Estimating Fundamental Sharpe Ratios: A Kalman Filter Approach

Abstract

A wide community of practitioners still focuses on classic Sharpe ratio as a risk adjusted performance measure due to its simplicity and easiness of implementation. Performance is computed as the excess return relative to the risk free rate whereas risk adjustment is provided by the asset return’s volatility as a denominator. However, such risk/return representation is only relevant under a Gaussian world. Moreover, Sharpe ratio exhibits time variation and can also be biased by market trend and idiosyncratic risk. As an implementation, we propose to filter out classic Sharpe ratios (SR) so as to extract their fundamental component on a time series basis. Time-varying filtered Sharpe ratios are obtained while employing the Kalman filter methodology. In this light, fundamental/filtered Sharpe ratios (FSR) are free of previous reported biases, and reflect the pure performance of assets. A brief analysis shows that SR is strongly correlated with other well-known comparable risk-adjusted performance measures while FSR exhibits a low correlation. Moreover, FSR is a more efficient performance estimator than previous comparable risk adjusted performance measures because it exhibits a lower standard deviation. Finally, a comparative analysis combines GARCH modeling, extreme value theory, multivariate copula representation and Monte Carlo simulations. Based on 10 000 trials and building equally weighted portfolios with the 30 best performing stocks according to each considered performance measure, the top-30 FSR portfolio offers generally higher perspectives of expected gains as well as reduced Value-at-Risk forecasts (i.e. worst loss scenario) over one week and one-month horizons as compared to other performing portfolios.