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Sunday, May 28, 2006

RISK, THE PRICING OF CAPITAL ASSETS, AND THE EVALUATION OF INVESTMENT PORTFOLIOS (2)


The main purpose of this study is the development of a model for evalu­ating the performance of portfolios of risky assets. In evaluating the per­formance of portfolios the effects of dif­ferential risk must be taken into con­sideration.1 If investors are generally averse to risk, they will prefer (ceteris pa-Hbus) more certain income streams to less certain streams. Under these conditions investors will accept additional risk only if they are compensated for it in the form of higher expected future returns. Thus, in a world dominated by risk-averse investors, a risky portfolio must be expected to yield higher returns than a less risky portfolio, or it would not be held.

The portfolio evaluation model devel­oped below incorporates these risk as­pects explicitly by utilizing and extend­ing recent theoretical results by Sharpe [52] and Lintner [37] on the pricing of capital assets under uncertainty. Given these results, a measure of portfolio "per­formance" (which measures only a man­ager's ability to forecast security prices) is denned as the difference between the actual returns on a portfolio in any par­ticular holding period and the expected returns on that portfolio conditional on the riskless rate, its level of "systematic risk," and the actual returns on the mar­ket portfolio. Criteria for judging a port­folio's performance to be neutral, superior, or inferior are established.
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Risk, the Pricing of Capital Assets, and the Evaluation of Investment Portfolios: Comment

In a classic article appearing in this Journal, Jensen presented empirical re­sults from which he concluded that mutual fund portfolios showed "inferior" performance over the 10-year period 1955-64 after the deduction of all oper­ating expenses, management fees, and brokerage commissions generated in trading activity.1 Jensen argued further that, as a group, the mutual funds performance was neutral when all operating expenses and brokerage commissions were added back to the fund returns; therefore, the resources spent by the funds in attempting to forecast security prices did not yield higher portfolio returns than those which could have been earned by randomly gen­erated portfolios. Finally, Jensen suggested that his evidence supported the "strong" form of the efficient market hypothesis—that is, the current prices of securities completely reflect the effects of all information concerning the securities, and efforts to acquire and analyze this information cannot pro­duce consistently superior results.
This comment will demonstrate that Jensen's empirical analysis and conclusions were based on questionable methods of estimating the mutual fund rates of return and levels of systematic risk. More specifically, it will be shown that Jensen's methodology (1) understated the mutual fund rates of return (and therefore understated the measures of excess return), and (2) introduced unnecessary measurement error into the analysis by assum­ing that the measures of systematic risk for the mutual funds were station­ary over time.
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MUTUAL FUND PERFORMANCE


Within the last few years consider­able progress has been made in three closely related areas—the theory of portfolio selection,1 the theory of the pricing of capital assets under con­ditions of risk,2 and the general behavior of stock-market prices.3 Results obtained in all three areas are relevant for evalu­ating mutual fund performance. Unfor­tunately, few of the studies of mutual funds have taken advantage of the sub­stantial backlog of theoretical and em­pirical material made available by recent studies in these related areas. However, one paper pointing the direction for future studies of mutual fund performance has appeared. Drawing on results ob­tained in the field of portfolio analysis, Jack L. Treynor has suggested a new predictor of mutual fund performance4— one that differs from virtually all those used previously by incorporating the vol­atility of a fund's return in a simple yet meaningful manner.

This paper attempts to extend Trey-nor's work by subjecting his proposed measure to empirical test in order to evaluate its predictive ability. But we will also attempt to do something more —to make explicit the relationships be­tween recent developments in capital theory and alternative models of mutual fund performance and to subject these alternative models to empirical test...
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