Determinants of Portfolio Performance,” the seminal 1986 paper on asset allocation by Gary P. Brinson, Randolph Hood, and Gilbert L. Beebower (BHB), begins by citing a study showing that most corporate pension funds focus their attention solely on the problem of manager selection. BHB’s research presents evidence, however, that 93.6% of total return variation is due not to manager selection, but to asset allocation. Often, the takeaway is that the variation in performance across investment funds is 93.6% attributable to asset allocation, and only marginally to manager decisions such as security selection and market timing.

But that’s not what it says at all.

The race is to the swift – or is it?

Let’s suppose you are doing research on the performance of 100 racers who run the Boston marathon – a hilly course over which lap times change from mile to mile. The runners all do their own stretching exercises before running, and they drink the energy drink and eat the granola bar that are handed out by the race sponsors.

You want to know how much the energy drink and the granola bar contribute to their performance. So here is what you do.

You have each runner run the course four times. The first time it is run, each runner does their stretching exercises and drinks the energy drink and eats the granola bar, and you record each runner’s times over the miles of the course and call them data series A.

The second time the runner stretches and only drinks the energy drink, and the recorded times are data series B. The third time the runner stretches and only eats the granola bar and the times are data series C, and the fourth time the runner only stretches and the times are data series D.

Then following BHB, you compute the correlation coefficient of D against A, C against A, and B against A (BHB call them “regressions”), and square each correlation coefficient to get an R-squared. The results are shown in Table 1.

Table 1. R-squareds of correlations of 26-mile sequences of running times

Only energy drink (sequence D), against both energy drink and granola bar (sequence A)

97.8%

Only granola bar (C ), against both (A)

95.3%

Only stretching (B), against both (A)

93.6%

The conclusion is that 93.6% of the variation in running times is explained by stretching, and only a relatively tiny percentage by the energy drink and the granola bar.

Huh?