Cross-Sectional Regression Equity Multi-Factor Models: Implementation Pitfalls

Abstract

Cross-sectional factor regressions have been used to model the cross-section of stock returns in terms of factors exposures. We illustrate the difficulties of implementing such models in practice for the purpose of managing multi-factor portfolios. First, the orthogonalisation of factors implicit in the approach can lead to some rather unintuitive orthogonal unit exposure factor portfolios in the presence of correlated factors. Dampening correlations reduces the problem but increases the weight of correlated factors in the final calculation of expected stock excess returns and defeats the purpose by failing to completely orthogonalise the factor portfolios. Second, the question of relying on trailing averages of factor returns in order to define factor weights can also be questioned because it leads to negative weights for factors after they performed poorly, which implies a follower momentum strategy at factor level without any prior justification. Third, the stock expected returns derived in this way are not robust for use in a mean-variance optimiser and require portfolio constraints likely to play a too strong role in the final portfolio solution.