Notes on Fano Ratio and Portfolio Optimization

Abstract

We discuss - in what is intended to be a pedagogical fashion - generalized "mean-to-risk" ratios for portfolio optimization. The Sharpe ratio is only one example of such generalized "mean-to-risk" ratios. Another example is what we term the Fano ratio (which, unlike the Sharpe ratio, is independent of the time horizon). Thus, for long-only portfolios optimizing the Fano ratio generally results in a more diversified and less skewed portfolio (compared with optimizing the Sharpe ratio). We give an explicit algorithm for such optimization. We also discuss (Fano-ratio-inspired) long-short strategies that outperform those based on optimizing the Sharpe ratio in our backtests.

Keywords: Portfolio, Stocks, Equities, Optimization, Sharpe Ratio, Fano Ratio, Risk, Return, Expected Return, Alpha, Specific Risk, Idiosyncratic Risk, Factor Loadings, Factor Covariance Matrix, Risk Factor, Volatility, Variance, Covariance, Correlation, Bounds, Trading Costs, Constraints, Regression, Weights

JEL Classification: G00