Take-the-Best in Portfolio Selection

Abstract

A well-known result in portfolio optimisation states that as the number of assets in a portfolio grows, the variance of portfolio return approaches the average covariance between the included assets. I argue that this result should not be read as a justification to emphasise forecasting correlations. I compare the textbook recipe for constructing the minimum-variance portfolio, which uses the full variance-covariance matrix, with a simple, sorting-based rule. Through a simulation I show that when there is diversity in the cross-section of assets and we cannot precisely predict future covariance (two empirically valid assumptions), then the simple rule is rarely worse (and if, not much) than the textbook approach, but often better.

Keywords: portfolio optimisation, heuristics, minimum-variance, forecasting

JEL Classification: G11, G17