Erratum - Formula for "Allocation effect" Book 6 - Performance Evaluation - looks incorrect

The formula for Allocation effect on page 182 Book 6 looks incorrect. Its given as Ai = (wp - wb) Bi


wp = weight of the sector/security on the portfolio

wb = weight of the sector/security on the benchmark

Bi = return of the sector/security on the benchmark

I think this formula should be (wp - wb) (Bi - B)

where B = return of the benchmark

In fact, on page 182 they use the first formula while on page 197 (same chapter) the allocation effect has been computed using the 2nd formula mentioned above.

Any one’s seen this.

Yeah,I noticed it. But I think the formula on

page 182 is right. If you add the allocation effect, the

selection effect and the interaction together, it should equal to wi*Ri-Wi*Bi.


formula (wp - wb) (Bi - B) is for interaction effect. The formula in the book is correct.

The interaction effect = (wp - wb) (Ri - Bi)

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There are actually two versions of the formula.

The one by Brinson and Fachler (1985) is (wp - wb) (Bi - B).

The one by Brinson, Hood, and Beebower (1986) is (wp - wb) (Bi).

The book collectively refers to the two above under the Brinson model.

The TOTAL allocation effect is the same for both formulas, but distinctly different when applied on an individual sector/security level.

Just to demonstrate, under the Brinson-Fachler (BF) approach,

Total allocation effect(BF) = SumOf(wp - wb) (Bi - B) = SumOf(wp - wb) (Bi) - SumOf(wp - wb) (B) = SumOf(wp - wb) (Bi) - 0 x (B) = SumOf(wp - wb) (Bi)