We consider a nonparametric method to estimate the expected shortfall, i.e.\ 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. Monte Carlo experiments with a vector autoregressive process of order one and truncated loss distributions with a generalized Pareto distributed right tail are reported to assess the behavior of the estimators. An empirical illustration is given for a portfolio of French stocks. Another empirical illustration deals with Danish data on fire insurance losses.

Keywords : Nonparametric, Kernel, Time Series, Expected Shortfall, Incremental  Expected Shortfall, Risk Management, Risk Adjusted Performance Measure, Portfolio Selection,  Loss Severity Distribution.

JEL : C14, D81, G10, G21, G22, G28.