The Virtue of Complexity Everywhere

We investigate the performance of non-linear return prediction models in the high complexity regime, i.e., when the number of model parameters exceeds the number of observations. We document a "virtue of complexity" in all asset classes that we study (US equities, international equities, bonds, commodities, currencies, and interest rates). Specifically, return prediction R-squared and optimal portfolio Sharpe ratio generally increase with model parameterization for every asset class. The virtue of complexity is present even in extremely data-scarce environments, e.g., for predictive models with less than twenty observations and tens of thousands of predictors. The empirical association between model complexity and out-of-sample model performance exhibits a striking consistency with theoretical predictions