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Performance attribution and appraisal

In this chapter: Brinson attribution (allocation, selection, interaction) · Multi-period geometric attribution · Sharpe, Treynor, Jensen alpha, IR · M² (M-squared) · Style analysis

~3 min readLayer 4 · Professional CertificationsFree

Attribution decomposes active return into sources. Appraisal ratios measure risk-adjusted returns. Together they evaluate manager skill.

Foundation

**Brinson-Hood-Beebower (BHB) attribution**: For multi-asset portfolio: - Allocation effect: sum_i (w_p,i – w_b,i) × (R_b,i – R_b) - Selection effect: sum_i w_b,i × (R_p,i – R_b,i) - Interaction effect: sum_i (w_p,i – w_b,i) × (R_p,i – R_b,i) - Total active = R_p – R_b = Allocation + Selection + Interaction. BHB tells you: was return from picking right asset classes (allocation) or right securities within (selection)? **Sharpe ratio** = (R_p – R_f) / σ_p. Total risk basis. **Treynor ratio** = (R_p – R_f) / β_p. Systematic-risk basis. **Jensen alpha** = R_p – [R_f + β(R_m – R_f)]. CAPM-implied excess. **Information ratio** = α / TE. Active-management measure. **M² (M-squared)** = R_f + Sharpe × σ_m. Levers/de-levers portfolio to match benchmark vol.

Deep Dive

Multi-period attribution: - Geometric linking handles compounding correctly. - Arithmetic linking sums attributions but misses compounding effects over long periods. GIPS-compliant performance: - Time-weighted returns mandatory for composites. - Quarterly+ when significant external cash flows. - Currency: report in firm's base currency or composite definition. - Disclose: gross vs net, fees, benchmark. Factor-based attribution (BARRA-style): - Decompose into factor exposures (size, value, momentum, etc.) + specific. - Says "30bps from value tilt, 20bps from momentum, –10bps from size, 60bps stock-specific."

Advanced

L3 essay traps: - Confusing TWR with money-weighted (IRR). TWR for manager skill (timing-controlled), MWR for client experience. - Allocation vs selection effect signs flip with benchmark choice. Define benchmark first. - Style drift: manager claims value but factor analysis shows growth tilt. Affects attribution interpretation. Manager evaluation framework: 1. Performance: TWR vs benchmark over multiple periods. 2. Risk-adjusted: Sharpe, IR. 3. Style consistency. 4. Process integrity. 5. People (key-person risk). 6. Operations (compliance, ops infrastructure).

Regulatory references
  • GIPS Standards
  • CFA Institute PM curriculum
  • AMFI Disclosure Norms
Common mistakes & pitfalls
  • Mixing TWR and MWR — different purposes, different stories.
  • Comparing manager vs wrong benchmark (style mismatch).
  • Annualising short-period attribution without geometric linking.

Frequently asked

Sharpe vs Treynor — which to use?
Sharpe for fully-diversified portfolio (total risk). Treynor for component of larger portfolio (only systematic risk relevant). IR for active managers vs benchmark.
Why does BHB allocation effect depend on benchmark return?
Allocation = (deviation × outperformance of class vs total benchmark). Excess class return relative to total benchmark drives allocation reward.

Practice questions

Click each question to reveal the answer and explanation.

Q 1
Sharpe ratio uses:
  1. (a)Beta
  2. (b)Total volatility (σ)
  3. (c)Tracking error
  4. (d)R²
Correct: (b) Total volatility (σ)
Sharpe = (R_p - R_f) / σ. Total risk in denominator.
Q 2
Treynor ratio uses:
  1. (a)σ
  2. (b)Beta
  3. (c)TE
  4. (d)Alpha
Correct: (b) Beta
Treynor = (R_p - R_f) / β. Systematic risk only.
Q 3
Information ratio uses:
  1. (a)σ
  2. (b)β
  3. (c)Tracking error
  4. (d)Variance
Correct: (c) Tracking error
IR = active return / tracking error.
Q 4
BHB attribution decomposes active return into:
  1. (a)α and β
  2. (b)Allocation, selection, interaction
  3. (c)Sharpe components
  4. (d)Risk components
Correct: (b) Allocation, selection, interaction
BHB: allocation + selection + interaction = total active.
Q 5
TWR is preferred over MWR for:
  1. (a)Client returns
  2. (b)Manager skill evaluation
  3. (c)Tax reporting
  4. (d)IRR calculation
Correct: (b) Manager skill evaluation
TWR removes effect of cash flow timing → reflects manager decisions only. MWR for client total experience.
Educational purposes only. The numbers, returns, and examples used in this lesson are illustrative. Past performance does not guarantee future results. Mutual fund and securities investments are subject to market risks. This lesson is not investment advice; for advice tailored to your circumstances, consult a SEBI-registered Investment Adviser. Read our full disclaimer.