Estimating Sharpe Ratio Uncertainty from Strategy Performance

Summary

The document asks how to update confidence in a strategy’s true future Sharpe ratio as returns arrive, distinguishing that unknown quantity from the Sharpe ratio calculated on a backtest. Strong or weak realized performance can reflect either luck or a genuinely different underlying Sharpe, so the inference problem concerns uncertainty about the strategy rather than a direct reading of its observed statistic.

The response points to confidence interval methods for Sharpe ratio estimation and says a bootstrap resampling approach combined with a Student’s t distribution is a practical option. It cautions that no fully satisfactory method is offered. The excerpt gives no derivation, assumptions, implementation details, or worked example, so the suggested procedure should be treated as a brief pointer rather than a complete statistical recipe.

Key ideas

• Observed performance does not reveal the true future Sharpe ratio with certainty.
• A Bayesian or confidence interval view should distinguish sampling luck from a change in underlying strategy quality.
• Bootstrap resampling can be used to estimate uncertainty in the Sharpe ratio.
• The response suggests using a Student’s t distribution to construct an interval.
• The excerpt offers no detailed method and cautions that satisfactory approaches are limited.

Tags

# Confidence in Sharpe ratio given performance


# Confidence in Sharpe ratio given performance












Suppose I have a strategy that I believe has a Sharpe ratio of X - not the Sharpe ratio of the backtest (this can be absolutely determined), but the ratio I expect it will actually take on over the next year.

Now, if I start trading this strategy, and my returns are bad, this could be due to either poor starting luck, or my strategy Sharpe ratio is actually less than X. Similarly, if my returns are unexpectedly high, it could be that my strategy Sharpe ratio is actually greater than X.

How should I model my confidence on the true value of the Sharpe ratio? That is, if I wanted to have a 90% confidence interval or a probably distribution on the true Sharpe ratio, given the year's performance so far, what would be some ways to go about doing this?

## Answer by Andrew (score 3)

https://quant.stackexchange.com/a/70894

I was wondering the same thing. I found your question, then I found this, so I came back to share the link:

https://www.twosigma.com/articles/sharpe-ratio-estimation-confidence-intervals-and-hypothesis-testing/

Hope this helps!

TLDR: There aren't any satisfactory ways to do that, but the best is to do a bootstrap resample of the data and use the Student's T to create a confidence interval.

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