Comparing Sharpe Ratios with Factor Alpha

Summary

The note distinguishes a portfolio’s Sharpe ratio from its alpha estimated against the Fama–French factors. Sharpe measures excess return relative to total return variability and can help compare portfolios. Alpha is benchmark-relative, so comparisons are meaningful only when portfolios use the same benchmark.

For a fairer comparison, the response suggests scaling portfolios to similar variance before comparing their alphas. It recommends reporting mean excess return, factor alpha, Sharpe ratio, and beta to the selected benchmark, with performance measures annualized consistently. It gives the example that a monthly Sharpe ratio can be annualized using the square root of twelve. The note is brief and provides no empirical results or detail on factor model specification, estimation uncertainty, or when annualization assumptions may fail.

Key ideas

• A Sharpe ratio expresses excess return relative to total return variability.
• Alpha comparisons require portfolios to share the same benchmark.
• Comparing alpha after scaling portfolios to similar variance can improve interpretability.
• Reporting excess return, alpha, Sharpe ratio, and benchmark beta gives complementary performance information.
• Annualize measures consistently when comparing results across time horizons.

Tags

# Alpha vs. Sharpe Ratio


# Alpha vs. Sharpe Ratio












What are the main differences between a strategy's Sharpe ratio, and its alpha based on the Fame French factors? Does it make sense to evaluate them both in a thesis?

## Answer by Bart (score 3, accepted)

https://quant.stackexchange.com/a/48988

A Sharpe ratio gives you a return per unit of risk as @KeSchn wrote. For investors, A Sharpe ratio is generally a good comparison measure between different portfolios. You can only compare Alphas if the benchmarks are the same.

The best comparison is one you can make with portfolios with equal variances (e.g. scale variance to 10 or 20% depending on your sample for all your portfolios) and then compare Alphas if they have the same benchmark.

I would show mean excess return (over the risk-free rate), mean risk-adjusted return (Alpha), Sharpe Ratio (Mean excess-return/standard deviation) and market beta (beta with your benchmark).

Make sure to annualize these. For the Sharpe Ratio monthly to Yearly you can multiply with square root of 12.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.