In the usual case where a single test is performed on the alpha of one fund (or one portfolio of funds), luck is controlled by setting the significance level γ (or equivalently the Size of the test). The standard approach differs from this framework because it boils down to running a multiple hypothesis test instead of a single one. The null hypothesis H0 of no performance is tested for each of the M funds in the population. In a multiple testing framework, luck refers to the number (or the proportion) of lucky funds among the significant funds that are discovered. Accounting for luck in this situation.
