Am I a Good Investor? How Long Should a Performance Track Record Be To Know For Sure

The Sharpe Ratio

The most commonly used tool to judge traders (and hedge funds) is the Sharpe Ratio (SR), defined as the ratio of the excess expected returns to the standard deviation of returns i.e.,

Estimation Error of the Sharpe Ratio

Lo (2002) shows how we can compute the standard errors for SR. A standard result from Statistics is that

Annualization of the Sharpe Ratio

As mentioned earlier, Sharpe Ratios are typically expressed in annualized terms with

Sharpe Ratios Can Be Misleading

There are a couple of problems with this procedure.

Estimation Error of the Marginal Sharpe Ratio (MSR)

I introduced the MSR in a prior post. It solves the market correlation problem because it directly benchmarks the SR against market returns. An ancillary benefit, as shown below, is that it almost always has a standard error less than that of the ordinary SR.

α vs MSR

To be sure, one might ask “why not just compute standard errors on alpha directly?” Of course, we could do so. However, the result is less elegant.

Conclusion

Finally, we can offer the following heuristic to measure performance quality.

References

Lo, A. W. (2002). The statistics of Sharpe ratios. Financial Analysts Journal, 58(4):36–52.

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