Understanding Regularization for Portfolio Construction

Abstract

Regularization for portfolio construction is shown to be equivalent to combining the unconstrained portfolio with a long - short portfolio. The latter is not correlated with the unconstrained portfolio which leads the constrained portfolio to have a beta of one with respect to the unconstrained portfolio. Regularization aiming at controlling for estimation risk makes thus investors tilt their original portfolio with noise. The noise portfolio is reminiscent of factor investing or reverse factor investing. Thus the benefits of regularization strongly depend on the test assets and the new decomposition provides forward guidance on why and when estimation risk management through regularization may or may not work.