Benchmark Analysis¶
Compare strategy performance against market benchmarks.
Specifying a Benchmark¶
Text Only
portfolio main:
weights = rank(signal).long_short(top=0.2, bottom=0.2)
backtest rebal=21 benchmark=SPY from 2020-01-01 to 2024-12-31
Common Benchmarks¶
| Benchmark | Description | Use For |
|---|---|---|
SPY |
S&P 500 ETF | US large cap |
QQQ |
Nasdaq 100 ETF | US tech/growth |
IWM |
Russell 2000 ETF | US small cap |
VTI |
Total US Market | Broad US |
EFA |
EAFE ETF | International developed |
EEM |
Emerging Markets ETF | Emerging markets |
AGG |
US Aggregate Bond | Bonds |
cash |
Risk-free rate | Absolute return |
Benchmark Metrics¶
Alpha¶
Excess return after adjusting for market exposure:
\[\alpha = R_p - (R_f + \beta (R_m - R_f))\]
Interpretation: Strategy generated 4.2% above what beta exposure would predict.
Beta¶
Sensitivity to benchmark:
\[\beta = \frac{\text{Cov}(R_p, R_m)}{\text{Var}(R_m)}\]
Interpretation: When benchmark moves 1%, strategy moves ~0.72%.
Tracking Error¶
Volatility of excess returns:
\[\text{TE} = \sigma(R_p - R_b)\]
Information Ratio¶
Alpha per unit of tracking error:
\[\text{IR} = \frac{\alpha}{\text{TE}}\]
| IR | Quality |
|---|---|
| < 0.25 | Poor |
| 0.25-0.5 | Average |
| 0.5-0.75 | Good |
| > 0.75 | Excellent |
Active Share¶
How different is the portfolio from benchmark:
- < 20%: Closet indexer
- 20-60%: Moderate active
-
60%: Truly active
Up/Down Capture¶
Up Capture Ratio¶
Performance when benchmark is up:
\[\text{Up Capture} = \frac{\text{Avg Strategy Return (up months)}}{\text{Avg Benchmark Return (up months)}}\]
Down Capture Ratio¶
Performance when benchmark is down:
\[\text{Down Capture} = \frac{\text{Avg Strategy Return (down months)}}{\text{Avg Benchmark Return (down months)}}\]
Capture Ratio¶
1.0 means strategy captures more upside than downside.
Relative Performance¶
Cumulative Excess Return¶
Text Only
Period | Strategy | Benchmark | Excess
-----------------+----------+-----------+-------
2020 | 21.2% | 18.4% | +2.8%
2021 | 18.5% | 28.7% | -10.2%
2022 | -8.2% | -18.1% | +9.9%
2023 | 25.8% | 26.3% | -0.5%
2024 (YTD) | 12.3% | 15.2% | -2.9%
-----------------+----------+-----------+-------
Cumulative | 85.2% | 75.4% | +9.8%
Rolling Excess Return¶
Shows 12-month rolling alpha over time.
Benchmark Attribution¶
Single-Factor Model¶
Text Only
Strategy Return = Alpha + Beta × Benchmark Return + Residual
Example:
Strategy: +12%
Benchmark: +10%
Beta: 0.8
Expected: 0.8 × 10% = 8%
Alpha: 12% - 8% = 4%
Multi-Factor Model¶
Output:
Text Only
Factor Attribution:
Factor | Exposure | Factor Return | Contribution
----------+----------+---------------+-------------
Market | 0.72 | 10.5% | 7.6%
SMB | 0.35 | 2.1% | 0.7%
HML | -0.15 | -1.5% | 0.2%
MOM | 0.45 | 5.2% | 2.3%
----------+----------+---------------+-------------
Factor Sum| | | 10.8%
Alpha | | | 3.4%
Total | | | 14.2%
Correlation Analysis¶
Rolling Correlation¶
Correlation Matrix¶
Text Only
Strategy SPY QQQ IWM
Strategy 1.00 0.72 0.65 0.58
SPY 0.72 1.00 0.88 0.82
QQQ 0.65 0.88 1.00 0.72
IWM 0.58 0.82 0.72 1.00
Regime Analysis¶
Performance in different market environments:
By Market Direction¶
Text Only
Market Regime | # Months | Strategy | Benchmark | Excess
-----------------+----------+----------+-----------+-------
Strong Up (>5%) | 18 | 4.2% | 8.5% | -4.3%
Mild Up (0-5%) | 32 | 2.8% | 2.1% | +0.7%
Mild Down (-5-0) | 25 | -1.5% | -2.3% | +0.8%
Strong Down(<-5%)| 10 | -3.2% | -8.5% | +5.3%
By Volatility Regime¶
Text Only
VIX Regime | # Months | Strategy | Benchmark | Excess
----------------+----------+----------+-----------+-------
Low (<15) | 28 | 1.8% | 1.5% | +0.3%
Medium (15-25) | 42 | 0.9% | 0.5% | +0.4%
High (>25) | 15 | -0.5% | -2.1% | +1.6%
Benchmark Selection¶
Match Your Universe¶
Text Only
// US large cap strategy
backtest benchmark=SPY ...
// Small cap strategy
backtest benchmark=IWM ...
// Tech focus
backtest benchmark=QQQ ...
Long-Short Strategies¶
For market-neutral strategies:
Text Only
// Compare to cash (risk-free rate)
backtest benchmark=cash ...
// Or no benchmark
backtest from ... // Absolute return
Multi-Asset¶
Custom Benchmarks¶
Equal-Weight Benchmark¶
Text Only
data benchmark:
source = "benchmark_weights.csv"
portfolio main:
backtest benchmark=benchmark from ...
Factor Benchmark¶
Text Only
// Your own factor portfolio as benchmark
signal benchmark_signal:
emit zscore(ret(prices, 60))
portfolio benchmark_port:
weights = rank(benchmark_signal).long_short(top=0.5, bottom=0.5)
portfolio main:
backtest benchmark=benchmark_port from ...
Best Practices¶
1. Use Appropriate Benchmark¶
Match benchmark to strategy universe and style.
2. Consider Multiple Benchmarks¶
3. Report Both Absolute and Relative¶
Text Only
Absolute Performance:
CAGR: 13.1%
Sharpe: 0.86
Relative Performance (vs SPY):
Alpha: 4.2%
Information Ratio: 0.45
4. Analyze Regime Dependence¶
Understand when strategy outperforms vs underperforms.
5. Check Benchmark Fit¶
Low R² means benchmark may not be appropriate.
Example: Complete Benchmark Report¶
Text Only
Benchmark Analysis Report
=========================
Strategy: momentum_strategy
Benchmark: SPY
Period: 2020-01-01 to 2024-12-31
Return Comparison:
| Strategy | Benchmark | Difference
-----------------+----------+-----------+-----------
Total Return | 85.2% | 75.4% | +9.8%
CAGR | 13.1% | 11.9% | +1.2%
Volatility | 15.2% | 18.5% | -3.3%
Sharpe Ratio | 0.86 | 0.64 | +0.22
Max Drawdown | -18.5% | -24.5% | +6.0%
Risk-Adjusted Relative:
Alpha: 4.2%
Beta: 0.72
Tracking Error: 9.3%
Information Ratio: 0.45
Capture Analysis:
Up Capture: 85%
Down Capture: 62%
Capture Ratio: 1.37
Correlation:
Full Period: 0.72
Rolling Min: 0.45
Rolling Max: 0.92
Active Share: 85%
Best Relative Months:
2022-10: Strategy -2.1%, Benchmark -9.3% (+7.2%)
2020-03: Strategy -8.5%, Benchmark -12.5% (+4.0%)
Worst Relative Months:
2021-11: Strategy +1.2%, Benchmark +6.8% (-5.6%)
2023-12: Strategy +2.1%, Benchmark +4.5% (-2.4%)
Next Steps¶
- Attribution - Detailed return attribution
- Metrics - All performance metrics
- Walk-Forward - Validation methodology