As with every hypothesis test, inference based on alpha estimates can lead to the detection of a lucky fund, namely a fund with a significant estimated alpha, while its true alpha is equal to zero. When a single performance test is run on the estimated alpha of one fund (or one portfolio of funds1), luck is easily controlled by setting the significance level γ (or alternatively the Size of the test). For instance, if γ is set to , the probability of finding one lucky fund under the hypothesis that its alpha is zero amounts to , by construction. The difficulty raised by the standard approach.
