Influence Functions for Risk and Performance Estimators

We first provide a brief introduction to influence functions and their use for computing standard errors of risk and performance estimators. We then derive the influence functions for a number of risk estimators and a number of performance estimators, and use the formulas to graphically display the shapes of the various influence functions. The latter provide a useful basis for comparing different risk and performance estimators with regard returns data influence on the estimators, including the influence of outliers and the appropriateness of the estimators with regard to how they reflect gains, losses, and performance. We briefly discuss an R package RPEIF, available on CRAN, forcomputing and plotting influence functions of risk and performance estimators