A Martingale Test for Alpha
Statistics and Probability
We present a new method for testing whether a fund manager’s track record allows us to infer that he is able to beat the market with high probability or is just plain lucky. The test is based on the martingale maximal inequality. Unlike other standard approaches the test is robust to the assumed distribution of returns while retaining substantial statistical power. The method is illustrated using stock market data from 1926‐2007.