Factor Glut in Asset Pricing through a Modern Optimization Lens

Abstract

This paper addresses questions regarding the dimensionality of the stochastic discount factor and the selection of the best factors that enter it. We analyze these questions theoretically and empirically with a novel methodology which performs both (i) estimation of factor loadings and (ii) best subset selection of factors in a single step via Mixed-Integer Linear Programming. We empirically illustrate how our approach eliminates worthless factors. Further, we rigorously justify our approach with formal statistical guarantees. Our methodology identifies the best five factors as (i) market, (ii) conservative minus aggressive, (iii) betting against beta, (iv) long-term reversal, and (v) leverage.

Keywords: Asset Pricing, Factor Models, Stochastic Discount Factor, Model Selection, Manhattan Distance, Mixed-Integer Optimization

JEL Classification: C01, C02, G10, G12, C13, C22, G13