A hybrid approach to the discrepancy in financial performance’s robustness

Performance measurement is a crucial ingredient in the industry of investment funds. Mainly grounded on indices of risk-adjusted returns, it requires historical data to estimate the relevant statistics such as the Sharpe ratio. Therefore the measurement process is sensitive to outliers in the time series underlying historical data. Since alternative measures are available for performance evaluation, we propose an iterative methodology for a set of eleven indices (including the Sharpe ratio) in order to: (a) quantify their intrinsic degree of statistical robustness; (b) find different sensitivity to alternative outliers configuration. This methodology is a combination of a reasonable definition of breakdown point and the definition of discrepancy of a finite point set. A suitable Monte Carlo simulation provides numerical evidence of changing sensitivity among all considered performance measures, instead the classical definition of breakdown point only shows lack of robustness among all indices without further specification. Our approach may be useful in choosing the most robust performance measure to be employed in investment management, especially when robust portfolio optimization has to be used.