How can I compare two mutual funds' performance with a sparse set of data? 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.
 A: There are more than a few considerations that could be invoked in comparing the performance of these funds. First of all, you should probably be calculating the geometric mean rather than the arithmetic mean in evaluating average performance. This 1979 paper The geometric mean: Confidence limits and significance tests offers guidance on the possible tests.
http://link.springer.com/article/10.3758%2FBF03204171
Additional metrics are possible which would expand the frame of your evaluation including NAV, CAGR, excess returns vs the market, excess returns vs the strategic group (competitive frame) in which these funds are classified, e.g., by Morningstar, Morningstar ratings, and so on.
(http://www.morningstar.com/funds.html).
Then there are the less easily addressed but much broader questions of the influence of industry, corporate, business unit and fund manager levels on performance. These are given extensive consideration within a nonparametric approach to performance evaluation in this paper by the late Tim Ruefli:
http://www.wiggo.com/mgmt8510/Readings/Readings4/ruefli2003smj.pdf
