The measure of relative risk aversion in the consumption CAPM with power utility

The study shows that in the consumption CAPM with power utility the Arrow--Pratt measure of relative risk aversion differs from the utility curvature parameter when the lottery an individual faces is not actuarially neutral. This implies that the measure of relative risk aversion in the CCAPM with power utility may be different for different individuals and may change over time even when the agents are assumed to have homogeneous preferences which are presented by the power utility function with the time-invariant curvature parameter. Another implication is that the elasticity of intertemporal substitution deviates from the reciprocal of the relative risk aversion coefficient unless the lottery is actuarially neutral. The study also shows the importance of the result obtained for assessing the empirical performance of the CCAPM with power utility.