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That formula for S_max looks super-useful. Do you have a reference for deriving it?
It's a very rough asymptotic result from extreme value theory -- follows from the fisher-tippett-gnedenko theorem if you throw out everything but the leading order term, googling "maximum of n gaussians" will get you some references.
Bear in mind that is full of assumptions that are not true! Backtests with different parameter combinations are not independent, backtest Sharpes are not drawn from a normal distribution, strategy performance is not stationary in time etc.
Thanks! I understand the caveats, I expected this had to be under the assumption of gaussian and uncorrelated returns and sounds like that's the case
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