 369 6,293 85 .46 92 4,660 82 Continued . . . - 59 - Appendix C, Table 1 - Continued Standard Coefficient of Mean-Absolute Deviation Variation Devi ati on (OOO's) (OOO's) Stock Magnitude Rank Magnitude Rank Magni tude Rank 372 652 21 .18 22 584 21 375 8,533 90 .28 66 7,610 91 381 564 19 .20 34 500 19 389 4,427 77 .17 17 3,570 72 393 1,498 47 .36 84 966 37 402 16,314 102 .24 48 12,100 99 407 2,099 53 .18 24 1,510 50 411 272 8 .22 41 232 10 413 416 15 .41 88 282 14 414 784 24 .50 98 658 25 417 2,346 57 .26 57 1,950 56 423 3,241 63 .25 50 2,780 64 426 952 29 .20 31 812 30 447 1,008 31 .45 91 910 34 450 6,835 86 .36 80 5,460 86 457 3,903 69 .48 95 3,660 73 463 5,430 83 .25 51 4,740 83 464 10,237 94 .43 89 9,220 94 466 7,275 87 .76 111 6,250 87 468 20,855 107 .13 11 15,900 105 471 1,466 45 .05 1 1,280 47 479 1,040 33 .81 112 848 32 481 1,246 40 .40 86 1,030 40 485 110 4 .21 39 90 4 489 49,529 113 .27 61 40,300 112 492 21,870 110 .11 9 17,800 108 495 18,643 106 .63 107 14,100 103 Continued . . . - 60 - Appendix C, Table 1 - Continued Standard Deviation (000's) Coefficient of Variation Mean-Absolute Deviati on (000's) Stock Magnitude Rank Magnitude Rank Magnitude Rank 496 8,763 91 .17 18 7,540 90 510 863 27 .21 36 790 29 513 1,051 34 .26 53 908 33 519 293 10 .27 60 236 11 522 4,372 76 .33 69 3,480 70 525 1,108 35 .51 100 1,000 39 546 17,490 104 .35 77 16,700 106 573 1,511 48 .20 32 1,370 48 579 22,664 111 .34 72 20,700 111 603 4,223 72 .22 43 3,560 71 612 1,315 42 .73 n o 1,070 43 628 151 5 .22 44 114 5 633 508 17 .55 102 430 18 647 20,890 108 .55 101 19,100 109 657 1,479 46 .35 78 1,220 46 663 1,696 51 .36 81 1,630 51 676 9,939 93 .59 105 8,400 93 678 521 18 .11 7 420 17 687 64 1 .08 2 56 1 691 5,906 84 .28 64 4,980 85 702 2,403 58 .34 73 2,070 58 741 892 28 .28 65 736 28 753 2,713 61 .36 82 2,310 60 756 1,205 38 .23 46 1,100 44 777 638 20 .50 99 540 20 786 855 26 .19 29 680 27 789 4,352 74 .26 54 3,870 78 798 1,577 49 .17 19 1,390 49 Continued - 61 - Appendix C, Table 1 - Continued Standard Coefficient of Mean-Absolute Deviation Vari ati on Devi ati on (OOO's) (OOO's) Stock Magnitude Rank Magnitude Rank Magnitude Rank 804 687 22 .24 49 610 22 813 21,599 109 .26 55 19,100 110 831 314 11 .21 37 270 12 855 18,525 105 .60 106 16,900 107 858 7,399 88 .34 74 6,260 88 909 13,010 97 .21 38 10,900 96 940 11,491 95 .40 87 9,690 95 949 2,266 54 .23 47 1,890 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 Coefficient of Mean-Absolute Deviation Variation Deviation (000's) (000's) Stock Magnitude Rank Magnitude Rank Magnitude Rank 001 4,953 94 .30 42 4,120 95 018 784 43 .42 61 703 47 021 8,458 101 .32 46 7,480 101 030 21,245 111 .45 62 18,700 112 033 1,379 56 .26 32 1,230 58 037 1,583 59 .70 92 1,450 60 051 1,789 64 .53 78 1,520 63 078 471 27 .21 18 380 26 087 26,742 113 .38 57 20,600 113 102 90 3 .14 4 76 3 104 163 10 .31 45 113 7 105 6,288 97 .19 9 5,200 97 108 3,318 76 .50 73 3,110 84 111 692 36 .75 93 578 38 117 4,703 92 .46 66 3,590 90 135 1,694 61 .20 11 1 ,530 64 141 2,645 73 .32 47 2,140 75 144 171 11 .35 52 152 11 150 1,969 68 .57 80 1,620 67 156 155 9 .11 3 122 9 159 1,771 63 .29 41 1,530 65 165 2,116 70 .24 25 1,770 72 171 1,974 69 .15 5 1,450 61 177 700 38 .60 83 665 45 Continued . . . - 62 - - 63 - Appendix C, Table 2 - Continued Standard Coefficient of Mean-Absolute Deviation Vari ati on Devi ati on (OOO's) (OOO's) Stock Magnitude Rank Magnitude Rank Magnitude Rank 195 846 48 .63 86 706 48 204 1,865 65 .25 28 1,650 70 207 902 49 .09 2 764 50 213 996 52 1.05 101 952 55 219 3,372 77 .60 84 2,820 76 231 421 24 .23 23 382 27 243 2,453 72 .99 99 1,940 73 252 62 2 .21 16 43 2 279 4,533 91 .24 27 3,730 91 282 269 18 1.75 107 217 17 285 3,913 86 .47 68 3,290 87 288 815 46 .75 94 569 36 294 656 33 .36 56 454 29 300 104 7 .27 37 75 2 315 534 29 .50 75 492 31 318 3,420 79 .28 39 3,080 83 319 268 17 .35 53 214 16 336 8,733 102 .25 29 7,790 103 339 3,434 80 .99 100 3,000 79 348 140 8 .27 34 119 9 354 12,112 106 .45 63 11,300 108 357 490 28 .21 19 352 24 360 663 34 .56 79 560 35 361 4,072 87 2.74 112 3,030 80 363 1,595 60 .18 8 1,490 62 366 9,509 104 .47 69 7,740 102 369 4,313 88 1.41 106 3,220 85 372 297 19 .22 20 260 18 Continued . . . - 64 - Appendix C, Table 2 - Continued Standard Deviation (000's) Coefficient of Variation Mean-Absolute Deviation (000's) Stock Magnitude 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 n o 471 952 51 .08 1 850 52 479 1,172 54 2.61 n o 920 54 481 837 47 .89 97 607 41 485 47 1 ; .23 24 33 1 489 33,146 114 .30 44 27,600 114 492 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 Standard Deviation (OOO's) Coefficient of Variation Mean-Absolute Deviation (OOO's) Stock Magnitude Rank Magnitude Rank Magnitude Rank 519 256 15 1.23 102 173 13 522 1,887 66 .35 51 1,620 68 525 808 45 1.23 103 732 49 546 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 i n Continued . . . - 66 - Appendix C, Table 2 - Continued Standard Coefficient of Mean-Absolute Deviation Variation Deviation (000's) (000's) Stock Magnitude Rank Magnitude Rank Magnitude Rank 831 104 5 .20 14 91 7 855 9,020 103 1.98 109 7,930 104 858 3,510 82 .48 70 2,930 78 909 6,185 96 .20 15 5,360 98 940 3,794 84 .33 49 3,450 89 949 1,200 55 .30 43 1,060 56 For computation of measures, see Chapter I I , SubsectioniB i i ) . APPENDIX C, TABLE 3 ACCOUNTING RISK MEASURES BASED ON NET INCOME PLUS DEPRECIATION , SELECTED STOCKS, 1958-671 Standard Coefficient of Mean-Absolute Deviation Variation Deviation (OOO's) (OOO's) Stock Magnitude Rank Magnitude Rank Magnitude Rank 001 5,413 85 .20 22 4,660 85 018 1,033 43 .29 48 951 46 021 10,183 97 .26 42 9,030 100 030 31,994 112 .30 57 28,500 112 033 1,391 51 .14 7 1,230 52 037 2,243 59 .62 101 2,120 64 051 1,845 56 .43 89 1,590 57 078 525 25 .18 18 410 24 087 52,141 114 .31 58 42,700 114 102 173 8 .19 19 136 7 104 196 9 .26 44 141 9 105 10,445 98 .14 8 9,270 101 108 5,172 84 .41 80 4,910 87 111 682 29 .34 65 582 31 117 10,787 99 .42 84 8,970 99 135 2,862 69 .21 25 2,510 71 141 2,310 61 ? .17 13 1,870 58 144 227 11 .26 45 208 13 150 2,490 66 .40 79 2,120 65 156 167 7 .07 2 136 8 159 2,373 63 .23 37 2,040 63 165 3,156 73 .21 26 2,650 73 171 2,984 72 .13 5 2,390 70 Conti nued - 68 - Appendix C, Table 3 - Continued Standard Coefficient of Mean-Absolute Devi ati on Variation Devi a t i on (000's) (000's) Stock Magnitude Rank Magnitude Rank Magnitude Rank 177 869 36 .42 85 845 41 195 1,447 53 .58 100 1,180 50 204 2,888 70 .17 14 2,580 72 207 1,859 57 .15 9 1,570 56 213 1,339 50 .57 99 1,200 51 219 4,769 81 .35 70 4,100 81 231 739 33 .23 34 630 34 243 2,681 68 .54 95 2,130 66 252 69 2 .19 20 47 2 279 6,388 89 .26 46 5,320 89 282 286 15 .89 112 241 15 285 5,737 87 .44 90 4,880 86 288 1,104 47 .56 98 809 38 294 726 32 .37 75 521 27 300 111 5 .17 15 90 4 315 675 28 .48 92 628 33 318 5,071 83 .23 35 4,640 84 319 360 16 .23 38 312 17 336 13,036 102 .29 49 11,600 104 339 3,590 75 .65 103 3,150 77 348 265 14 . .33 63 209 14 354 15,836 106 .41 81 14,700 106 357 439 20 .11 3 338 18 360 560 26 .29 56 476 26 361 4,061 78 .51 94 3,000 75 363 2,567 61 .19 21 2,350 69 366 13,469 103 .35 71 10,700 103 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 4,050 77 .42 86 3,270 78 372 440 21 .21 27 392 22 375 6,919 90 .32 62 6,360 93 381 397 18 .22 31 357 19 389 10,891 100 .35 72 8,950 98 393 993 41 .34 66 579 30 402 12,032 101 .24 40 8,910 97 407 2,966 71 .33 64 2,140 67 411 225 10 .24 39 201 12 413 242 12 .34 67 190 11 414 699 31 .77 109 588 32 417 2,335 62 .34 68 1,940 60 423 4,265 80 .45 91 3,800 79 426 482 23 .18 16 426 25 447 801 34 .54 96 698 36 450 5,527 86 .41 82 4,190 83 457 4,129 79 .74 107 3,890 80 463 3,769 76 .22 32 3,110 76 464 9,484 96 .42 87 8,460 96 466 5,803 88 .81 110 5,190 88 468 19,464 109 .16 11 17,600 109 471 942 39 .06 1 860 42 479 1,056 44 .99 113 824 39 481 1,085 45 .73 105 888 43 485 47 1 .15 10 30 1 489 37,502 113 .28 47 31,400 113 492 19,290 108 .13 6 16,900 108 Continued . . . - 70 - Appendix C, Table 3 - Continued Standard Coefficient of Mean-Absolute Devi ati on Variation Deviation (000's) (000's) Stock Magnitude Rank Magnitude Rank Magnitude Rank 495 14,259 105 .74 108 10,600 102 496 4,852 82 .16 12 4,170 82 510 455 22 .20 23 407 23 513 629 27 .26 43 550 28 519 243 13 .35 73 171 10 522 2,300 60 .29 50 1,960 61 525 973 40 .65 102 892 44 546 8,270 94 .32 61 7,830 95 573 1,093 46 .22 29 921 45 579 17,294 107 .37 74 15,800 107 603 2,418 64 .21 28 2,030 62 612 803 35 .65 104 657 35 628 138 6 .22 33 116 6 633 361 17 .82 111 290 16 647 19,589 no .54 97 17,700 110 657 1,148 48 .34 69 1,020 48 663 1,210 49 .31 59 1,170 49 676 8,649 95 .73 106 7,320 94 678 1,006 42 .29 51 966 47 687 101 3 .18 17 84 3 691 7,141 93 .41 83 6,350 92 702 1,465 54 .31 60 1,250 53 741 910 38 .39 78 767 37 753 2,168 58 .42 88 1,870 59 756 889 37 .29 52 834 40 777 421 19 .49 93 370 20 786 687 30 .22 30 573 29 Continued . . . - 71 - Appendix C, Table 3 - Continued Standard Coefficient of Mean-Absolute Deviation Vari ati on Deviation (OOO's) (OOO's) Stock Magnitude Rank Magni tude Rank Magni tude Rank 789 2,467 65 .29 53 2,210 68 798 1,442 52 .23 36 1,280 54 804 521 24 .25 41 381 21 813 24,818 111 .38 76 21,700 111 831 108 4 .12 4 99 5 855 13,518 104 1.01 114 12,000 105 858 3,552 74 .29 54 2,970 74 909 7,109 92 .20 24 6,090 90 940 7,019 91 .38 77 6,110 91 949 1,631 55 .29 55 1,430 55 For computation of measures, see Chapter I I , Subsection B i i ) . 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T i i ; 1 1 i i i i > L > r. i i i 1 J r i i 1 1 r fj > 1 • i t Ki 1 i i 1 i U Y < rv > V 1 L 1 i i > c A > > t. 1 «; / \ / I ) 1 y > if 1 > > A / 1 > I 1 I t r c 1̂  X k 1 • > C) ,> { r • t > K It* > ] / c l * V «/ k S i i i < r X / A I X i. / \ / / I 1 f v • > , 1 A / 1 1 f l A 1 1 1 1 1 ! i ii "lean I ! i 1 i_ i / r̂iriiiajl-1 ! A >• ps r-> 0 2, * 1 6t i V i \ > > * J i ^ p •teturn i ! 1 1 1 U N ! 1 1 1 1 1 ! J ! i ! "1 1 ! 1 1 0 A i T t I 1 I ur "( BID 1 2 1 1 1 1 i 1 l i I 1 1 1 1 1 1 1 1 j F2 i G u }' t t j i 1 —1— 1 I e V tit 0 i 1 1 canacT ra L '\ c rT A N--\nr !E -D I-31 J- N •I- -E > n - F 3 }_ c A M 3. _C > i-9-5£ 6 7 1 1 ! 1 Cm T_ L_X_ r \\ < \ ). i\ _ L 5 / X 1 1 1 | \ | " 1 u ) I ! I / Si ! 1 1 /- 1 1 I 1 1 | 1 Ik ! I I | : 1 i / i | i I 1 i I 1 I It i hi* 1 1 1 ! i 1 i I I I i i i , 1 ! I i i j ( > i I i i 1 i 1 : 1 \ 1 1 1 1 1 1 > 1 i i 1 i 1 i ] I 1 i | } 1 | 1 I | I 1 i 1 1 1 1 1 I 1 i i t I i { 1 1 1 k 1 y 1 1 1 1 A 1 1 \ 1 1 j 1 * f 1 I * | - i Y I 1 r < 1 1 ,5 1 i i 1 ') 1 i 1 1 1 1 9! i ? 1 1 1 i i ! ! i •»l r 7 / i I 1 1 1 1  i • i i i i • / r J/ 1 1 1 1 i i ! i ,/ L r\ y *f *" 1 i ! ! .1.1 1 A. 1 I I 1 i ! ! i ; I A> I 1 ' 1 • i i / , ! 1 1 1 t f 7 «x ( > <c > 1 ' i 1 \ > 7 )<. r 1 ; 1 1 Meao_ 1 > J k j.. > XX i - A'nrruc 1 i i 1 > > ; >< \ < * ^ 1 X i 1 1 1 1 / 1 i i ! / « ! Return ! 1 ! 1 f _ i r 3 i r c | i i , 1 1 i • I _ 3< n Si • ? -* 0 4 i / k i 1 1 i ! ! 1 ~ A t i * i • 1 i j I | I i I ! ! 1 I 1 i ! 1 1 ! 1 1 _ rc r P > 7 a i | 1 1 — _ ce _ "i X Ie. ."2 _ i — 1 — — — |- — — — — — - — — — — - -+ — — - AW Mm 10 -Mean^ ̂bs^Ttite f'EA™S£) mm -V-S REFURfv F3R- -SAM3-L-ET +358-67- 5 * x ^ ±x 1* S_0L(rice Appendi x Tab-le_i3 1 •i 1 I 1 I I f ,P p w -X 0 J G U 1 1 1 | I 1 1 f f i n t r ,Q E F E N r Ac Vi \f l l • f l -T I- / N T R H ,N P Df 3_ s A .-E > 6 7 t -i D | I 1 f r \ 1 u l / 1 a tic )r (-N- 4 • m i —y cwp. — ! u ? 1 1 i f.QQ i i 1 I i | / ri X o i I X A I 1 t < < r r\ 4 i» I i / > i 1 / r 1 . i (v. I i / t / # 7 . t a n XV <• > r / A > r * 4 i; <• y 5 5 s / f > Y \ t > 7 k. / > < . A \ 4 : > X > fx X 1 V s r f > ? /V > k K 1 • f > s >< A C / H "3 \ / < > > I t < l < > \ # > i / 1 ) | 1 i i 1 Kean_ j n ' 1 • I i 1 i 1 i i < £< '« i t Dot 11 v.n I > > ? • roj i < > > 1 ! I r r ! i i I 1 t i 1 --. . . - - - 5c - i — ur -r- -- D. ).cjr c i 4 i —, a ).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 Abi t i bi Paper 315 Crown Cork & Seal 18 Algoma Central Railway 318 Crown Zellerbach 21 Algoma Steel Corp. 319 Crows Nest Industries 30 Alcan Aluminium 33 Anglo-Canadian P. & P. 336 Distillers-Seagram 37 Anthes Imperial 339 Dom. Bridge 51 A t l a n t i c Sugar 348 Electrohome 54 Auto E l e c t r i c 354 Dom. Foundaries & Steel 357 Dom Glass 78 Beaver Lumber 360 Domco Industries 87 Bell Canada 361 Dom. Steel 102 Bright T. G. 363 Dom. Stores 104 B. A. Bank Note 366 Domtar 105 B. A. Oil 369 Dom. Tex t i l e 108 B. C. Forest Products 372 Donohue Bros. 111 B. C. Packers 375 Du Pont of Canada 117 B. C. Telephone 381 Eddy Match 135 Calgary Power 141 Can. Cement 389 Falconbridge Nickel 144 Can C. & Cut Stone 393 Federal Grain 150 Canron 402 Ford Canada 156 Can. Malting 407 Fraser Companies 159 Can. Packers 165 Can. Steamship Lines 411 General Bakeries 171 Cdn. Breweries 413 General Products 177 Cdn. Canners 414 General Steel Wares 195 Cdn. Hydrocarbons 417 Goodyear Ti r e 204 Cdn. Industries 423 Great Lakes Paper 207 Cdn. Int. Power 426 Great Lakes Power 213 Cdn. Marconi 219 Cdn. Petrofina 447 Harding Carpet 231 Cdn. U t i l i t i e s 450 Hawker Siddeley 243 Cdn. Westinghouse 457 Home Oil 252 Chateau-Gai Wines 463 Hudson Bay Mining 279 Consolidated-Bathurst 464 H. B. Oil & Gas 282 Consolidated T e x t i l e 466 Husky Oil 285 Consumers' Gas 288 Consumers Glass 294 H. Corby 300 Cosmos Imperial - 85 - - 86 - Appendix E, Table 1 - Continued 468 Imperial Oil 471 Imperial Tobacco 479 Inglis 481 Inland Natural Gas 485 Int e r i o r Breweries 489 International Nickel 492 International Paper 495 International U t i l i t i e s 496 Interprov. Pipelines 510 Jockey Club 513 Kelly, Douglas 519 Kelvinator 522 Labatt, John 525 Lafarge cement 546 Loblaw Cos. 573 Maple Leaf M i l l s 579 Massey-Ferguson 603 Molson Breweries 612 MLW Worthington 628 Nabors D r i l l i n g 647 Noranda 657 Ocean Cement 663 Ogilvie Flour 676 P a c i f i c Petroleum 678 Pembina Pipe 687 Photo Engravers 691 Price Co. 702 Quebec Telephone 741 Roll and Paper 753 St. Lawrence Cement 756 Salada Foods 777 Shop & Save 786 Silverwood Dairies 789 Simpsons 798 Southam Press 804 Standard Paving 813 Steel Co. of Canada 831 Tamblyn 855 Trans-Canada Pipelines 858 Trans-Mt. Oil Pipe Line 909 Walker-G. & W. 904 Weston, Geo. 949 Woodward Stores

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