Optimal Portfolio Size under Parameter Uncertainty

Abstract

We introduce a method to determine the investor's optimal portfolio size that maximizes the expected out-of-sample utility under parameter uncertainty. This portfolio size trades off between accessing investment opportunities and limiting the number of estimated parameters. Unlike sparse methods such as lasso that exclude assets during the optimization step, our approach fixes the optimal number of assets before computing the portfolio weights, which improves robustness and provides greater flexibility in practical implementations. Empirically, our restricted portfolios outperform their counterparts applied to all available assets. Our methodology renders portfolio theory valuable even when the dataset dimension and sample size are comparable.

Keywords: portfolio selection, estimation risk, dimension reduction, out-of-sample performance, portfolio combination rules JEL Classification: G11

JEL Classification: G11