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I have 10 years of backtested simulated performance of some trading strategy (using historical prices), and N months of actual trading performance. What statistical test can I do find out if I'm on target with the backtesting numbers? (both, in terms of expected annual returns and expected annual Sharpe ratio)

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Letting $\psi_1, \psi_2$ be the sample Sharpe ratios of the two periods, the difference $\Delta \psi = \psi_1 - \psi_2$ is asymptotically normal. Under the null hypothesis that the population Sharpe ratios in the two periods are equal, the difference is asymptotically mean zero. The standard deviation is approximately $\sqrt{\frac{1}{120} + \frac{1}{n}}$, when your Sharpe ratios are 'annualized' to monthly terms. So the simplest test would be to reject the null if $|\Delta\psi|> 1.96 \sqrt{\frac{1}{120} + \frac{1}{n}}$.

My answer here is just a realization of @drnexus' answer to this question.

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  • $\begingroup$ I would like to amend my answer to state that a slightly more 'precise' version of the test is available via the upsilon distribution: arxiv.org/abs/1505.00829 . However, the 2-term approximation to the CDF of the upsilon is exactly the asymptotically normal approach given above. $\endgroup$
    – shabbychef
    May 11, 2015 at 16:57

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