Third, we find that after accounting for luck, the percentage of funds with negative alphas in the population is approximately equal to 20% across all categories, while the proportion of funds with positive performance is much lower (it amounts to of all funds in the population). It implies that the performance of the industry as a whole is not so bad because about 80% of the funds generate a performance sufficiently high to cover their expenses. The negative average performance documented in past studies is not due to the majority of funds but is caused by 20% of the funds
