AUTHORS:

Carl Bacon, CIPM

Summarized by Laurence B. Siegel

Portfolio performance evaluation is a critical aspect of investment management. A proper assessment of performance results can lead to improvements in investment approach, client communications, and portfolio manager incentives, as well as sophisticated, rather than capricious, manager hiring and firing.

Performance evaluation consists of three components: measurement, attribution, and appraisal. Attribution is the attempt to determine which investment decisions over a given period are the source of the active return (positive or negative) of a portfolio relative to its equity. That is, the objective of performance attribution is to explain the source of return of a portfolio, not in isolation, but in relation to a benchmark.

A good attribution system should include a solid theoretical foundation and consistent approach for valuation and analysis. It should also provide the user with the ability to access, analyze, and summarize security details and transactions and convert these inputs into meaningful attribution results. Furthermore, the attribution framework should be consistent with the portfolio’s decision-making process and should be compatible with the organization’s risk and performance systems.

Performance measurement and evaluation started in the 1960s with efforts to develop methods for comparing the performance of pension funds. Although the analysis was not done relative to a benchmark, the conclusions of the studies conducted in the 1960s are widely accepted today: that market values (not cost) should be used, that total and time-weighted returns are the relevant measure of performance, that risk should be considered as well as return, and that funds should be classified on the basis of their objectives.

The first paper specifically on attribution analysis was written by Eugene Fama in 1972. He provided a decomposition of the sources of observed return into the part related to the ability to select securities at a given level of risk (roughly speaking, alpha) and the part related to general market movements (beta). In the same year, a study by the Society of Investment Analysis in the United Kingdom introduced the ideas of macro (i.e., asset classes or sectors) and micro (i.e., securities within an asset class) levels of decision making and of intermediate notional portfolios to serve as comparators for separating asset allocation and security selection effects.

A series of papers by Gary Brinson and his co-authors in the 1980s separated a portfolio’s return in excess of its benchmark into a timing component (i.e., over/underweighting an asset class or sector), a security selection component, and an interaction or cross-product effect (a controversial effect explained in detailed in this literature review). These papers provided the basic formulas for the effects that are commonly used today.

Classical attribution models apply to single-period performance. Although extending this analysis to multiple periods might sound simple, it is not, and as a result, we have no commonly accepted approach to combining attribution effects in a multi-period analysis. Because of compounding, the sum of geometric (compound) return differences does not equal the difference between geometric returns, as is the case with arithmetic returns. Proposed solutions include those that effectively redistribute the residual across the other factors and those that link arithmetic instead of geometric returns. Other authors have proposed exact approaches based on geometric excess returns.

The performance attribution literature has also considered the multicurrency case. One approach extends the Brinson attrbution framework to produce a currency return with two components: (1) a forward premium that is predictable because it depends on interest rate differentials and (2) a currency surprise that is uncertain. An influential 1994 paper by Karnosky and Singer resolved the compounding return issue by using continuously compounded returns (which are additive), showed why managing currency separately from markets in a multicurrency portfolio is optimal, and provided an attribution framework for global portfolios.

In practice, the three broad types of attribution approach depend on the information that is needed to calculate the attribution effects: beginning-period positions (holdings-based attribution); beginning-period positions plus purchases and sales (transactions-based attribution), and historical portfolio returns (returns-based, or factor, attribution). Asset managers will select an approach on the basis of their investment objectives and approaches, data availability, and the cost and complexity of each approach, although a factor attribution can, in general, complement the other two approaches.

The standard allocation/selection model may lead to attribution results that do not reflect the investment process. This issue is an ongoing challenge in the science of performance evaluation. Some authors have proposed using risk-adjusted performance attribution, but it is rarely used in practice.

Classic attribution models focused explicitly or implicitly on equity investments. Fixed-income attribution requires its own model because of the significant differences between the investment decision processes of equity and fixed-income portfolio managers. Typical fixed-income attribution effects include carry (coupon and the rolling-down effect); yield curve (parallel shift, twist, and curvature); spread; selection (convexity and optionality); and other (e.g., currency). No standardized fixed-income attribution approach is available.

In contrast, the standard equity attribution approach can be adapted to derivatives (options, index futures, and swaps) and short positions in general.

Performance attribution has evolved considerably since early work in the 1960s, but current practice continues to rely on the intuition and tools of the classical models. The passage of time has made not only the models but also performance attribution, more broadly, an essential component of the investment management process.