Excess Sharpe Ratio

A reader pointed out an interesting problem with rolling alphas that I showed two weeks ago: When the model fit is bad (as shown by a low R-squared), the interpretation of alpha and beta is not very meaningful. In such cases, alpha typically has a very wide confidence interval and tracking alpha over time is of limited value or even misleading.

So, if we're not really interested in the relation between a system and an index because we think such a relation is rather weak or non-existent, we could instead compare the Sharpe ratio of the system to the Sharpe ratio of the index.

The figure below (upper panel) shows the 100-day rolling Sharpe ratio for Trend Plays #1 and the S&P 500. The difference between the two Sharpe ratios, which I call the system's excess Sharpe ratio, is shown in the lower panel. Most of the time the excess Sharpe ratio of Trend Plays #1 is greater than zero, i.e. the 100-day rolling Sharpe ratio of Trend Plays #1 is greater than the 100-day rolling Sharpe ratio of the S&P 500 index. In other words: The system does better than the index on a risk-adjusted basis.



The bad news is that the difference is not significantly different from zero (with 95% confidence) for any of the 100-day periods shown in the plot. Even when we construct a confidence interval for the difference between the Sharpe ratio of the system and the Sharpe ratio of the S&P using all 294 trading days, the difference is not significant: A bootstrapped confidence interval for the difference (with 10,000 replications, bias-corrected) shows [-0.886, 3.039].