Định giá tài sản rủi ro và đánh giá danh mục đầu tư theo Michael Jensen

Risk, The Pricing of Capital Assets, and The Evaluation of Investment Portfolios Michael C. Jensen The Journal of Business, Vol. Stable URL: http://links.org/sici?sici=0021-9398%28196904%2942%3A2%3C167%3ARTPOCA%3E2.CO%3B2-Z The Journal of Business is currently published by The University of Chicago Press. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.org/about/terms.

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INTRODUCTION certain streams. Under these conditions A. RISK L I D THE EVALUATION investors will accept additional risk O F PORTFOLIOS only if they are compensated for it in the HE main purpose of this study is the form of higher expected future returns. T development of a model for evalu- ating the performance of portfolios of risky assets.

In evaluating the per- Thus, in a world dominated by risk- averse investors, a risky portfolio must be expected to yield higher returns than formance of portfolios the effects of dif- a less risky portfolio, or it would not ferential risk must be taken into con- be held.' If investors are generally The portfolio evaluation model devel- averse to risk, they will prefer (ceteris pa- oped below incorporates these risk as- ribus) more certain income streams to less pects explicitly by utilizing and extend- ing recent theoretical results by Sharpe * The research on this study was supported by [52] and Lintner [37] on the pricing of fellowship grants from the U. Steel Foundation, capital assets under uncertainty. Given the American Banking Association and a research grant from the Research Fund in Finance made these results, a measure of portfolio "per- available by the University of Chicago Graduate formance" (which measures only a man- School of Business. Extensive computer time at the ager's ability to forecast security prices) 7094 Computation Center at the University of Chi- cago was financed by the Graduate School of Busi- is defined as the difference between the ness, and the College of Business of the University of actual returns on a portfolio in any par- Rochester provided additional time at the 360 Com- ticular holding period and the expected putation Center a t the University of Rochester.

returns on that portfolio conditional on t Assistant professor, College of Business Admin- the riskless rate, its level of "systematic istration, University of Rochester. I wish to ac- knowledge a great debt to my dissertation commit- risk," and the actual returns on the mar- tee; Eugene Fama (chairman), Lawrence Fisher, ket portfolio. Criteria for judging a port- Merton Miller (who originally suggested this area folio's performance to be neutral, superior, of research to me), and Harry Roberts, all of whom have given generously of their time and ideas and or inferior are established. have continually forced me to rethink and defend A measure of a portfolio's "efficiency" my position on numerous issues.

I am especially in- is also derived, and the criteria for judg- debted to Professor Fama for his penetrating criti- cisms of several drafts of this paper. I also wish to ing a portfolio to be eficient, superefi- thank the members of the Finance Workshop a t the cient, or ine$icient are defined. I t is also University of Chicago for many stimulating and shown that it is strictly impossible to de- helpful discussions, especially M. I have also benefited from fine a measure of efficiency solely in conversations with M.

Black, and Profes- terms of ex post observable variables. In sors Peter Pashigian, Arnold Zellner, Donald Gor- addition, it is shown that there exists a don, and Julian Keilson. natural relationship between the meas- Risk, a critical concept in this paper, will be de- fined and discussed extensively in Sections 11, 111, ure of portfolio performance and the and V. measure of efficiency.

168 THE JOURNAL OF BUSINESS B. SECURITY PRICE MOVEMENTS, EFFICIENT prices to forecast future prices are MARKETS, MARTINGALES AND THEIR IMPLI- doomed to failure. The best forecast of CATION FOR SECURITY ANALYSIS future price is merely the present price There has recently been considerable plus the normal expected return over the interest in the behavior of security prices period. in an "efficient market" and more spe- The stock market has been subjected cifically in the martingale hypothesis of to a great deal of empirical investigation price behavior.

There seem to be two dif- aimed a t determining whether (1.1) is an ferent forms of the hypothesis which adequate description of the serial be- have arisen out of differing definitions of havior of stock price^.^ The available evi- the concept of an "efficient market," defi- dence suggests that it is highly unlikely nitions which are seldom explicitly enu- that an investor or portfolio manager merated. will be able to use the past history of One can define a weakly efficient mar- stock prices alone (and hence mechani- ket in the following sense: Consider the cal trading rules based on these prices4) arrival in the market of a new piece of to increase his profits. information concerning the value of a se- However, the conclusion that stock curity. A weakly efficient market is a mar- prices follow a submartingale of the form ket in which it may take time to evaluate (1 .l) does not imply that an investor can- this information with regard to its impli- not increase his profits by improving his cations for the value of the security.

Once ability to predict and evaluate the con- this evaluation is complete, however, the sequences of future events affecting stock price of the security immediately adjusts prices. Indeed, it has been suggested by (in an unbiased fashion) to the new value Fama [I21 that the existence of sophisti- implied by the information. I n such a cated "market participants" who are weakly efficient market, the past price adept a t evaluating current information series of a security will contain no infor- and predicting future events is one of the mation not already impounded in the cur- reasons why market prices a t any point rent price. Mandelbrot [39] and Samuel- in time represent an unbiased estimate son 1477 have rigorously demonstrated of "true" values and adjust rapidly, and that prices in such a market will follow a accurately, to new information regarding submartingale-that is, the expected these value^.^ + value of all future prices X(t T), (7 = 1, This brings us to an alternative defini-.

a), as of time t is independent of tion of an "efficient market,'' that is, one the sequence of past prices X(t - 7 ) , in which all past information available (7 = 1 ,. a),and is equal to: up to time t is impounded in the current where f(r) is the "normal" accumula- Charting techniques are one example. 3 See especially the work by Fama [12] and the works reprinted in Cootner [9]. Thus, in a market in which security 'For an example of the testing of one class of prices behave as a submartingale of the such rules see [12].I), forecasting techniques2 6 For an example of an examination of such ad- which use only the sequence of past justment, see Fama et al.

RISK, C A P I T A L ASSETS, A N D EVALUATION O F P O R T F O L I O S 169 price. Within this definition of an effi- able to earn them systematically through cient market the Mandelbrot-Samuelson time. proofs imply that the martingale prop- While the weak form of the martingale erty can be written as hypothesis is well substantiated by em- pirical evidence, the strong form of the hypothesis has not as yet been subjected where the conditioning variable O t now to extensive empirical tests.8 The model represents all information available a t developed below will allow us to submit time t.'j The reader will note that (1.2) the strong form of the hypothesis to such is a much stronger form of the martin- an empirical test-at least to the extent gale hypothesis than (1.1), which is con- that its implications are manifested in ditioned only on the past price series. As the success or failure of one particular such (1.2) might be labeled the "strong" class of extremely well-endowed security form of the martingale hypothesis and analysts.1) the ((weak" form.' Indeed, if secu- C.

APPLICATIONS O F THE MODEL rity prices follow a martingale of the strong form, no analyst will be able to The portfolio evaluation model devel- earn above-average returns by attempt- oped below will be used to examine the ing to predict future prices on the basis results achieved by the portfolio man- of past information. The only individual agers of open end mutual funds in an at- able to earn superior returns will be that tempt to answer the following questions: person who occasionally is the first to 1) Do the historical patterns of risk acquire a new piece of information not and return observed for our sample of generally available to others in the mar- portfolios of risky assets indicate a pre- ket. But as Roll [46] argues, in attempt- dominance of risk aversion in the capital ing to act immediately on this informa- markets? If so, do these patterns confirm tion, this individual (or group of indi- the implications of the theoretical models viduals) will insure that the effects of of capital asset pricing founded on the this new information are quickly im- assumption of risk aversion? pounded in the security's price. Further- 2) Have open-end mutual funds in more, if new information of this type general exhibited an ability to select arises randomly, no individual will be portfolios which earn returns higher than able to assure himself of systematic re- those they may have been expected to ceipt of such information.

Therefore, earn given their level of risk? Altern- while an individual may occasionally re- atively, have they exhibited an ability to alize such windfall returns, he will be un- earn returns higher than those which could have been earned by a naive selec- 6 See Roll [46] for a discussion of the reasoning tion policy consistent with the theory of which leads to (1. capital asset pricing? 7 To the best of my knowledge, this terminology The main conclusions will be: is due to Harry Roberts, who used it in an unpub- lished speech entitled "Clinical vs. Statistical Fore- 1) The observed historical patterns of casts of Security Prices," given a t the Seminar on systematic risk and return for the mutual the Analysis of Security Prices sponsored by the funds in the sample are consistent with Center for Research in Security Prices a t the Univer- sity of Chicago, May, 1967. 8The only evidence on this question that I am Subsequent to writing the present paper, an ar- aware of is contained in Fama et d.1191, and that ticle by Shelton [59] has appeared which contains a evidence suggests that security prices adjust rapidly very similar statement of the hypotheses.

and in an unbiased fashion to new information.