Performance Attribution: Measuring Dynamic Allocation Skill

Abstract

Classical performance attribution methods do not explicitly assess managers’ dynamic allocation skill in the factor domain. The authors propose a generalized framework for performance attribution that decomposes the allocation effect into value added from both static and dynamic factor exposures and thus yields additional insight into sources of manager alpha.

Classical Brinson attribution was designed to analyze manager returns over a single period under the assumption of static holdings. It has since been extended to cover multiple periods to account for changing portfolio weights over the span of analysis. Commonly used multiperiod attribution analyses, however, do not explicitly measure a manager’s ability to allocate dynamically in the factor domain. This deficiency is important for a number of reasons.

For example, value stocks have historically outperformed growth stocks. A particular manager may seek to exploit this apparent value premium to generate a higher return against his benchmark by increasing the portfolio weights in value stocks. We term this approach static factor allocation, and the resulting alpha arises from persistent style tilts toward factors with a risk premium. Another manager, skilled in forecasting whether value stocks will outperform growth stocks in a given year, may dynamically adjust the value/growth tilt in her portfolio by increasing the weights in value stocks when she believes value will do well relative to growth, and vice versa. We term this approach dynamic factor allocation.

Although the sources of added value for these two managers are markedly different, traditional multiperiod Brinson-type analyses do not explicitly distinguish between them. The existing methods thus provide an incomplete assessment of a portfolio manager’s investment style. In this article, we propose a dynamic allocation attribution methodology that retains the intuition and familiar characteristics of traditional Brinson attribution analysis. In addition to distinguishing between security selection and factor selection, our methodology subdivides the allocation effect into static and dynamic components. The static component measures performance attributable to the persistent factor profile of the manager’s portfolio. The dynamic component measures the performance attributable to the manager’s timing ability. Distinguishing between static and dynamic allocation skills in the factor domain is important because doing so gives further insight into the investment approach of managers and more fully characterizes manager skill and drivers of manager alpha.

Notes

¹See Investment Company Institute, 2009 Investment Company Fact Book (Washington, DC: Investment Company Institute, 2009).

²See, for example, Carino (1999); Laker (2005); Menchero (2000, 2004); and Davies and Laker (2001).

³Grinblatt and Titman (1993) made a similar observation in measuring manager performance without benchmarks.

⁴The interaction effect is positive when a manager overweights sectors in which she has a positive stock selection ability and underweights sectors in which she does not. The effect is often added to classical security selection to simplify the analysis (see Fabozzi and Markowitz 2002).

⁵For convenience, our focus is on arithmetic attribution analysis. For representative examples of a geometric approach, see Bacon (2002) and Menchero (2000/2001).

⁶Note that when summing allocation effects among all factors, ${\displaystyle \sum _{i=1}^N\left(w_i^p-w_i^b\right)R^b}=0.$ Thus, the portfolio-level returns $(R_t^b)$ can be omitted from the allocation effects in Equations 8a–8c without changing the aggregate result, which eases the complexity of calculating allocation effects at the portfolio level.

⁷We defined book-to-market ratio as the ratio of a company’s book equity to its market equity. We calculated the book value of equity as the book value of stockholders’ equity plus balance sheet deferred taxes and investment tax credit minus the book value of preferred stock (as of the most recent reporting date in Capital IQ Compustat). We calculated the market value of equity as the share price multiplied by the number of shares outstanding.

⁸Total added value may be slightly different for each fund among the panels. This difference arises from the fact that we were unable to obtain industry or book-to-market information for every stock in the sample.