Notes on Fano Ratio and Portfolio Optimization

Journal of Risk & Control 5(1) (2018) 1-33

29 Pages Posted: 10 Oct 2017 Last revised: 18 Apr 2018

See all articles by Zura Kakushadze

Zura Kakushadze

Quantigic Solutions LLC; Free University of Tbilisi

Willie Yu

Duke-NUS Medical School - Centre for Computational Biology

Date Written: October 9, 2017


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

Suggested Citation

Kakushadze, Zura and Yu, Willie, Notes on Fano Ratio and Portfolio Optimization (October 9, 2017). Journal of Risk & Control 5(1) (2018) 1-33. Available at SSRN: or

Zura Kakushadze (Contact Author)

Quantigic Solutions LLC ( email )

1127 High Ridge Road #135
Stamford, CT 06905
United States
6462210440 (Phone)
6467923264 (Fax)


Free University of Tbilisi ( email )

Business School and School of Physics
240, David Agmashenebeli Alley
Tbilisi, 0159

Willie Yu

Duke-NUS Medical School - Centre for Computational Biology ( email )

8 College Road
Singapore, 169857

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