BAFI6010 · Advanced Investment Management
Performance Attribution
Performance attribution is the review stage of the investment-management process in BAFI 6010: after you set objectives, allocate, and implement, you decompose a fund's realised return into the risk factors and manager decisions that produced it, so you can separate luck (market risk) from skill. The method is forced by the data — with only a return history you run top-down returns-based measures (Sharpe, Treynor, information ratio, Jensen's alpha), and with holdings you run a bottom-up Brinson decomposition into allocation and selection effects. The single most tested idea is that raw outperformance is not the same as a statistically significant alpha: a fund can beat its benchmark simply by taking more beta risk, so skill is judged by the p-value, not the size of the number.
What this chapter covers
- 011. Three evaluation steps — measurement (how well), attribution (which factors), appraisal (skill vs luck)
- 022. Top-down vs bottom-up gate — the method is decided by whether holdings/exposures are available
- 033. A valid attribution benchmark — Identifiable, Investable, Pre-specified, Representative
- 044. Top-down measures — Sharpe (total σ), Treynor (β), information ratio (tracking error), Jensen's alpha (β-adjusted)
- 055. Jensen's alpha & its test — α = actual − CAPM-required; t = α/SE(α); low p-value ⇒ significant skill
- 066. Bottom-up Brinson — allocation (market timing) + selection (stock picking) + interaction, summing to total
- 077. Returns-based style analysis — regress on style indices, weights sum to 1, positive intercept = value added
- 088. The headline trap — bottom-up outperformance ≠ top-down alpha; judge skill by significance, not size
Brinson decomposition — allocation, selection and interaction
- +1Totals. Benchmark = 0.65(8%) + 0.35(3%) = 6.25%; portfolio = 0.55(9%) + 0.45(5%) = 7.20%; so out-performance = +0.95%.
- +1Allocation (market timing) = Σ (wP − wB)(rB,segment − rB,total): Equities (−0.10)(8 − 6.25) = −0.175%; Bonds (+0.10)(3 − 6.25) = −0.325%; total = −0.50%.
- +1Selection (stock picking) = Σ wB (rP,segment − rB,segment): Equities 0.65(9 − 8) = 0.65%; Bonds 0.35(5 − 3) = 0.70%; total = +1.35%.
- +1Interaction = Σ (wP − wB)(rP,segment − rB,segment): Equities (−0.10)(1) = −0.10%; Bonds (0.10)(2) = +0.20%; total = +0.10%.
- +2Reconcile and interpret: −0.50 + 1.35 + 0.10 = +0.95% ✓. Selection (+1.35%) dominates while allocation is negative, so the manager's edge is stock selection; segment timing was poor (equities, the stronger segment, were under-weighted).
Key terms
- Performance measurement / attribution / appraisal
- The three steps of portfolio evaluation: measurement is the raw realised return and risk (how well it did), attribution decomposes that into risk factors and decisions (which explain it), and appraisal interprets whether the result was market risk or genuine manager skill.
- Top-down (returns-based) analysis
- Used when only the return history is available. Risk-adjusted return measures TEST for skill but give limited attribution — you can tell whether there is an edge, but not exactly where it came from.
- Bottom-up (Brinson) analysis
- Used when segment weights and returns are available. It both tests for skill AND decomposes value added into allocation and selection effects that reconcile to total outperformance.
- Jensen's alpha
- The active/abnormal return: α = r_fund − [r_f + β(E(r_m) − r_f)], the return above the CAPM-required level for the fund's beta. It captures all sources of relative performance in one number and is estimated as the intercept of a regression of excess fund returns on excess benchmark returns.
- Alpha significance test
- A two-sided t-test with t = α/SE(α), H0: α = 0 (no skill / efficient markets) vs H1: α ≠ 0 (skill). A low p-value means the alpha is statistically distinguishable from zero — evidence of repeatable skill; a fat p-value means it could just be luck.
- Allocation effect (market timing)
- The part of outperformance from over- or under-weighting segments: Σ (wP − wB)(rB,segment − rB,total). Positive means the manager over-weighted the segments that beat the benchmark average — good timing.
- Selection effect (stock selection)
- The part of outperformance from picking within segments: Σ wB(rP,segment − rB,segment). Positive means the manager's holdings beat the segment benchmark — good stock picking.
- Returns-based style analysis
- Sharpe's method of regressing fund returns on a set of style-index returns with weights constrained to sum to 1. The coefficients estimate the fund's average style mix (its tilt), and a positive intercept implies value added over passive style investing.
Performance Attribution FAQ
Why can a fund have large bottom-up outperformance but an insignificant top-down alpha?
Bottom-up (Brinson) outperformance is a raw weight × return gap with NO risk adjustment, while alpha is beta-adjusted — it strips out the return earned simply by taking more market (beta) risk. A fund can beat its benchmark by holding more systematic risk; once that beta is removed, the genuine skill (alpha) is much smaller. And a numerically large alpha with a high p-value is statistically indistinguishable from zero, so it is no evidence of repeatable skill. Judge skill by significance, not size.
How do I decide between top-down and bottom-up attribution?
The DATA decides, not preference. If you only have a return history, you are limited to top-down returns-based measures that test for skill. Once you can see the manager's holdings and segment weights, you can run a full bottom-up Brinson decomposition that both tests skill and attributes where it came from — allocation vs selection.
What is the difference between the allocation and selection effects, and how do I avoid mixing them up?
Allocation (market timing) uses EXCESS weight × BENCHMARK segment return relative to the benchmark total: Σ (wP − wB)(rB,i − rB). Selection (stock picking) uses BENCHMARK weight × RELATIVE segment return: Σ wB(rP,i − rB,i). The classic mistake is swapping the weights and returns; if you do, both effects come out wrong and will not reconcile to the total outperformance — which is your built-in check.
Which performance measure should I use — Sharpe, Treynor, the information ratio or alpha?
Match the measure to the risk that matters. For a stand-alone fund use Sharpe (total σ). For a sleeve inside a diversified portfolio use Treynor or alpha (systematic β). For an active manager versus a benchmark use the information ratio (α over tracking error). The exam often penalises discussing MORE measures than asked, so pick the two most decisive — usually the significance of alpha plus the information or Sharpe ratio — and defend them.
What does returns-based style analysis tell me, and what are its limits?
Regressing fund returns on style-index returns (with weights forced to sum to 1) estimates the fund's average style mix — for example a small-value tilt — and a positive intercept implies value added over passive style investing. Its limits, which the exam wants named: the chosen style benchmarks may not match the portfolio, the loadings are estimated with error (high standard errors), and because real weights change daily the regression recovers only the AVERAGE exposure over the window.
Is a positive alpha enough to conclude a manager is skilled?
No. A positive alpha only signals skill if it is statistically significant. Run the t-test t = α/SE(α) against H0: α = 0 and read the p-value: a low p-value (say below 0.05) means the alpha is distinguishable from zero and is evidence of repeatable skill, while a fat p-value means the outperformance cannot be separated from luck. Always report the number WITH its significance test.
Exam move
Attribution is examined in the end-of-semester final, which is about 80% applied discussion, and a favourite set-piece asks you to run top-down, bottom-up and style analysis on competing funds and then recommend a manager. Drill the two computations until they are automatic: Jensen's alpha with its t-test (compute the CAPM-required return, subtract to get alpha, then t = α/SE(α) and translate to a skill/luck verdict), and the Brinson decomposition (totals, then allocation, selection and interaction each on its own line, reconciled to the raw outperformance). Because this is a closed-book course with no formula sheet, write from memory the three evaluation steps, the four risk-adjusted measures and the two Brinson formulae. Above all, internalise the headline distinction the exam is built to test — raw outperformance is not the same as a significant alpha — and remember the exam penalises discussing more measures than asked, so choose the two most decisive and defend them. Confirm the provided-materials policy in your course outline.
