| name | performance-attribution |
| description | Performance attribution analysis — Brinson sector/stock-selection attribution, factor alpha/beta decomposition, market-timing evaluation, and benchmark comparison framework. |
| category | analysis |
Performance Attribution Analysis
Overview
Decompose portfolio excess returns into explainable sources: sector allocation, stock selection, factor exposure, timing contribution, and more. This helps explain why a strategy made or lost money, rather than only how much it made or lost.
Brinson Attribution Model
Single-Period Brinson-Fachler Model
Total excess return = portfolio return - benchmark return
Decomposed into three parts:
1. Allocation effect: sector-weight deviation × sector benchmark return deviation
2. Selection effect: stock selection within a sector × sector benchmark weight
3. Interaction effect: weight deviation × stock-selection deviation
Mathematical formulas:
Let w_p,i = portfolio weight of sector i
w_b,i = benchmark weight of sector i
r_p,i = portfolio return of sector i
r_b,i = benchmark return of sector i
R_b = total benchmark return
Allocation_i = (w_p,i - w_b,i) × (r_b,i - R_b)
Selection_i = w_b,i × (r_p,i - r_b,i)
Interaction_i = (w_p,i - w_b,i) × (r_p,i - r_b,i)
Total excess = Σ(Allocation_i) + Σ(Selection_i) + Σ(Interaction_i)
Example Brinson Attribution
### Brinson Sector Attribution
| Sector | Portfolio Weight | Benchmark Weight | Portfolio Return | Benchmark Return | Allocation | Selection | Interaction |
|------|---------|---------|---------|---------|---------|---------|---------|
| Food & Beverage | 20% | 10% | 15% | 8% | +0.3% | +0.7% | +0.7% |
| Electronics | 15% | 12% | 5% | 10% | -0.1% | -0.6% | +0.2% |
| Banks | 5% | 20% | 3% | 2% | +0.3% | +0.2% | -0.2% |
| Others | 60% | 58% | 8% | 7% | +0.0% | +0.6% | +0.0% |
| **Total** | 100% | 100% | 9.5% | 6.2% | **+0.5%** | **+0.9%** | **+0.7%** |
Excess return 3.3% = allocation effect 0.5% + selection effect 0.9% + interaction effect 0.7% + residual 0.2%
Multi-Period Attribution (Linked Brinson)
Directly summing single-period attribution creates residuals (compounding effect). Common approaches:
Method 1: arithmetic linking (simple sum of each period's attribution)
- Advantage: simple
- Disadvantage: residual remains
Method 2: Carino logarithmic linking
- Advantage: no residual
- Disadvantage: more complex
Practical recommendation: arithmetic linking is enough for monthly attribution; residuals are usually <0.1%
Factor Attribution
Alpha-Beta Decomposition
R_p = α + β × R_m + ε
α (alpha): excess return, manager skill
β (beta): market exposure, systematic risk
ε (epsilon): residual, idiosyncratic risk
Regression method: OLS regression, with at least 60 data points
Multi-Factor Attribution (Fama-French Extension)
R_p - R_f = α + β_mkt × (R_m - R_f) + β_smb × SMB + β_hml × HML + β_mom × MOM + ε
| Factor | Meaning | China A-share Proxy |
|------|------|--------|
| MKT | Market | CSI 300 return |
| SMB | Small-cap premium | CSI 500 - CSI 300 |
| HML | Value premium | high-PB group - low-PB group |
| MOM | Momentum | top past-12M winners - bottom group |
Factor Exposure Analysis Template
### Factor Exposure Analysis
| Factor | Beta | t-stat | Significance | Interpretation |
|------|------|---------|--------|------|
| Market (MKT) | 0.85 | 12.3 | *** | Below 1, defensive profile |
| Small-cap (SMB) | 0.25 | 3.2 | ** | Small-cap tilt |
| Value (HML) | -0.15 | -1.8 | * | Growth tilt |
| Momentum (MOM) | 0.30 | 4.1 | *** | Significant momentum exposure |
| **Alpha** | **0.8% / month** | **2.5** | ** | **Significant alpha** |
R² = 0.72 → factors explain 72% of return variation
Alpha = 0.8% / month = 10% / year, significant
Market-Timing Evaluation
Treynor-Mazuy Model
R_p - R_f = α + β × (R_m - R_f) + γ × (R_m - R_f)² + ε
γ > 0 and significant → timing ability exists (adds risk in bull markets, cuts risk in bear markets)
γ ≤ 0 → no timing ability
Henriksson-Merton Model
R_p - R_f = α + β × (R_m - R_f) + γ × max(R_m - R_f, 0) + ε
γ > 0 → portfolio beta is higher in bull markets (successful timing)
Practical Timing Metrics
| Metric | Calculation | Meaning |
|---|
| Bull capture ratio | portfolio return in bull markets / benchmark return | >100% = outperforming |
| Bear capture ratio | portfolio return in bear markets / benchmark return | <100% = better downside defense |
| Timing hit rate | proportion of months where market direction was called correctly | >55% = shows skill |
| Correlation between position changes and market | corr(position_change, future_return) | >0 = timing is correct |
Benchmark Comparison Framework
Benchmark Selection
| Strategy Type | Recommended Benchmark | China A-share Code |
|---|
| China A-share large cap | CSI 300 | 000300.SH |
| China A-share small cap | CSI 500 / CSI 1000 | 000905.SH |
| China A-share broad market | CSI All Share | 000985.SH |
| Hong Kong equities | Hang Seng Index | HSI |
| US equities | S&P 500 | SPX |
| Crypto | BTC | BTC-USDT |
| Multi-asset | 60/40 portfolio | self-constructed |
Risk-Adjusted Performance Metrics
| Metric | Formula | Excellent | Good | Average |
|---|
| Sharpe | (R_p - R_f) / σ_p | >1.5 | 1.0-1.5 | 0.5-1.0 |
| Sortino | (R_p - R_f) / σ_down | >2.0 | 1.5-2.0 | 1.0-1.5 |
| Calmar | R_p / MaxDD | >1.0 | 0.5-1.0 | 0.2-0.5 |
| Information Ratio | (R_p - R_b) / TE | >1.0 | 0.5-1.0 | 0.2-0.5 |
| Treynor | (R_p - R_f) / β | used comparatively | | |
Rolling Analysis
Use rolling windows (such as 12 months) to analyze:
- Rolling Sharpe: strategy stability
- Rolling alpha: whether alpha persists
- Rolling beta: whether market exposure is stable
- Rolling information ratio: persistence of benchmark outperformance
Suggested windows: 252 days for daily data, 12-36 months for monthly data
Analysis Framework
Step 1: Aggregate Analysis
1. Cumulative return vs benchmark
2. Excess-return decomposition (annual / monthly)
3. Summary risk metrics (volatility / max drawdown / Sharpe)
Step 2: Attribution Decomposition
1. Brinson attribution (if sector information is available)
2. Factor attribution (alpha / beta / factor exposure)
3. Timing attribution (TM / HM models)
Step 3: Style Analysis
1. Large cap vs small cap exposure
2. Growth vs value exposure
3. Style drift detection (rolling style analysis)
Step 4: Conclusions and Recommendations
1. Main sources of excess return
2. Whether risk exposure is reasonable
3. Suggested improvement directions
Output Format
## Performance Attribution Report
### Performance Overview
| Metric | Strategy | Benchmark | Excess |
|------|------|------|------|
| Cumulative return | +85.2% | +32.1% | +53.1% |
| Annualized return | 12.5% | 5.8% | +6.7% |
| Annualized volatility | 18.2% | 20.5% | - |
| Sharpe | 0.69 | 0.28 | - |
| Information Ratio | 0.82 | - | - |
### Attribution Breakdown
| Source | Contribution (annualized) | Share |
|------|-----------|------|
| Sector allocation | +2.1% | 31% |
| Stock selection | +3.8% | 57% |
| Timing | +0.8% | 12% |
### Factor Exposure
[factor exposure table]
### Conclusion
Excess return mainly comes from stock selection (57% contribution), followed by sector allocation.
Alpha is significant (`t=2.5`), indicating real stock-picking ability.
Watch the risk of excessive small-cap exposure (`SMB beta=0.25`).
Notes
- Attribution ≠ prediction: attribution explains the past; it does not guarantee persistence in the future
- Benchmark selection affects attribution: switch the benchmark and alpha may disappear, so benchmark choice must be appropriate
- Data frequency: daily attribution is noisy, monthly attribution is more stable but has fewer samples; recommended workflow is daily computation with monthly reporting
- Survivorship bias: delisted stocks may be excluded in backtests, creating false alpha
- Multiple-testing problem: if you test 100 strategies, about 5 may appear significant by chance (
p=0.05); use multiple-comparison correction
- Factor data requirement: factor attribution requires factor return data, which can be obtained from DNSE API or self-constructed
- Attribution in backtest reports:
metrics.csv already provides basic metrics after a backtest; this skill adds deeper attribution analysis
