A Markov test for alpha

Alpha is the amount by which the returns from a given asset exceed the returns from the wider market. The standard way of estimating alpha is to correct for correlation with the market by regressing the asset's returns against the market returns over an extended period of time and then apply the t-test to the intercept. The difficulty is that the residuals often fail to satisfy independence and normality; in fact, portfolio managers may have an incentive to employ strategies whose residuals depart by design from independence and normality. To address these problems we propose a robust test for alpha based on the Markov inequality. Since it is based on the compound value of the estimated excess returns, we call it the compound alpha test (CAT). Unlike the t-test, our test places no restrictions of returns while retaining substantial statistical power. The method is illustrated on the distribution for three assets: a stock, a hedge fund, and a fabricated fund that is deliberately designed to fool standard tests of significance.