Estimated study time: 45 minutes
Content:
Performance attribution explains the sources of a portfolio's return relative to a benchmark. At Level 3, candidates must understand both the Brinson-Hood-Beebower (BHB) model and its extensions, be able to interpret attribution results, and distinguish between return attribution and risk attribution. Attribution is essential for evaluating active managers — it answers the question: "Where did the alpha come from?"
The Brinson-Hood-Beebower attribution model decomposes active return (portfolio return minus benchmark return) into three effects: allocation effect, selection effect, and interaction effect. Allocation effect measures the value added (or lost) from overweighting or underweighting sectors relative to the benchmark, using benchmark sector returns to isolate the pure sector-weighting decision. Allocation effect for sector i = (w_pi − w_bi) × (R_bi − R_b), where w_pi is portfolio weight, w_bi is benchmark weight, R_bi is benchmark sector return, and R_b is total benchmark return. A manager adds value from allocation if she overweights sectors that outperform the overall benchmark.
Selection effect measures value added from choosing better securities within each sector. Selection effect for sector i = w_bi × (R_pi − R_bi), where R_pi is portfolio sector return. If the manager's stock picks outperform the benchmark sector return within that sector, selection is positive. Interaction effect captures the joint impact of overweighting a sector where selection was also positive: interaction = (w_pi − w_bi) × (R_pi − R_bi). Some attribution frameworks combine selection and interaction into a single "selection + interaction" term to avoid the ambiguity of attributing interactive effects separately.
Fixed income attribution is more complex than equity attribution because returns are driven by multiple factors: the overall level of interest rates (duration effect), the slope of the yield curve (curve effect), credit spreads (spread effect), and security-specific effects (selection). The duration effect captures the impact of the portfolio's duration positioning relative to the benchmark on overall rate changes. The curve effect captures the impact of yield curve positioning (bullet vs. barbell, yield curve bets). The spread effect captures the impact of credit spread changes on portfolios overweighted in credit.
Risk attribution assigns the portfolio's total risk (tracking error) to its sources rather than assigning return. Factor-based risk attribution uses a factor model to decompose tracking error into contributions from each active factor exposure. This tells the manager where her active risk budget is being "spent." If a manager's active risk is concentrated in one factor (say, value), that factor's risk contribution dominates — useful for assessing whether the active risk is intentional and compensated.
Key Terms:
Quiz Questions:
Q1. A manager overweights the technology sector (benchmark weight 20%, portfolio weight 30%). The technology sector return was 15%, and the overall benchmark returned 10%. The allocation effect for the technology sector is:
A) (30% − 20%) × (15% − 10%) = 0.5% B) (30% − 20%) × (10% − 10%) = 0% C) (30% − 20%) × (15% − 10%) = 0.5% D) 20% × (15% − 10%) = 1.0%
Answer: A — Allocation effect = (w_pi − w_bi) × (R_bi − R_b) = (30% − 20%) × (15% − 10%) = 10% × 5% = 0.50%. The manager added 0.50% through the sector overweight decision.
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Q2. Within the technology sector, the manager's stock picks returned 18% while the benchmark technology sector returned 15%. The portfolio weight in technology is 30%, and the benchmark weight is 20%. The selection effect for technology is:
A) 30% × (18% − 15%) = 0.9% B) 20% × (18% − 15%) = 0.6% C) 10% × (18% − 15%) = 0.3% D) 30% × (18% − 10%) = 2.4%
Answer: B — Selection effect = w_bi × (R_pi − R_bi) = 20% × (18% − 15%) = 20% × 3% = 0.60%. Note: the selection effect uses the benchmark weight (20%), not the portfolio weight (30%). This isolates the pure stock-picking contribution, holding the sector weighting constant at the benchmark level.
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Q3. A fixed income portfolio has a modified duration of 7.5 years versus the benchmark duration of 6.0 years. If rates fall by 50 basis points, the approximate contribution of the duration position to active return is:
A) +0.75% B) +0.375% C) −0.75% D) +1.5%
Answer: A — Active duration = 7.5 − 6.0 = 1.5 years. Rate change = −0.50%. Duration contribution to active return ≈ −(active duration) × (rate change) = −1.5 × (−0.50%) = +0.75%. The long duration position benefited from falling rates.
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Q4. A manager's annual active return is +1.8%. Attribution analysis shows: allocation effect = +2.5%, selection effect = −0.3%, interaction effect = −0.4%. Which component contributed most to the outperformance?
A) Security selection within sectors B) Sector allocation — overweighting outperforming sectors C) The interaction between overweighting and selection within those sectors D) Currency management
Answer: B — The allocation effect (+2.5%) is the largest positive contributor. Despite negative selection (−0.3%) and interaction (−0.4%), the manager's sector allocation decisions drove the overall active return of +1.8%. This tells us the manager's value comes from top-down sector rotation, not bottom-up stock picking.
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Q5. A risk attribution analysis shows that 80% of a manager's total tracking error comes from her value factor exposure. The expected return from the value factor this year is negative. The most appropriate conclusion for an investment committee is:
A) The manager is diversified and appropriately positioned B) The manager is taking concentrated, uncompensated risk — most of the active risk budget is spent on a factor expected to generate negative returns C) 80% tracking error from one factor is normal for a well-diversified active manager D) The manager should add leverage to earn more return per unit of risk
Answer: B — Risk attribution revealed that the manager's active risk is highly concentrated in one factor (value), and that factor is expected to underperform. This means she is spending most of her risk budget on a likely losing bet. A well-managed active portfolio would have diversified factor exposures or be concentrated in factors where the manager has conviction of positive expected returns.
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