is a set of techniques that performance analysts use to explain why aportfolios performance differed from thebenchmark. This difference between the portfolio return and the benchmark return is known as theactive return. The active return is the component of a portfolios performance that arises from the fact that the portfolio isactively managed.

Different kinds of performance attribution provide different ways of explaining the active return.

Attribution analysisattempts to distinguish which of the two factors of portfolio performance,superior stock selectionorsuperiormarket timing, is the source of the portfolios overall performance. Specifically, this method compares the total return of the managers actual investment holdings with the return for a predetermined benchmark portfolio and decomposes the difference into aselection effectand anallocation effect.

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.

The portfolio performance was 4.60%, compared with a benchmark return of 2.40%. Thus the portfolio outperformed the benchmark by 220 basis points. The task of performance attribution is to explain the decisions that the portfolio manager took to generate this 220 basis points of value added.

Under the most common paradigm for performance attribution, there are two different kinds of decisions 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 [(10% − 30%) (1% benchmark return for cash − 2.4% total benchmark return)], and over-weighting equities [(90% − 70%) (3% benchmark return for equities − 2.4% total benchmark return)]. 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 portfolios return [(5% − 3%) 70%].

Interaction captures the value added that is not attributable solely to the asset allocation and stock selection decisions. It is positive when outperformance is overweighted and when underperformance is underweighted. 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 outperformed its benchmark [(90% − 70%) (5% portfolio return for equities − 3% benchmark return for equities)].

The three attribution terms (asset allocation, stock selection, and interaction) sum exactly to the active return without the need for anyfudge factors.

Some other versions of decision attribution analysis omit the interaction effect. As opposed to determining the contribution of uncontrollable market factors to active return, the type of analysis described here is meant to evaluate the effect of each (type of) controllable decision on the active return, and interaction is not a clearly defined controllable decision.

Decision attribution also needs to address the combined effect of multiple periods over which weights vary and returns compound.

In addition, more structured investment processes normally need to be addressed in order for the analysis to be relevant to actual fund construction.

Such sophisticated investment processes might include ones that nest sectors within asset classes and/or industries within sectors, requiring the evaluation of the effects of deciding the relative weights of these nested components within the border classes.

They might also include analysis of the effects of country and/or currency decisions in the context of the varying risk-free rates of different currencies or the decisions to set fund or bucket values for continuous properties like capitalization or duration.

In addition, advanced systems allow for the decision process within asset classes, such as, following an asset allocation, when capitalization decisions are only made for the equity assets but duration decisions are only made for the fixed income assets.

The most robust attribution models precisely address all of these aspects of decision attribution without residuals.

Furthermore, modern portfolio theory requires that all return analysis be conjoined with risk analysis, else good performance results can mask their relationship to greatly increased risk. Thus, a viable performance attribution system must always be interpreted in parallel to a precisely commensurate risk attribution analysis.

There are a number of characteristics of a valid benchmark. The following is a list of such properties.1

In 1972, a working group of the Society of Investment Analysts (UK) publisheda paper about analysing the performance of investment portfolios. This paper, although never verified, claims to have 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 decisions.

The 1972 paper, if in fact it exists, introduced the key elements of modern performance attribution: notional portfolios, asset allocation, and stock selection. The perhaps fictional paper presents this analytic paradigm as an extension of previously known concepts. Since it was not an academic publication, it did not claim novelty, even though the approach introduced was new and novel. An excerpt from the fictional paper reads:

The working group recommend that the notional fund concept be extended to cover the whole fund, i.e. fixed interest, equity and cash investments and by using appropriate indices the actual fund is compared with a notional fund chosen such that the proportions in the different investment sectors follow those laid down by the trustees.

The 1972 paper is ignored, because there is not any evidence that it was actually published and may be a fictional creation, by many of the standard texts on performance attribution (for exampleSpaulding 2003).citation needed

It is believedcitation neededthatGary P. BrinsonBrinsonet al.1985introduced the idea of using notional portfolios to attribute investment performance. For this reason, many of the standard texts (e.g.Spaulding 2003) correctly acknowledge their work and devote copious numbers of pages to Brinson Fachler attribution (pp.177-180) and Brinson Hood Beebower attribution (pp.29-51). The Brinson-Fachler methodology underpins many public performance attribution analyses. Morningstar, for example, includes a whitepaper2on their mode of employing the Brinson-Fachler methodology.Morningstaris known for its analysis of long-only mutual funds, but the Brinson-Fachler analysis is also applicable to hedge ranking funds.3

The most common approach to performance attribution (found in sources such asBrinsonet al.1985andCarino 1999) can be described as arithmetic attribution. It isarithmeticin 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. Another reason for using geometric attribution is that it is theoretically sound for both single period and multi period analyses, for arithmetic attribution additional smoothing is required to apply it to a multi period setting.2

One limitation of portfolio attribution is the reliance on a pre-determined benchmark. The stated benchmark may not be appropriate or may change over time (Style Drift.)2It is difficult to render effective comparisons between funds with different benchmarks. Proponents of adaptive benchmarking maintain that by understanding the characteristics of the portfolio at each point in time, they can better attribute excess returns to skill.4

Risk-based performance attribution decomposes the performance of a portfolio based on various risk factors or risk exposures (seefactor analysis). For complex or dynamic portfolios, risk-based profit attribution may have some advantages over methods which rely only on realized performance. This may be the case for somehedge fundstrategies.5

Risk-based profit attribution should not be confused with risk attribution which decomposes the total risk of a portfolio into smaller units.6

Outline of financePortfolio theoryandPerformance measurement

Jeffery V. Bailey, CFA; Thomas M. Richards, CFA; David E. Tierney (2016). Reading 31. In CFA Institute (ed.).

Trading and Rebalancing, Performance Evaluation, and Global Investment Performance Standards

Morningstarwhitepaperon Brinson-Fachler methodology; May 2011

Publisher: The Reformed Broker;Analysis of the top Hedge Funds, citing analysis fromAlpha Attribution

The Society of Investment Analysts, The measurement of Portfolio Performance for Pension Funds, 1972, revised 1974, available from the National Library of Australia, Call Number p 332.6725 S678-2

Bacon, Carl, Practical portfolio performance measurement and attribution 2nd edition, Wiley 2008,

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.

Articles with unsourced statements from October 2014

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