Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall

We consider a nonparametric method to estimate the expected shortfall—that is, the expected loss on a portfolio of financial assets knowing that the loss is larger than a given quantile. We derive the asymptotic properties of the kernel estimators of the expected shortfall and its first‐order derivative with respect to portfolio allocation in the context of a stationary process satisfying strong mixing conditions. An empirical illustration is given for a portfolio of stocks. Another empirical illustration deals with data on fire insurance losses.