Risk and Return Revisited

Abstract

This paper questions the CAPM's assumption of global risk-aversion. I develop an expected return-risk framework that allows tests of restrictions on marginal utility conditional on the states-of-the-world. Empirical tests using monthly stock returns data show a decreasing marginal utility from the states of market losses (Region L1) to the large decumulative probability states of market gains (Region G2) and an increasing marginal utility from Region G2 to small decumulative probability states of market gains (Region G1). The latter is in contrast to the globally decreasing marginal utility implied by the CAPM's assumption of risk-aversion, but consistent with the prediction of Singh's (2006) model with biases in beliefs that implies risk-seeking behavior over Region G1. Moreover, in the specification where the distribution of market returns is divided into the 3 regions with an objective probability of 0.30 each, the difference between objective probability and risk-neutral probability of Regions L1, G2 and G1 are -0.05, 0.08 and -0.03 respectively. This is in sharp contrast to the CAPM's prediction that this difference for Region G1 must be positive and larger than that of Region G2, but is consistent with Singh's (2006) model. The paper also provides evidence that assets that have higher returns when the market returns are high have lower average returns, in contrast to the CAPM's prediction of higher average returns.