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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?

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  • $\begingroup$ quant.stackexchange.com/questions/54921/… $\endgroup$ Nov 18, 2021 at 19:55
  • $\begingroup$ Start from Section 3.5.1 of Short Sharpe Course, and see also equation 4.34 for the Mertens' standard error. $\endgroup$
    – shabbychef
    Dec 6, 2021 at 17:58
  • $\begingroup$ I would be careful of estimating future performance of Sharpe ratio. One just can look at performances of mutual funds over long periods of time to see that they change and many times converge to 1. Sharpe has 3 parts, the performance, the volatility, and the risk free return. So you have to be more or less correct on all 3 $\endgroup$ May 15 at 21:57

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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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