Since such a fund is determined according to a pre-ranking of all fund alphas, a correct inference about its alpha must take into account the entire cross-section of the fund alphas3. In this context, they advocate to use a bootstrap procedure, and conclude that they account for luck in the sense that they correctly compute the p-values of the individual funds4. This definition of luck is not related to the issue of multiple testing investigated in this paper. In fact, we would face a similar multiple testing problem in their setting if we wanted to know how many individual funds corresponding to the various quantiles of the cross-section.
