Capital Asset Pricing Model and the Risk Appetite Index: Theoretical Differences, Empirical Similarities and Implementation Problems*

Abstract

AbstractWe perform 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's study (2003), we first argue that the theoretical assumptions granting that the RAI correctly distinguishes between changes in risk and changes in risk aversion are very restrictive. Then, by comparing the RAI with a measure of risk aversion obtained from the Capital Asset Pricing Model (CAPM), we find that the 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 RAI and CAPM suffer from exactly the same implementation problems – the main one being the difficulty in measuring ex‐ante returns. At high and medium frequencies, the standard method of measuring ex‐ante with ex‐post returns may generate negative risk aversion and other inconsistencies. Hence, future research is needed to address this problem.