The Virtue of Complexity Everywhere

We empirically investigate the performance of return prediction models in the high complexity regime, i.e.,  when the number of parameters exceeds the number of observations. Using data across diverse markets and asset classes, we document a ``virtue of complexity'": return prediction $R^2$ and optimal portfolio Sharpe ratio generally increase with a model parameterization for all asset classes and the vast majority of single security returns in our sample. 
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—observed patterns of the dependence of out-of-sample performance on model complexity exhibit a striking consistency with theoretical predictions.