On false discoveries of standard t-tests in investment management applications

Financial managers routinely use the one-sample t-test to evaluate whether the mean returns of investment assets, strategies or funds are significantly different from zero. Simultaneously, however, they often ignore the fact that its application is not generally justified, in other words, that its usefulness depends on the properties of the population. We show by Monte Carlo simulation that, especially in skewed and/or autocorrelated populations, test decisions based on the t-test can be severely biased. More specifically, for sample sizes typically used in investment performance evaluation, the probability of falsely diagnosing a significant mean return–the false discovery rate–is significantly higher than the nominal error probability set in testing. We additionally illustrate that the popular empirical practices of (i) replacing the t-quantile with the standard normal quantile and (ii) removing outliers before conducting the t-test have crucial elevating impact on the false discovery rate.