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I want to compare the performance of two mutual funds. The only data I have is annual returns for the past 7 years. So I have 7 observations for Fund 1 and 7 observations for Fund 2. In addition, I have data for market returns.

To compare the mean return of the two funds, I performed a $t$-test. Since the sample size is small, I expected to get no significant difference in mean return of two funds, and the result fits this expectation. What I want to know is which fund performed better in the past, Fund 1 or Fund 2? Is there any way to compare the performance of two funds?

I also performed bootstrapping to calculate the standard error of the mean. But, as per literature, bootstrapping is also not very efficient when the sample size is very small.

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I think the only valid answer is you can't. The techniques you describe would work of the signal was much stronger than the noise but it seems that with your fund returns this is not the case.

You could try to get more data or look at other risk measures like max drawdown to get some idea of the risks involved.

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  • $\begingroup$ Does it mean, no statistical test can be performed on this data ? One of my friend recommended me about using Sharpe ratio and Treynor ratio. Is it sensible to use them to compare two funds' performance ? Can you further explain what is max drawdown and how they can be used to compare performance the two mutual funds ? $\endgroup$ – Neeraj Aug 14 '15 at 6:56
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    $\begingroup$ Off course you can perform these statistical tests, they will just lack power and will thus not be very useful. I don't it would help to use those ratios. There is quite some material here on max drawdown, if you have any further questions on them not already answered here or on Google you could ask a new question. $\endgroup$ – Bob Jansen Aug 14 '15 at 7:24

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