Research interview, often about the candidate's own backtest.
How long to trust a Sharpe ratio
The question
A strategy shows a Sharpe of 2 over six months. How much should that convince you?
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
Show the worked solution
The answer
Not much. The standard error over half a year is roughly 1.4.
The standard error of an estimated Sharpe is approximately sqrt((1 + S^2/2)/T) with T in years.
With S = 2 and T = 0.5, that is sqrt(3/0.5) divided by... more directly, sqrt((1+2)/0.5) is about 2.4, and even the simpler approximation 1/sqrt(T) gives 1.4.
Either way the estimate is not separable from zero at conventional confidence, so a six-month Sharpe of 2 is consistent with a genuinely mediocre strategy that had a good run.
Add selection bias, since you are usually shown the strategy because it looked good, and the honest position is that six months tells you very little.
What it is testing
Quantifying uncertainty in a performance statistic rather than reading it at face value.
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