Ranking of Investment Funds: Acceptability Versus Robustness

Within the class of performance ratios, the Sharpe measure can lead to misleading evaluation and various modifications have been investigated. As a starting point, we consider the axiomatic approach based on the notion of acceptable index of performance. Our goal is to show how the promising properties possessed by alternative measures such as the Gain–Loss ratio or the Average-Value-at-Risk ratio are not compatible with the statistical robustness of their estimated counterparts. This clearly affects the ranking of funds and consequently the performance persistence. We study the qualitative robustness along with the quantitative resistance of the corresponding estimators in a nonparametric setting. We include the Value-at-Risk ratio which is not an acceptability index of performance. These measures do not possess qualitative robustness, nonetheless we show how some degree of resistance to data contamination restricted to bounded intervals can be recovered. Using the relationship between the influence function of estimators and their bias for large samples, we suggest the Average-Value-at-Risk ratio and the Value-at-Risk ratio as the less sensitive to outliers. As a consequence, acceptability is no longer a prerequisite for performance evaluation. To limit the alteration of a given ranking among alternative investment funds, one can use the not acceptable Value-at-Risk ratio as well. Eventually, we propose a modified ratio either of the α-trimmed mean or of the median to the Value-at-Risk.