# Comparing two sharpe ratios computed over different number of years

I was asked this question in an interview.

Let's say we have two Sharpe ratio's-
1) Sharpe of 3 computed over two years of data.
2) Sharpe of 2 computed over twelve years of data.

Is there a way to say quantitatively which one is better than the other?

I thought of using confidence intervals, using the fact that if the samples are from a normal distribution, then $\sqrt{n}$(sample mean - population mean)/Sample deviation is T student (n-1).

But then all we know is the Sharpe for the two years and twelve years. We don't have samples for yearly Sharpe to get a mean and variance, neither do we have the returns.

Can you please provide a general framework for solving these kinds of problems or any hint for the particular question?
I know i might be missing a few details, please feel free to make any assumptions to make the case simpler.

• You can do this with the upsilon distribution, which for two Sharpes is the same as LeCoutre's lambda-prime. See also section 3.5 of my Short Sharpe Course. Jan 25, 2019 at 6:30
• I swear there should be a simpler answer here Jun 15, 2020 at 9:53