Is complexity virtuous?

(Kelly et al., 2024) show that increasing complexity in linear models, with potentially thousands of predictors, is “virtuous”. Their work contradicts the dogma of model selection, including the Principles of Parsimony and Occam’s Razor. They find that when the number of predictors far exceeds the number of observations, the bias–variance trade-off breaks down, the variance declines, and the Sharpe ratio increases. In the context of ridge regression, we find that very high complexity coupled with large penalty terms (excessive shrinkage) generate forecasts that converge to a rolling window of past returns. For example, we show the past twelve-month moving average of actual returns is 97.5% correlated to the forecasts from a twelve-month rolling window of random Fourier features with a large penalty. This finding is consistent with the theory of ridge regression. As the penalty term increases, the forecasts closely approximate the mean, and ignore the explanatory variables. Thus, increasing complexity does not outperform the standard ridge regression, and increasing complexity does not generate high Sharpe ratios, abnormal returns, utility gains or profitable investment strategies.