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F actor-based performance attribution is commonly used to explain the sources of realized return of a portfolio. The methodology relies on a factor model of asset returns to decompose a portfolio's return according to a set of factors. The portion of the portfolio return that can be explained by the model factors is called thefactor contribution , and the remainder is called theasset-specific contribution , orspecific contribution for short. (For a description of factor-based performance attribution, see Fischer and Wermers [2013], chapter 4.)
Unfortunately, the inferences from a standard attribution report can be misleading for several reasons--one of which is the misclassification of factor contributions as asset-specific contributions or vice-versa. Aside from missing factors, this misclassification can also be due to biased factor exposure estimates. As a result, inferences on the statistical significance of the contributions may also be incorrect. With the trend toward "smart beta" and factor investing in general, the ability to draw correct inferences about factor contributions from attribution reports is increasingly critical. In this article, we will address the causes of erroneous attribution analysis and propose a methodology that produces better representations of reality from which more accurate inferences can be drawn.
Before we jump into the causes of inaccurate inferences and our proposed solution, we will illustrate the types of inaccurate inferences that can be made from a standard attribution on a particular example. We constructed a portfolio that is rebalanced monthly from January 1995 to October 2013 according to the following strategy:
[Figure omitted. See PDF]
We used exposure to a growth factor as the expected return and the Russell 1000 Index as the benchmark. We then considered two different returns models to use in attributing returns of this portfolio. The first model, RM1, uses 10 sector factors and 4 style factors--market sensitivity, momentum, size, and value. The second model, RM2, adds the exact growth factor used to construct the portfolio to those factors present in RM1.1 The active risk constraint used a factor risk model based on the RM2 returns model.2
Exhibit 1 summarizes the attribution results for the active portfolio using these two models. All contributions are annualized values computed using the linking methodology of Cariño [1999]. When we use RM1 to...