Thus, whether evaluating the performance of a fund manager, or assessing the merits of socially responsible investing, it is necessary to decompose the difference in the return between the managed and benchmark portfolios into a security selection component and an asset allocation component.
Specifically, they identify [summation]([w.sub.Pi]-[w.sub.Bi]) [r.sub.Bi] as a timing component (which technically is actually just asset allocation in one period), [summation] [w.sub.Bi] ([r.sub.pi]-[r.sub.Bi]) as a security selection component, and [summation] [w.sub.Pi] ([r.sub.Bi]-[w.sub.B] [r.sub.Pi]) as "other," where [r.sub.Bi] is the weight of the [i.sup.th] asset class and [r.sub.Bi] is its return for a passive portfolio, and [w.sub.Pi] and [r.sub.Pi] are similarly defined for the active portfolio.
They perform three regressions in an attempt to decompose total return into asset allocation and "active management" components (which for cross-sectional tests means security selection.).
Unlike most researchers dealing with performance measurement, Rennie and Cowhey do not test for consistent superior performance, but, in a case setting, decompose the actual return less benchmark return for three managers into market timing, industry exposure, sector emphasis, security selection, and unreconciled return components.
Since the only difference between this hypothetical benchmark and the actual benchmark is the return on the securities within the portfolios, one will attribute the difference in performance, 11% - 10% = 1%, to the security selection.
Equation (2) shows that we have measured the security selection component using the weights, [w.sub.Bi], of the benchmark portfolio and have measured the asset allocation component using the returns, [r.sub.Pi], of the managed portfolio assets.
We again attribute the remaining 1% to security selection using the following argument.
This example suggests that the decomposition of excess return into a 4% asset allocation component and a 1% security selection component is unique.
Table 2 Example 2 Asset Class The Portfolio The Benchmark Weight Return Weight Return Bond Portfolio 10% 6% 50% 4% Stock Portfolio 90% 16% 50% 12% Total Return 15% 8% To decompose the 7% excess return into asset allocation and security selection components, we assume, as we did earlier, that the managed portfolio contains the same securities, but applied the benchmark weights to allocate investment funds between bond and stock portfolio.
We again attribute the remaining 3.8% to security selection in the same way as in the first example.
and the security selection component = [N.summation over (i=1)][w.sub.Bi] ([r.sub.Pi] - [r.sub.Bi])