or Investment Performance Attribution
is a set of techniques that performance analysts use to explain why a portfolio
's performance differed from the benchmark. This difference between the portfolio return and the benchmark return is known as the active return. The active return is the component of a portfolio's performance that arises from the fact that the portfolio is actively managed.
Different kinds of performance attribution provide different ways of explaining the active return.
Consider a portfolio whose benchmark consists of 30% cash and 70% equities. The following table provides a consistent set of weights and returns for this example.
|| 1.92% |
|| 0.28% |
|| 2.20% |
The portfolio performance was 4.60%, compared with a benchmark return of 2.40%. This leaves an active return of 2.20%. The task of performance attribution is to explain the decisions that the portfolio manager took to generate this 2.20% of value added.
Under the most common paradigm for performance attribution, there are two different kinds of decision that the portfolio manager can make in an attempt to produce added value:
- Asset Allocation: the manager might choose to allocate 90% of the assets into equities (leaving only 10% for cash), on the belief that equities will produce a higher return than cash.
- Stock Selection: Especially within the equities sector, the manager may try to hold securities that will give a higher return than the overall equity benchmark. In the example, the securities selected by the equities manager produced an overall return of 5%, when the benchmark return for equities was only 3%.
The attribution analysis dissects the value added into three components:
- Asset allocation is the value added by under-weighting cash (0.12%), and over-weighting equities (0.28%). The total value added by asset allocation was 0.40%.
- Stock selection is the value added by decisions within each sector of the portfolio. In this case, the superior stock selection in the equity sector added 1.40% to the portfolio's return.
- Interaction captures the value added that is not attributable solely to the asset allocation and stock selection decisions. In this particular case, there was 0.40% of value added from the combination that the portfolio was overweight equities, and the equities sector also outperfomed its benchmark.
The three attribution terms (asset allocation, stock selection, and interaction) sum exactly to the active return without the need for any "fudge factors".
In 1972, a Working Group of the Society of Investment Analysts (UK) published a paper about analysing the performance of investment portfolios. This paper introduced the key concept in performance attribution, that active performance can be analysed by comparing the returns of different notional portfolios. In particular, if one examines the performance of a portfolio that holds each sector at the active weight, while earning a passive return within each sector, one can measure exactly the amount of value that is added by asset allocation decisons.
The 1972 paper introduced the key elements of modern performance attribution: notional portfolios, asset allocation, and stock selection. Because the paper doesn't present this analytic paradigm as novel, it remains entirely possible that this form of analysis was well-understood in professional circles even earlier than 1972, but simply not published. The 1972 paper is ignored by many of the standard texts on performance attribution (for example Spaulding 2003).
It is commonly (but incorrectly) believed that Brinson et al. 1985
introduced the idea of using notional portfolios to attribute investment performance. For this reason, many of the standard texts (e.g.Spaulding 2003) make no acknowledgement of the 1972 paper, while devoting copious numbers of pages to "Brinson Fachler attribution" (pp. 177-180.) and "Brinson Hood Beebower attribution" (pp. 29-51).
The most common approach to performance attribution (found in sources such as Brinson et al. 1985
and Carino 1999
) can be described as "arithmetic attribution". It is arithmetic
in the sense that it describes the difference between the portfolio return and the benchmark return. For example, if the portfolio return was 21%, and the benchmark return was 10%, arithmetic attribution would explain 11% of value added.
In Europe and the UK, another approach (known as geometric attribution) has been common. If the portfolio return was 21% while the benchmark return was 10%, geometric attribution would explain an active return of 10%. The reasoning behind this is that 10% of active return, when compounded with 10% of benchmark performance, produces a total portfolio return of 21%.
Adherents of the geometric approach consider it to be highly intuitive. See, for example, Bacon (2002). However, not everybody agrees on this.
One advantage of doing attribution in geometric form is that the attribution results translate consistently from one currency to another. It is plausible that this explains the popularity of geometric approaches in Europe. This is discussed further in the external link by Davies (undated).
- Brinson, Gary P., and Nimrod Fachler, “Measuring Non-US Equity Portfolio Performance,” Journal of Portfolio Management, Spring 1985, pp. 73-76.
- Bacon, Carl, “Excess Returns – Arithmetic or Geometric?”, Journal of Performance Measurement, Spring 2002, pp. 23-31.
- Cariño, David, “Combining Attribution Effects Over Time,” Journal of Performance Measurement, Summer 1999, pp. 5-14.
- Laker, Damien, “What is this Thing Called Interaction?” Journal of Performance Measurement, Fall 2000, pp. 43-57.
- Laker, Damien, "Arithmetic Performance Attribution" (Chapter) in Bacon, Carl, Advanced Portfolio Attribution Analysis: New Approaches to Return and Risk London: Risk Books, 2007.
- Spaulding, David, Investment Performance Attribution: A Guide to What it is, How to Calculate it, and How to Use it, New York: McGraw-Hill, 2003.
- (Working Group of) The Society of Investment Analysts (UK), The Measurement of Portfolio Performance for Pension Funds (1972, Revised 1974). Copies of this document are very hard to obtain. A page from the document is available (along with commentary) at