What is the proper way to test the significance of Sharpe Ratios or Information Ratios? The Sharpe Ratios will be based on various equity indices and may have variable look-back periods.
One solution that I have seen described simply applies a Student t-test, with the df set to the length of the look-back period.
I am hesitant to apply the above method due to the following concerns:
- I believe that the t-test is sensitive to skewness, however equity returns are generally negatively skewed.
- The mean return calculated using log returns is less than a mean return calculated using simple returns. I assume that this would make it more likely for a simple return based Sharpe Ratio to register as being significant compared to a log return based Sharpe Ratio, yet the underlying asset returns are technically the same.
- If the look-back period is small (i.e. sample size is small), the t-test might be appropriate, but at what threshold would it make sense to use a different test?
My first inclination is to avoid using the Student-t distribution and instead create a test based on the Asymmetric Power Distribution, which I have read has been shown to be a very close approximation of equity market returns, allowing for control over kurtosis and skewness.
My second inclination is to look at non-parametric tests, but having limited experience in their usage I'm not sure where to start and what pitfalls to avoid.
Am I overthinking this problem, are my concerns irrelevant?