CVaR sensitivity with respect to tail thickness

► We analyze sensitivity of conditional value-at-risk (CVaR) to tail index. ► CVaR sensitivity to tail index is finite for regularly varying tails. ► Stable Paretian, Student's t, and generalized normal laws are studied. ► We discuss implications for modeling returns and marginal rebalancing decisions. ► Empirical results for US, Japan, and European equity markets are reported.