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But there may be one other methodology in decreasing the variety of predictors. It’s known as stepwise regression. The thought is straightforward: we decide one predictor from the unique set at a time, and add that to the mannequin provided that BIC (Bayesian Data Criterion) decreases. BIC is actually the adverse log likelihood of the training information based mostly on the regression mannequin, with a penalty term proportional to the number of predictors. That is, if two fashions have the same log likelihood, the one with the larger variety of parameters can have a bigger BIC and thus penalized. As soon as we reached minimal BIC, we then try to take away one predictor from the mannequin at a time, until the BIC couldn’t lower any further. Applying this to our fundamental factor loadings, we obtain a fairly vital enchancment of the CAGR over the bottom mannequin: 19.1{e55097f473eef706691b2c0582f998c4e7af494b1f880e47ade53a9b7bea5bb5} vs. 14.7{e55097f473eef706691b2c0582f998c4e7af494b1f880e47ade53a9b7bea5bb5}, with the same Sharpe ratio.