The Statistics of Sharpe Ratios
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What they found
Lo derived the standard error of a Sharpe ratio estimate and showed how large it is: with monthly data over a few years, the confidence interval around a Sharpe ratio is wide enough that a reported 1.0 might easily be 0.5 or 1.5. He also showed that the common practice of annualizing a monthly Sharpe ratio by multiplying by the square root of 12 is wrong when returns are serially correlated: positive autocorrelation (typical of illiquid or smoothed strategies) causes the naive annualization to overstate the true Sharpe ratio, sometimes by a large factor.
What you can use
- A Sharpe ratio from a few years of data has a huge margin of error; treat differences between 0.8 and 1.2 as noise.
- Strategies with smooth, autocorrelated returns (illiquid assets, some options strategies) have overstated annualized Sharpe ratios.
- Ask how many independent observations a track record contains before believing its risk-adjusted return.
Caveats
Derivations assume stationarity; fat tails widen the intervals further. Practitioner journal.
Tags: backtesting, sharpe-ratio, statistics, performance-measurement
Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.