Chapter 8: Advanced Analytics¶

Factor models, attribution, and deep performance analysis.

Factor Models¶

What are Factors?¶

Factors are systematic drivers of returns:

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Stock Return = Factor Returns + Idiosyncratic Return
             = β₁F₁ + β₂F₂ + ... + ε

Common Factor Models¶

CAPM (1 factor):

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R = α + β(Rm - Rf) + ε

Fama-French 3 Factor:

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R = α + β₁(MKT) + β₂(SMB) + β₃(HML) + ε

Carhart 4 Factor:

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R = α + β₁(MKT) + β₂(SMB) + β₃(HML) + β₄(MOM) + ε

Factor Definitions¶

Factor	Name	Construction
MKT	Market	Market return - Risk-free
SMB	Size	Small cap - Large cap
HML	Value	High B/M - Low B/M
MOM	Momentum	Winners - Losers
QMJ	Quality	High quality - Low quality

Factor Exposure Analysis¶

Calculate Factor Exposures¶

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signal market_beta:
  stock_ret = ret(prices, 1)
  market_ret = ret(market, 1)
  beta = rolling_cov(stock_ret, market_ret, 60) / rolling_var(market_ret, 60)
  emit beta

signal size_exposure:
  // Negative of market cap (small = positive exposure)
  emit -zscore(ln(market_cap))

signal value_exposure:
  emit zscore(book_value / market_cap)

signal momentum_exposure:
  emit zscore(ret(prices, 252) - ret(prices, 21))

Portfolio Factor Exposures¶

Bash

sigc run strategy.sig --factor-analysis

Output:

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Factor Exposure Analysis
========================

Portfolio Factor Exposures:
  Market (β):    0.05 (near neutral)
  Size (SMB):   -0.12 (slight large-cap tilt)
  Value (HML):   0.28 (value exposure)
  Momentum:      0.35 (momentum exposure)
  Quality:       0.18 (quality tilt)

Factor Contribution to Return:
  Market:      +2.1%
  Size:        -0.4%
  Value:       +1.8%
  Momentum:    +2.5%
  Quality:     +0.9%
  Alpha:       +1.3%
  -------------------------
  Total:       +8.2%

Performance Attribution¶

Returns-Based Attribution¶

Decompose returns by source:

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Total Return = Factor Returns + Selection Return
             = Σ(βᵢ × Fᵢ) + α

Holdings-Based Attribution¶

Decompose by position:

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Portfolio Return = Σ(wᵢ × rᵢ)
                 = Σ(contribution per stock)

Sector Attribution¶

Bash

sigc run strategy.sig --attribution sector

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Sector Attribution
==================

Sector          Weight  Return  Contribution
Technology      +0.15   +12.3%      +1.85%
Healthcare      +0.08    +8.1%      +0.65%
Financials      -0.12    +5.2%      -0.62%
Consumer Disc.  +0.05   +15.2%      +0.76%
...

Total Sector Effect: +3.2%
Selection Effect:    +4.8%
Interaction:         +0.2%
Total Return:        +8.2%

Risk Attribution¶

Factor Risk Decomposition¶

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Total Variance = Factor Variance + Idiosyncratic Variance
               = β'Σβ + σ²ε

Risk Attribution Report¶

Bash

sigc run strategy.sig --risk-attribution

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Risk Attribution
================

Total Volatility: 9.5%

Factor Risk Contribution:
  Market:     35%  (3.3%)
  Size:        8%  (0.8%)
  Value:      12%  (1.1%)
  Momentum:   15%  (1.4%)
  Quality:     5%  (0.5%)
  -----------------------
  Total Factor: 75%

Idiosyncratic Risk: 25% (2.4%)

Risk Concentration:
  Top 10 positions: 18% of risk
  Top sector (Tech): 22% of risk

Advanced Performance Metrics¶

Information Coefficient¶

Correlation of signal with forward returns:

Python

# In Python with pysigc
import pysigc
import numpy as np

results = pysigc.run("strategy.sig")
signals = results.signals
forward_returns = results.forward_returns

ic = np.corrcoef(signals, forward_returns)[0, 1]
print(f"IC: {ic:.4f}")

Turnover Analysis¶

Bash

sigc run strategy.sig --turnover-analysis

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Turnover Analysis
=================

Annual Turnover: 420%
  Long Side: 210%
  Short Side: 210%

Average Holding Period: 58 days

Turnover by Quintile:
  Q1 (longs):   35%
  Q2:           42%
  Q3:           55%
  Q4:           48%
  Q5 (shorts):  38%

Cost Analysis:
  Gross Return: 9.8%
  Trading Costs: -1.6%
  Net Return: 8.2%

Hit Rate Analysis¶

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Win Rate: 54%
Average Win: +2.1%
Average Loss: -1.8%
Profit Factor: 1.3

By Market Condition:
  Bull Markets: 58% win rate
  Bear Markets: 49% win rate
  High Vol: 52% win rate
  Low Vol: 56% win rate

Regime Analysis¶

Performance by Regime¶

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signal volatility_regime:
  vol = rolling_std(ret(market, 1), 20) * sqrt(252)
  long_vol = rolling_std(ret(market, 1), 60) * sqrt(252)
  emit where(vol > long_vol * 1.3, "high_vol", "normal")

signal trend_regime:
  ma_50 = rolling_mean(market, 50)
  ma_200 = rolling_mean(market, 200)
  emit where(ma_50 > ma_200, "bull", "bear")

Bash

sigc run strategy.sig --regime-analysis

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Regime Analysis
===============

By Volatility:
  Normal Vol:   Sharpe 0.95, Return +9.2%
  High Vol:     Sharpe 0.42, Return +4.1%

By Trend:
  Bull Market:  Sharpe 1.05, Return +11.3%
  Bear Market:  Sharpe 0.28, Return +2.1%

By Combination:
  Bull + Low Vol:   Sharpe 1.15
  Bull + High Vol:  Sharpe 0.55
  Bear + Low Vol:   Sharpe 0.45
  Bear + High Vol:  Sharpe 0.15

Correlation Analysis¶

Strategy Correlation with Factors¶

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Correlation with Common Factors:
  Market (SPY):     0.05
  Size (IWM-SPY):  -0.12
  Value (IVE-IVW):  0.35
  Momentum:         0.42
  Quality:          0.22

Strategy is most correlated with momentum factor.

Strategy Correlation Over Time¶

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Rolling 1-Year Correlation with SPY:
  2020: 0.15
  2021: 0.08
  2022: 0.22
  2023: 0.05
  2024: 0.03

Correlation has decreased over time (good for diversification).

Stress Testing¶

Historical Stress Tests¶

Bash

sigc run strategy.sig --stress-test

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Historical Stress Tests
=======================

Event                    Date        Return    Max DD
2008 Financial Crisis    2008-09    -12.3%    -18.5%
2011 Euro Crisis         2011-08     -5.2%     -8.1%
2015 China Deval         2015-08     -3.8%     -6.2%
2018 Vol Spike           2018-02     -4.5%     -7.8%
2020 COVID Crash         2020-03    -10.2%    -15.3%
2022 Rate Hikes          2022-06     -6.8%    -11.2%

Worst Single Day:        -4.2% (2020-03-12)
Worst Single Month:      -8.5% (2020-03)

Hypothetical Scenarios¶

YAML

stress_scenarios:
  - name: "Market Crash"
    market_return: -20%
    volatility_multiplier: 2.5

  - name: "Rate Shock"
    yield_change: +200bps
    duration_impact: true

  - name: "Sector Rotation"
    tech_return: -15%
    financials_return: +10%

Complete Analytics Example¶

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data:
  source = "prices_fundamentals.parquet"
  format = parquet

signal momentum:
  emit neutralize(zscore(ret(prices, 60)), by=sectors)

signal value:
  emit neutralize(zscore(book_to_market), by=sectors)

signal combined:
  emit 0.5 * momentum + 0.5 * value

portfolio analyzed:
  weights = rank(combined).long_short(
    top = 0.2,
    bottom = 0.2,
    cap = 0.03
  )

  constraints:
    gross_exposure = 2.0
    net_exposure = 0.0
    max_sector = 0.20

  costs = tc.bps(10)

  backtest rebal=21 from 2010-01-01 to 2024-12-31

  // Request full analytics
  analytics:
    factor_attribution: true
    risk_attribution: true
    regime_analysis: true
    turnover_analysis: true
    stress_tests: true

Bash

sigc run strategy.sig --full-analytics --output reports/analysis.html

Best Practices¶

1. Understand Your Factor Exposures¶

Know what you're betting on: - Intended exposures (from your signals) - Unintended exposures (check and hedge)

2. Monitor Attribution Over Time¶

Factor contributions change: - Is momentum still working? - Has value exposure increased?

3. Test Across Regimes¶

Ensure robustness: - Bull and bear markets - High and low volatility - Different economic conditions

4. Regular Deep Dives¶

Beyond daily monitoring: - Monthly factor analysis - Quarterly stress tests - Annual strategy review

Exercises¶

Calculate factor exposures for your strategy
Perform returns-based attribution
Analyze performance across volatility regimes
Run historical stress tests

Next Chapter¶

Continue to Chapter 9: Deployment and Safety for production safety systems.