Abstract
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.
Highlights
New performance measures incorporating high moments and disaster risk are proposed by Kadan and Liu (2014)
The current study focuses on the issue of sensitivity of the new performance measures to disaster risk
We examined how sensitive the new performance measures of the AS and FH performance measures are to disaster risk or maximal loss
Summary
New performance measures incorporating high moments and disaster risk are proposed by Kadan and Liu (2014). Demonstrated the use of the new performance indexes is useful to provide risk-averse assessments of various assets compared to the de facto industry standard performance measure, i.e., the Sharpe ratio. These conservative assessments shed new light to provide very different evaluations compared to the Sharpe ratio, which incorporates only the first two moments. There are no further studies of the properties of the new performance measures since Kadan and Liu (2014) except Hodoshima (2019), who only studies the property of the AS performance measure. The IRRA turns out to be equivalent to the AS performance index (cf., Hodoshima and Miyahara 2020)
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