The Capital Asset Pricing Model and the Investment Horizon

Abstract

TN following the mean-variance analysis developed by Markowitz (1952) and Tobin (1958), Sharpe (1964), Lintner (1965a, b) and Treynor (1961) have developed the theory for determination of asset prices under conditions of uncertainty. The equilibrium asset pricing model, and its implication for measuring ex post performance of individual securities, have been empirically tested by Lintner,1 Jensen (1968, 1972), Miller and Scholes (1972), Douglas (1969), Roll (1969) and others. The empirical results obtained by both Douglas and Lintner deviated from the theory of the model. Moreover, Miller and Scholes have run empirical tests similar to those of Douglas and Lintner and found a significant disparity between the theoretical model and the empirical evidence. They maintain that part of this discrepancy can be explained by possible statistical biases, measurement errors, and consideration of the skewness of the distribution of returns. Black, Jensen, and Scholes (1972) (hereafter B-J-S) confirm the systematic bias. Using monthly data covering a 35 year period, they discovered that, on average, high risk securities earned less than the amount predicted by the model. Similarly, earnings on low risk securities exceeded the amount predicted.2 Although these disparities clearly suggest some systematic empirical bias, we are not examining a possible statistical bias but a mathematical bias stemming from one of the assumptions underlying the capital asset pricing model (CAPM). To be more specific, the model assumes that all investors are single period, expected utility of terminal wealth maximizers. There is no particular restriction on the length of this period as long as it is identical for all investors. Clearly, the length of the true investment horizon affects asset prices under conditions of uncertainty. We claim that the disparities noted above may result from using data calculated for an investment horizon that differs from the true investment horizon. In the various empirical tests, the investment horizon has been selected arbitrarily. For example, Lintner and Miller and Scholes use annual data (i.e., they implicitly assume a one-year horizon), Douglas uses quarterly and annual data; Black, Jensen and Scholes, as well as Friend and Blume (1970), use monthly rates of return in their empirical tests, while Roll uses weekly data. It has been shown elsewhere by Levy (1972) that the Reward to Variability index (developed by Sharpe, 1966) is a function of the investment horizon assumed. Hence, there exists a systematic mathematical bias that is a function of the horizon assumed. The above theoretical findings are related to the theory of pricing capital assets, but deal only with efficient portfolios and not individual stocks. In this paper we illustrate that the assumed horizon plays a crucial role in empirical testing. Any deviation from the true horizon causes a systematic bias in the regression coefficient (i.e., in the security systematic risk). This in turn causes a systematic bias in the performance measures of each security, and hence the deviation between the theoretical model and the empirical evidence. The results of this paper are not limited to the theory of pricing capital assets; they are applicable to any econometric study in which the variables have multiplicative rather than additive properties. In such a case the regression coefficients will have a matheReceived for publication February 27, 1975. Revision accepted for publication March 8, 1976. The authors acknowledge the technical assistance of Moshe Smith and two anonymous referees. The first author has been partially financed by the Maurice Falk Foundation, and the second author has been financed by the Ford Foundation. 1 Lintner's paper Security Prices and Risk: The Theory and a Comparative Analysis of A.T.&T. and Leading Industrials was presented at the Conference on Economics of Regulated Public Utilities, June 24, 1965, Chicago. 2 Miller and Scholes show that the presence of certain biases could have accounted for the Douglas and Lintner findings. BJ-S maintain that the assumption of borrowing at riskless interest rates could have accounted for these deviations.