Performance Attribution - Simple Example

Simple Example

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%. 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:

1. 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.
2. 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, and over-weighting equities . 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. 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.

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

More modern and enhanced versions of decision attribution analysis omit the economically problematic 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.