Sensitivity of performance indexes to disaster risk

We examine how sensitive the new performance indexes incorporating high moments and disaster risk are to disaster risk. The new performance indexes incorporating high moments and disaster risk are the Aumann-Serrano performance index and Foster-Hart performance index proposed by Kadan and Liu. These performance indexes provide evaluations sensitive to the underlying risk. We show, by numerical examples and empirical examples, how sensitive these indexes are to disaster risk. Although these indexes are known to be either quite sensitive or excessively sensitive to disaster risk or maximum loss in the literature, we show by the regression analysis of the index and summary statistics these indexes are in fact not excessively sensitive to maximum loss in representative stock data, which contain disastrous observations. The numerical estimate of the Foster-Hart performance index is found to be effective in showing the performance index. Our analysis suggests these indexes can handle various empirical data containing quite disastrous observations.