Risk, The Pricing of Capital Assets, and The Evaluation of Investment Portfolios

Abstract

THE MAIN PURPOSE of this study is to develop a model for evaluating the of portfolios of risky assets. The model begins from the Sharpe-Lintner theory of capital-asset prices, but allows explicitly for the effects of differential degrees of risk on the returns of portfolios-a problem which has never been satisfactorily solved. The Sharpe-Lintner results (originally detived in the context of a singleperiod model under the assumption of identical investor horizons) are extended to a multi-period world. In this model investors' horizons may be of different lengths and assets may be traded continuously. In addition, the Sharpe-Lintner ex ante model is extended to include ex post relationships. The resulting model expresses the expected returns on a security (or portfolio) as a function of its level of the risk-free return, and the actual realized returns (instead of the expected future return) on the over any holding period. Given these results, a measure of portfolio performance (which measures only a manager's ability to forecast security prices) is defined 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 to be neutral, superior, or inferior are established. A measure of a portfolio's efficiency is also derived, and criteria for judging a portfolio to be efficient, superefficient, or inefficient are defined. It is also shown that it is strictly impossible to define a measure of efficiency solely in terms of ex post observable variables. In addition it is shown that there exists a natural relationship between the measure of portfolio and the measure of efficiency. The model is then applied to the evaluation of the portfolios of 115 open-end mutual funds in the period 1945-1964. The main results are: