Sharpe Ratios and Their Fundamental Components : An Empirical Study

In this article, we considered a risk-adjusted performance measure which benefits from a large success among the portfolio management community. Namely, Sharpe ratio considers the ratio of a given stock's excess return to its corresponding standard deviation. Excess return is commonly thought as a performance indicator whereas standard deviation is considered as a risk adjustment factor. However, such considerations are relevant in a stable setting such as a Gaussian world. Unfortunately, Gaussian features are scarce in the real world so that Sharpe performance measure suffers from various biases. Such biases arise from deviations from normality such as skewness and kurtosis patterns, which often exhibit the non-negligible weights of large and/or extreme return values. To bypass the potential biases embedded in Sharpe ratios, we propose a robust filtering method based on Kalman estimation technique so as to extract fundamental Sharpe ratios from their observed counterparts. Obtained fundamental Sharpe ratios are free of bias and exhibit a pure performance indicator. Results are interesting with regard to two findings. First, fundamental Sharpe ratios are obtained after removing directly the market trend impact whereas the kurtosis bias is removed at the volatility level. Second, fundamental Sharpe ratios exhibit a cross section dependency in the light of the well known size and book-to-market factors of Fama and French [1993]. Consequently, it is possible to extract pure performance and bias-free indicators, which are of primary importance for asset selection and performance ranking. Indeed, such concern is of huge significance given that the asset allocation policy, performance forecasts and cost of capital assessment, among others, are driven by performance indicators (Farinelli, Ferreira, Rossello, Thoeny, and Tibiletti [2008]; Lien [2002]; Christensen, and Platen [2007])