Risk Policy and Long-Term Investment

Abstract

Empirical tests of the Sharpe-Lintner-Black - Capital Asset Pricing Model (CAPM) have generally concluded that there is a positive, approximately linear, trade-off between average return and systematic risk (beta) for portfolio returns of common stocks. Most of the empirical studies, however, have reported data for short, usually monthly, time intervals. Exceptions to this rule include Blume and Friend and Sharpe. pp. 289-292. Their data provide evidence that long-term wealth ratios are concave, possibly non-monotonic, functions of beta. These data are surprising since, if returns are inter-temporally independent and the linear return model of CAPM is correct, expected multiperiod terminal wealth is a convex, monotone increasing function of beta. The results of this paper provide a theoretical framework for interpreting the long-term empirical data which does not violate the notion of a monotone increasing expected terminal wealth-beta relationship.