When Factors Don't Span Their Basis Portfolios

Abstract

To price assets with a parsimonious set of factor-mimicking portfolios, one typically identifies and weights well-diversified basis portfolios - assets grouped by a set of characteristics. Traditional weightings - like long-short return spreads - lead to factors that are unlikely to price even the basis portfolios they are formed from. This is because the number of true factors likely exceeds the number of factor-mimicking portfolios. To avoid generating non-zero alphas for spurious reasons, we offer a method to combine basis portfolios into a single factor that tends to span the optimal portfolio, thereby producing zero alphas. In practice, this adjustment significantly improves the pricing accuracy of parsimonious factor models, even for investment strategies that have long been regarded as having abnormal returns.