Comparing Mutual Funds with Only a Few Annual Returns

Summary

The document considers how to compare two mutual funds when only a short sequence of annual returns is available, alongside market returns. A standard test of mean returns and a bootstrap estimate are mentioned, but the central issue is that a small sample may not distinguish a real performance gap from random variation. The answer cautions that neither method can reliably rank the funds when the signal is weak relative to the noise.

The suggested practical responses are to obtain more observations or examine other aspects of risk, such as maximum drawdown. These may offer additional context, but they do not establish which fund is superior from the limited record. The exchange provides no calculations, performance estimates, or comparison of risk-adjusted measures. Its main lesson is about the limits of inference: a failure to find a statistically significant difference is not evidence that the funds performed identically, and a sparse sample cannot support a confident ranking.

Key ideas

• A small sample of annual returns may not support a reliable ranking of funds.
• A nonsignificant difference in sample means does not show that the funds are equivalent.
• Bootstrap uncertainty estimates can also be unreliable when observations are very limited.
• More return history can improve the basis for comparison.
• Maximum drawdown can add information about risk but does not by itself prove which fund performed better.

Tags

# How can I compare two mutual funds' performance with a sparse set of data?


# 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.

## Answer by Bob Jansen (score 2, accepted)

https://quant.stackexchange.com/a/19306

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.