Notes on Fano Ratio and Portfolio Optimization

TL;DR

This paper explores generalized mean-to-risk ratios for portfolio optimization, focusing on the Fano ratio, which offers advantages over the Sharpe ratio, including horizon independence and improved diversification, with explicit algorithms and backtest results.

Contribution

It introduces the Fano ratio as a new mean-to-risk metric, providing explicit optimization algorithms and demonstrating its benefits over the Sharpe ratio in portfolio diversification and performance.

Findings

Fano ratio is horizon-independent and promotes diversification.

Optimizing Fano ratio can outperform Sharpe ratio-based strategies.

Backtests show improved long-short strategy performance.

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.