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Every factor model, from Fama-French to a neural net, is one equation: the SDF. Same skeleton, but the choice of characteristics and weighting function swings out-of-sample Sharpe from 0.45 to 3.4.
The |t|>3 rule is right for testing one factor, wrong for building a portfolio. A book of 18,000 signals, 80% noise, beats the strict filter because diversification pays where selection does not.
Regional models beat global, said 20 years of linear studies. Redone with neural nets across 24 markets, it flips: complex models want global data. The global NN hits 0.74%/mo, t=5.73.
Test 316 factors at a t of 2 and about 16 are pure luck. The factor zoo is a multiple-testing failure: raise the bar to t above 3, expect a 36% out-of-sample haircut, but don't prune to five.
ML promises to triple your Sharpe. Bryan Kelly, who builds the models, says expect 20%. Headline numbers die under fair tests, 166% turnover, and alpha trapped in tiny illiquid stocks.
Alpha is the gap between what a portfolio earned and what your model predicts. The GRS test grades all those gaps at once, and the usual verdict is blunt: you are missing a factor.
Fama-MacBeth gets you the factor premium in two passes, even for untradable factors. But the second pass uses estimated betas, so skipping the Shanken correction inflates every t-stat.
You never see factor exposure. So you rank stocks on a proxy, go long the top decile and short the bottom, and test the spread. Deciles, a t-stat, and a monotonicity check, from scratch.
Factor investing runs on one equation: expected return equals alpha plus beta times lambda. Beta is exposure, lambda is the premium, alpha is the leftover. The market is factor #1, and CAPM fails on its own.
Sweeping 50/200, 60/210, 70/220 holds the ratio fixed: you test one concept along a line, not the space. That flat sweep is a thin ridge, not a plateau. Fix one parameter, vary the other, then reverse.
Five "diversified" state-election arb positions share one national driver. Correlation 0.75 hides tail dependence 0.90, so a single shock turns a ±$0.10 book into a -$2.50 loss: a 25:1 ratio, not 5:1.
Prediction-market prices cluster near 0 and 1, and that is exactly where the log-scoring arbitrage math breaks. Worse, it can fail silently: no crash, just a wrong trade with a confident profit number.