Reconciling Stock Selection and Factor Allocation

Abstract

This article contributes to the longstanding debate about the relative merits of building multifactor portfolios using a bottom-up approach, informed by factor-based expected returns, and a top-down approach that allocates across factor portfolios. Its main contribution is to prove formally that the solution of the mean–variance optimization solved by a stock picker who uses factors to select securities and that of a mean–variance-efficient allocation across factors are in fact largely equivalent. This finding is corroborated empirically and holds under stringent investment constraints. Moreover, while demonstrating this equivalence, an alternative methodology emerges that makes the best of both approaches.