《投资学原理 Investments》课程教学资源（阅读资料）How to Use Security Analysis to Improve Portfolio Selection.pdf

Jack L, Treynor and Fischer black How to Use Security Analysis to Improve Portfolio selection It has been argued convincingly in a series of papers on the Capital Asset Pricing Model that, in the absence of insight generating expect tions different from the market consensus the investor should hold a replica of the market portfolio. 1 A number of empirical papers have demonstrated that portfolios of more than 50-100 randomly selected securities tend to correlate very highly with the market portfolio, so that, as a practical matter, replicas are relatively easy to obtain. If the investor has no special insights, therefore, he has no need of the elaborate balancing algorithms of Markowitz and Sharpe. 2 On the other hand if he has special insights, he will get little, if any, help from the portfolio-balancing literature on how to translate these insights into the expected returns, variances, and covariances the algorithms require What was needed, it seemed to us, was exploration of the link etween conventional subjective, judgmental, work of the security analyst, on one hand--rough cut and not very quantitativeand the essentially objective, statistical approach to portfolio selection of Markowitz and his successors on the other The void between these two bodies of ideas was made manifest b our inability to answer to our own satisfaction the following kinds of questions: Where practical is it desirable to so balance a portfolio be- tween long positions in securities considered underpriced and short positions in securities considered overpriced that market risk is com- pletely eliminated (i.e, hedged)? Or should one strive to diversify a portfolio so completely that only market risk remains? As this implies, in the highly diversified portfolio market sensitivity in individual secu- rities seems to contribute directly to market sensitivity in the overall portfolio, whereas other sources of return variability in individual securities seem to average out. Does this mean that the latter sources w Editor, Financial Analysts Journal, sor of finance, University Chicago; and executive director, Center for Re in Security Prices lliam F. Shar a Theory of Market equi of Risk, Journal of Finance 19, no. 3 964):425-42; John Lintner, "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, " Review of Economics and Statistics 57, no. 1( February 1954): 13-37; and Jack L. Tre Toward a Theory of the Market values of Risky Assets"(u 2. Harry Markowitz, Portfolio Selection: Efficient Diversification of In- vestments(New York: John Wiley Sons, 1959; New Haven, Conn. Yale Uni- versity Press, 1970);and William Sharpe, "A Simplified Model Portfolio Analysis, Management Science 9 (January 1963 ): 277-93 Cone doal25m313024153M

Jack L. Treynor and Fischer Black" How to Use Security Analysis to Improve Portfolio Selection It has been argued convincingly in a series of papers on the Capital Asset Pricing Model that, in the absence of insight generating expectations different from the market consensus, the investor should hold a replica of the market portfolio.' A number of empirical papers have demonstrated that portfolios of more than 50-100 randomly selected securities tend to correlate very highly with the market portfolio, so that, as a practical matter, replicas are relatively easy to obtain. If the investor has no special insights, therefore, he has no need of the elaborate balancing algorithms of Markowitz and Sharpe.2 On the other hand if he has special insights, he will get little, if any, help from the portfolio-balancing literature on how to translate these insights into the expected returns, variances, and covariances the algorithms require as inputs. What was needed, it seemed to us, was exploration of the link between conventional subjective, judgmental, work of the security analyst, on one hand-rough cut and not very quantitative-and the essentially objective, statistical approach to portfolio selection of Markowitz and his successors, on the other. The void between these two bodies of ideas was made manifest by our inability to answer to our own satisfaction the following kinds of questions: Where practical is it desirable to so balance a portfolio between long positions in securities considered underpriced and short positions in securities considered overpriced that market risk is completely eliminated (i.e., hedged)? Or should one strive to diversify a portfolio so completely that only market risk remains? As this implies, in the highly diversified portfolio market sensitivity in individual securities seems to contribute directly to market sensitivity in the overall portfolio, whereas other sources of return variability in individual securities seem to average out. Does this mean that the latter sources * Editor, Financial A nalysts Journal; professor of finance, University of Chicago; and executive director, Center for Research in Security Prices. 1. William F. Sharpe, "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk," Journal of Finance 19, no. 3 (September 1964): 425-42; John Lintner, "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets," Review of Economics and Statistics 57, no. 1 (February 1954): 13-37; and Jack L. Treynor's paper, "Toward a Theory of the Market Values of Risky Assets" (unpublished, 1961). 2. Harry Markowitz, Portfolio Selection: Efficient Diversification of Investments (New York: John Wiley & Sons, 1959; New Haven, Conn.: Yale University Press, 1970); and William Sharpe, "A Simplified Model for Portfolio Analysis," Management Science 9 (January 1963): 277-93. 66 This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:47:55 AM All use subject to JSTOR Terms and Conditions

Security Analysis to Improve Portfoli of variability are unimportant in portfolio selection? When balancing risk against expected return in selection of individual securities, what risk and what return are relevant? Will increasing the number of securities analyzed improve the diversification of the optimal port- folio? Is any measure of the contribution of security analysis to port- folio performance invariant with respect to both levering and turnover? How do analysts opinions enter in security selection? Is there an simple way to characterize the quality of security analysis that will tell us when one analyst can be expected to make a greater contribu tion to a portfolio than another? What role, if any, does confidence in an analysts forecasts have in portfolio selection? This paper offers answers to these questions. The paper has a normative favor. We offer no apologies for this. In some cases, institutional practice and, in some cases, law are short sighted; in all cases they reflect what is by anybody's standard an old fashioned idea of what the about. If we tried to develop a body of theory which reflected some of the constraints imposed institutionally and legally, it would inevitably on an idealized world in which there are no restrictions on borrowing, or on selling securities short; in which the interest rate on loans is equal to the interest rate on short-term assets such as savings accounts; and in which there are no taxes, We expect that the major conclusions derived from the model will largely be valid, however, even with the constraints and frictions of the real world Those that are not valid can usually be modified to fit the constraints that actually exist Certain recent research has suggested that professional invest ment managers really have not been very successful, but we make the assumption that security analysis, properly used, can improve portfolio performance. This paper is directed toward finding a way to make the best possible use of the information provided by security The basic fact from which we build is one that a number of writers have recognized-namely, that there is a high degree of co- prices. Perhaps the simplest mo ability among securities is Sharpe's Diagonal Model. As Sharpe sees it, The major characteristic of the Diagonal Model is the assumption that e returns of various securities are related only through common elationships with some basic underlying factor... This model has two irtues: it is one of the simplest which can be constructed without assuming away the existence of interrelationships among securities and there is considerable evidence that it can capture a large part of such interrelationships. This paper takes Sharpe's Diagonal Model as its 3. Michael Jensen. "The Performance of Mutual Funds in the Period 1945- 1964,"Journal of Finance 23(May 1968): 389-41 Cone doal25m313024153M

67 Security Analysis to Improve Portfolio of variability are unimportant in portfolio selection? When balancing risk against expected return in selection of individual securities, what risk and what return are relevant? Will increasing the number of securities analyzed improve the diversification of the optimal portfolio? Is any measure of the contribution of security analysis to portfolio performance invariant with respect to both levering and turnover? How do analysts' opinions enter in security selection? Is there any simple way to characterize the quality of security analysis that will tell us when one analyst can be expected to make a greater contribution to a portfolio than another? What role, if any, does confidence in an analyst's forecasts have in portfolio selection? This paper offers answers to these questions. The paper has a normative flavor. We offer no apologies for this. In some cases, institutional practice and, in some cases, law are shortsighted; in all cases they reflect what is by anybody's standard an oldfashioned idea of what the investment management business is all about. If we tried to develop a body of theory which reflected some of the constraints imposed institutionally and legally, it would inevitably be a theory with a very short life expectancy. Our model is based on an idealized world in which there are no restrictions on borrowing, or on selling securities short; in which the interest rate on loans is equal to the interest rate on short-term assets such as savings accounts; and in which there are no taxes. We expect that the major conclusions derived from the model will largely be valid, however, even with the constraints and frictions of the real world. Those that are not valid can usually be modified to fit the constraints that actually exist. Certain recent research has suggested that professional investment managers really have not been very successful,' but we make the assumption that security analysis, properly used, can improve portfolio performance. This paper is directed toward finding a way to make the best possible use of the information provided by security analysts. The basic fact from which we build is one that a number of writers have recognized-namely, that there is a high degree of comovement among security prices. Perhaps the simplest model of covariability among securities is Sharpe's Diagonal Model. As Sharpe sees it, "The major characteristic of the Diagonal Model is the assumption that the returns of various securities are related only through common relationships with some basic underlying factor. . . . This model has two virtues: it is one of the simplest which can be constructed without assuming away the existence of interrelationships among securities and there is considerable evidence that it can capture a large part of such interrelationships."4 This paper takes Sharpe's Diagonal Model as its 3. Michael Jensen, "The Performance of Mutual Funds in the Period 1945- 1964," Journal of Finiance 23 (May 1968): 389-416. 4. See Sharpe, n. 2. This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:47:55 AM All use subject to JSTOR Terms and Conditions

The Journal of Business starting point; we accept without change the form of the Diagonal Model and most of Sharpes assu Use of the Diagonal Model for portfolio selection implies de- parture from equilibrium in the sense of all investors having the same information (and appraising it similarly )-as, for example, is assumed in some versions of the Capital Asset Pricing Model. The viewpoint in this paper is that of an individual investor who is attempting to trade profitably on the difference between his expectations and those of a monolithic market so large in relation to his own trading that market prices are unaffected it. Throughout, we ignore the costs of buying and selling. This makes it possible for us to treat the portfolio-selection problem as a single-period problem(implicitly assuming a one-period utility function as given), in the tradition of Markowitz, Sharpe, et al We believe that these costs are often substantial and, if incorporated into this analysis, would modify certain of our results substantially DEFINITIONS on short-term risk-free assets over that interval A regression of the excess return on a security against the market's excess return gives two regression factors. The first is the market or“beta.” of the securit le error the second should be zero. We define the explained return on the security over a given time interval to be its market sensitivity times the market's excess return over the interval We define the independent return to be the excess return minus the explained return. The independent return, because of the of regression, is statistically independent of the markets excess re turn. Our model assumes that the "independent returns of different securities are almost, but not quite, statistically independent. The"risk premium"on the ith security is equal to the securitys market sensitivity times the market's expected excess return. Symbols for these concepts re defined as r= riskless rate of return x turn on the ith security, yi=excess return on the ith security, ym= excess return on the market b i= market sensitivity of the ith security, bi ym= explained, or systematic, return on ith security, zi= independent return on ith Let E[ and var I represent the expectation and variance, respec tively, of the variable in brackets. Then define Cone doal25m313024153M

68 The Journal of Business starting point; we accept without change the form of the Diagonal Model and most of Sharpe's assumptions. Use of the Diagonal Model for portfolio selection implies departure from equilibrium in the sense of all investors having the same information (and appraising it similarly)-as, for example, is assumed in some versions of the Capital Asset Pricing Model. The viewpoint in this paper is that of an individual investor who is attempting to trade profitably on the difference between his expectations and those of a monolithic market so large in relation to his own trading that market prices are unaffected by it. Throughout, we ignore the costs of buying and selling. This makes it possible for us to treat the portfolio-selection problem as a single-period problem (implicitly assuming a one-period utility function as given), in the tradition of Markowitz, Sharpe, et al. We believe that these costs are often substantial and, if incorporated into this analysis, would modify certain of our results substantially. D E F I N I T I O N S Following Lintner, we define the excess return on a security for a given time interval as the actual return on the security less the interest paid on short-term risk-free assets over that interval. A regression of the excess return on a security against the market's excess return gives two regression factors. The first is the market sensitivity, or "beta," of the security; and, except for sample error, the second should be zero. We define the explained return on the security over a given time interval to be its market sensitivity times the market's excess return over the interval. We define the independent return to be the excess return minus the explained return. The independent return, because of the properties of regression, is statistically independent of the market's excess return. Our model assumes that the "independent" returns of different securities are almost, but not quite, statistically independent. The "risk premium" on the ith security is equal to the security's market sensitivity times the market's expected excess return. Symbols for these concepts are defined as: r riskless rate of return, xi return on the ith security, y- excess return on the ith security, Ym excess return on the market, bi market sensitivity of the ith security, biym explained, or systematic, return on ith security, zi independent return on ith security. Let E [ ] and var [ ] represent the expectation and variance, respectively, of the variable in brackets. Then define This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:47:55 AM All use subject to JSTOR Terms and Conditions