Beta in Linear Risk Tolerance Economies

Management Science · 1985 · Volume 31 · Issue 11

Abstract

This paper employs numerical means to examine: (i) the expected return-beta plot in power utility Linear Risk Tolerance (LRT) economies, and (ii) whether, in the power utility economies, a valuation equation containing covariance and coskewness terms might better explain expected returns than one containing covariance terms alone. The results show that the expected return-beta plots constructed from real world return distributions are very similar to the plots found in empirical tests of the Mean Variance Capital Asset Pricing Model (MV CAPM). Hence a power utility LRT CAPM may provide a better theory of asset pricing than the MV CAPM does. While beta is not the correct measure of risk in power utility LRT economies, the results show that on average a valuation equation containing covariance terms only explains expected returns better than a valuation equation containing both covariance and coskewness terms.

Keywords

portfolio selection, linear risk tolerance, utility functions, generalized risk measures, capital asset pricing

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