## Meaningful Sharpe Ratios

To review, the Sharpe ratio is a measurement that tells us the risk-adjusted performance of a portfolio or strategy. It is calculated by subtracting the risk-free rate from the strategy returns and dividing that by the standard deviation of returns. The idea is to determine whether absolute returns are due to some desirable feature of the strategy or simply due to excess risk-taking.

Not all Sharpe ratio figures are created equal. To be more specific, one should be careful when comparing the Sharpe ratios of very different systems or portfolios. To see why, consider two hypothetical strategies that both trade the S&P 500 exclusively. The particular products don’t matter – be they futures, ETFs, index funds, etc. Strategy A is nearly a buy-and-hold approach, with added ability to change its status from long to flat or flat to long on the first trading day of each year. Strategy B is fairly active, and may change its status each Friday at the close.

Strategy A just *is* the market during a year in which it is long, and the only way for it to improve performance is to get flat during declining years, but that doesn’t offer much opportunity. Contrast that with Strategy B, which can generate more returns from the same sequence of price movement (by going long, short, or flat each week) but will retain essentially the same volatility. These strategies aren’t different at all except in terms of trading frequency. But changing that one factor has a significant impact on the upper limit of the Sharpe ratio: Strategy B can obviously reach much higher.

As a result, we would look unfavorably on Strategy B if over some multi-year period its ratio wasn’t significantly better than Strategy A’s. Conversely, active systems with high ratios may be impressive, but we suggest that they can be evaluated more effectively by comparison with systems with similar frequency, rather than in comparison to some anodyne market benchmark. Of course, it should go without saying that virtually any active strategy with a genuine edge will be superior to the market average on a risk-adjusted basis.

For some meaningful information derived from an entirely different Mr. Sharpe, listen here.

Tags: risk, sharpe ratio

Fri, Feb 13, 2009 | Jared Woodard

Financial Geekery, Strategy