CVaR sensitivity with respect to tail thickness

The sensitivity of a risk measure with respect to the parameters of the hypothesized distribution is a useful tool in investigating the impact of marginal rebalancing decisions on the portfolio return distribution and also in the analysis of the asymptotic variability of the risk estimator. We calculate the relative importance of the conditional value-at-risk (CVaR) sensitivity with respect to tail thickness and scale of the portfolio return distribution in the case of regularly varying tails and in the case of exponential and faster-than-exponential decay. We discuss the implications for asset return modeling and the asymptotic variability of the risk estimator.