Performance Evaluation with High Moments and Disaster Risk

Abstract:     
Tail events and rare disasters have been fundamental to the recent financial crisis. However, traditional performance evaluation measures do not account for such events, even when they are present in the data. To address this issue, we propose reinterpreting the recent riskiness measures of Aumann and Serrano (2008) and Foster and Hart (2009) as performance indices. We derive the high moment properties of these indices and show that they are increasing in all odd moments (e.g., mean and skewness) and decreasing in all even moments (e.g., variance and tail-risk). The sensitivity of the performance indices to the moments is not monotone, implying that high moments can have a strong effect on performance. Furthermore, we show that the Foster and Hart (2009) index is extremely sensitive to the risk of rare disasters, making it a useful tool for evaluating such risks. We illustrate the applicability of these indices by using them to evaluate popular anomalies and investment strategies, and by applying them to the selection of mutual funds. Our analysis demonstrates that high moment properties and disaster risk are important factors in performance evaluation.

Number of Pages in PDF File: 47

working papers series