The reference to the Efficient Market Hypothesis (EMH) here is puzzling. Foremost, the strongest form of the EMH implies that consistent outperformance is not p

The reference to the Efficient Market Hypothesis (EMH) here is puzzling. Foremost, the strongest form of the EMH implies that consistent outperformance is not possible, contradicting the rest of the writing and what I believe is its main point: that evidence in the real world is often much stronger than in models. But also when switching from the model world of the EMH to real world markets this application is problematic because of the multiple testing problem. For a trader who recently had a short run of excess profits, the likelihood P(excess returns | skilled) would be high. However, because many diverse traders are in the market and some will show strong performance purely by chance, P(excess returns) or the marginal likelihood of observing such a winning streak would also be high. This dilutes the high likelihood term, leading to a less dramatic update in the posterior P(skilled | excess returns) . Then, the prior P(skilled) should be adjusted to be much more conservative.