Factor Attribution and the Impact of Investment Constraints

We customize factor attribution for quantitative equity portfolios to better align the measurement of factor returns with how factor tilts were taken on. Specifically, we provide a theoretical argument for including the absolute value of factor exposures in the attribution to account for the impact of a long-only constraint, as well as intuition for including lagged factor exposures in the presence of turnover limits. This may reduce any long-term unexplained performance resulting from priced distortions of unconstrained factor tilts. In addition, we find that targeting the most accurate estimates of factor returns irrespective of investment constraints can amplify the impact of stock-specific risk on performance attribution. Instead, restricted least squares estimates of the factor returns may retain good accuracy while letting factor attribution explain short-term portfolio performance in full, based on minimally adjusted factor-mimicking portfolios that span the portfolio under consideration. We report back-tests of quantitative equity strategies that confirm our intuition, and suggest diagnostics for portfolio managers who consider adopting the proposed attribution framework.