The CAPM and the Risk Appetite Index: Theoretical Differences, Empirical Similarities, and Implementation Problems

Abstract

We make a thorough analysis of the Risk Appetite Index (RAI), a measure of changes in risk aversion proposed by Kumar and Persaud (2002). Building on Misina (2003), we first argue that the theoretical assumptions granting that the RAI correctly distinguishes between changes in risk versus changes in risk aversion are very restrictive. Then, by comparing the RAI with a measure of risk aversion obtained from the CAPM, we find that estimates are surprisingly similar. We prove that, if the variance of returns is sufficiently smaller than the variance of asset riskiness, then RAI and CAPM provide essentially the same information about risk aversion. We also show, however, that the RAI and the CAPM suffer from exactly the same implementation problems - the main one being the difficulty in measuring expected returns. At high and medium frequencies, the standard method of using ex post returns generates negative risk aversions and other inconsistencies. Hence, future research is needed to address this problem.

Keywords: risk aversion, asset pricing, financial crisis

JEL Classification: G11, G12