Custom Factor Attribution

Portfolio analysts often use one set of decision variables for attributing portfolio returns and a different set for attributing risk. This practice obscures the relationship between the sources of risk and return. This article demonstrates how to align the attribution model with the investment process. The attribution methodology can be applied ex ante or ex post. A factor-based investment process illustrates the general framework. Specifically, active return, tracking error, and the information ratio are attributed to a user-defined set of factors that reflect the manager’s investment decision-making process. A concrete example with actual market data, a style portfolio, and a parsimonious set of custom factors illustrates how to apply the analysis.Portfolio analysts often use one set of decision variables for attributing portfolio returns and an entirely different set for attributing risk. For instance, active return is often decomposed into allocation and selection effects by using a sector-based model whereas tracking error is usually attributed to a set of factors within a fundamental risk model. Unfortunately, this practice obscures the relationship between the sources of portfolio risk and return.In this article, we present a general methodology for aligning the attribution model with the investment process. We begin by decomposing portfolio returns into a set of attribution effects that reflects the investment process. We then show how portfolio risk can be attributed to the same underlying decision variables. The final step in our framework is to combine the return and risk attribution analyses to obtain a decomposition of the risk-adjusted performance, or information ratio. We show that the portfolio information ratio can be expressed as a weighted average of component information ratios. The relevant weights are not the investment weights, however, but the risk weights. The component information ratios are simply the stand-alone information ratios of the attribution effects magnified by the reciprocal of the correlation between the attribution effect and the active return. This “magnification effect” reflects the benefit of diversification. Our attribution framework can be applied on an ex ante or an ex post basis.To illustrate our general framework, we consider an investment process based on a set of custom factors that do not directly correspond to the factors in the risk model. A major challenge is to cleanly attribute returns to the investment factors without the confounding effects (because of colinearity) of the risk factors. One approach is simply to suppress the risk factors. This method has the benefit of cleanly attributing the returns to the custom factors, but it has the disadvantage of not accounting for all of the factor risk, which can be fully explained only by the risk factors. Our solution to this problem is to include the risk factors in the analysis—but only after orthogonalizing them to the custom factors. In this approach, because the “residual” factors are orthogonal to the custom factors, the return and risk attributable to the custom factors can be cleanly explained. Furthermore, all of the factor risk not explained by the custom factors will now be captured by the residual factors.We use a concrete example with actual market data to illustrate how to apply our analysis in practice. We use well-known indices to construct an active portfolio with strong tilts to value and size. We then attribute the portfolio return, risk, and information ratio to the Fama–French factors.