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. The difficulty raised by the standard approach is that it implies a multiple hypothesis test since the null hypothesis of no performance is not tested once, but M times. Accounting for the presence of luck in a multiple testing framework is much more complex, because luck cannot be measured by the significance level applied to each fund. Specifically, if this level is set to 5 percent, the probability of finding at least.
