Tools › Investing › Portfolio and Risk › Performance Attribution › Example

Performance attribution: a five-sector portfolio 1.10 points ahead of its benchmark, split into allocation, selection and interaction

Tool	Performance Attribution
Source	Brinson, G. P., Hood, L. R., and Beebower, G. L. (1986). Determinants of Portfolio Performance. Financial Analysts Journal, Vol. 42, No. 4; Brinson, G. P., and Fachler, N. (1985). Measuring Non-U.S. Equity Portfolio Performance. Journal of Portfolio Management, Vol. 11, No. 3 (the definitions). The case is illustrative, not a printed example.
Level	Undergraduate

Problem

A portfolio and its benchmark are divided into five sectors. Portfolio weights 30, 15, 20, 5, 30 % with returns 12, 4, 7, −3, 5 %; benchmark weights 25, 15, 20, 10, 30 % with returns 10, 6, 5, −2, 5.5 % (Technology, Health Care, Financials, Energy, Consumer). Find the active return and split it by sector into allocation, selection and interaction effects, with the Brinson-Fachler form of the allocation effect.

Inputs to Enter

Portfolio weights 30 / 15 / 20 / 5 / 30 %, portfolio returns 12 / 4 / 7 / −3 / 5 %
Benchmark weights 25 / 15 / 20 / 10 / 30 %, benchmark returns 10 / 6 / 5 / −2 / 5.5 %

Open the Performance Attribution tool (loaded with this example)

Answers

Portfolio return (30·12 + 15·4 + 20·7 + 5·(−3) + 30·5) / 100 = 6.95 %; benchmark return (25·10 + 15·6 + 20·5 + 10·(−2) + 30·5.5) / 100 = 5.85 %; active return 1.10 points
Technology: allocation (30 − 25) · 10 / 100 = +0.500; selection 25 · (12 − 10) / 100 = +0.500; interaction (30 − 25)(12 − 10) / 100 = +0.100
Energy: allocation (5 − 10)(−2) / 100 = +0.100; selection 10 · (−3 + 2) / 100 = −0.100; interaction +0.050
Selection of the sectors held at benchmark weight: Health Care −0.300, Financials +0.400, Consumer −0.150
Totals: allocation +0.600, selection +0.350, interaction +0.150; 0.600 + 0.350 + 0.150 = 1.100, the active return
Brinson-Fachler allocation: Technology (30 − 25)(10 − 5.85) / 100 = +0.2075, Energy (5 − 10)(−2 − 5.85) / 100 = +0.3925; total +0.600 as before
Advanced mode, second period (portfolio 0.390 %, benchmark 1.075 %): compounded returns 7.367 % and 6.988 %, active +0.379; Carino factors 0.93986, 0.99273 and 0.93303; linked allocation +0.136, selection +0.007, interaction +0.236

Notes

The tool's default inputs are this case; press Submit. The numbers are invented for illustration and are not market data. Every effect is checked against an independent numpy implementation on 60 seeded cases (test_performance_attribution.php). An effect says where a difference arose, not whether it came from skill. A calculator for education and analysis, not investment advice.