How does the Brinson-Fachler holdings-based attribution model decompose active return into allocation and selection effects?
I'm studying performance attribution for CFA Level III and need to understand the Brinson model. How do you calculate the allocation effect (sector betting) versus the selection effect (stock picking) from actual holdings data?
The Brinson-Fachler model (and its predecessor, Brinson-Hood-Beebower) is the standard holdings-based performance attribution framework. It decomposes the portfolio's active return into three components: allocation effect, selection effect, and interaction effect.
Definitions
| Component | Formula | What It Measures |
|---|---|---|
| Allocation | SUM[(w_p,i - w_b,i) x (R_b,i - R_b)] | Value from over/underweighting sectors relative to benchmark |
| Selection | SUM[w_b,i x (R_p,i - R_b,i)] | Value from picking better/worse stocks within sectors |
| Interaction | SUM[(w_p,i - w_b,i) x (R_p,i - R_b,i)] | Joint effect of overweighting AND selecting well |
| Total Active | Allocation + Selection + Interaction = R_p - R_b | Complete explanation |
Worked Example
Hathaway Active Fund vs. S&P 500 benchmark (simplified to 4 sectors):
| Sector | Port Weight | Bench Weight | Port Return | Bench Sector Return |
|---|---|---|---|---|
| Technology | 35% | 30% | 18.0% | 15.5% |
| Healthcare | 20% | 15% | 8.2% | 9.0% |
| Financials | 25% | 30% | 12.5% | 11.0% |
| Consumer | 20% | 25% | 6.8% | 7.5% |
| Total | 100% | 100% | 12.38% | 11.25% |
Benchmark total return: 0.30(15.5) + 0.15(9.0) + 0.30(11.0) + 0.25(7.5) = 11.25%
Allocation Effect (sector betting):
| Sector | w_p - w_b | R_b,i - R_b | Allocation |
|---|---|---|---|
| Technology | +5% | 15.5 - 11.25 = 4.25% | +0.213% |
| Healthcare | +5% | 9.0 - 11.25 = -2.25% | -0.113% |
| Financials | -5% | 11.0 - 11.25 = -0.25% | +0.013% |
| Consumer | -5% | 7.5 - 11.25 = -3.75% | +0.188% |
| Total Allocation | +0.300% |
Selection Effect (stock picking):
| Sector | w_b,i | R_p,i - R_b,i | Selection |
|---|---|---|---|
| Technology | 30% | 18.0 - 15.5 = 2.5% | +0.750% |
| Healthcare | 15% | 8.2 - 9.0 = -0.8% | -0.120% |
| Financials | 30% | 12.5 - 11.0 = 1.5% | +0.450% |
| Consumer | 25% | 6.8 - 7.5 = -0.7% | -0.175% |
| Total Selection | +0.905% |
Interaction: Total active (1.13%) - Allocation (0.300%) - Selection (0.905%) = -0.075%
Insight: Hathaway's active return of 1.13% came primarily from stock selection (+0.91%), with a smaller contribution from sector allocation (+0.30%). The manager is a better stock picker than sector allocator.
Limitations:
- Single-period only — multi-period attribution requires geometric linking (Carino, Menchero methods)
- Does not explain why the manager made those bets (need qualitative overlay)
- Currency effects require separate attribution for international portfolios
For more on attribution methodology, check our CFA Level III question bank.
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