Pairs Trading

Pairs Trading

name: pairs-trading description: Pairs trading methodology — cointegration, distance, copula methods. Use when designing market-neutral pairs strategies.

When to Activate

• User wants to trade the spread between two related securities
• Selecting pairs using cointegration, correlation, or fundamental linkage
• Constructing and monitoring spread positions
• Managing risk in market-neutral pair portfolios
• Evaluating pair stability and when to exit broken pairs

First Questions

1. What universe are you selecting pairs from (sector, index, asset class)?
2. What pair selection method — cointegration, distance, fundamental, or ML-based?
3. What is the trading frequency (intraday, daily, weekly)?
4. Long-short (market neutral) or long-only (switch between pair members)?
5. How many pairs do you intend to trade simultaneously?

Core Concepts

Why Pairs Trading Works

Pairs trading exploits temporary mispricings between related securities. Two stocks with a fundamental economic link (same sector, similar business, shared risk factors) should move together over time. When they diverge, the spread is expected to revert.

Sources of edge:

• Mean reversion of residual mispricings
• Market microstructure effects (temporary supply/demand imbalance)
• Slow information diffusion between related securities
• Investor behavioral biases (overreaction to firm-specific news)

Key property: Market neutral. The long and short legs offset market risk, leaving only the spread as the bet.

Pair Selection Methods

1. Cointegration-based (preferred):

• Two prices are cointegrated if a linear combination is stationary
• Does not require high correlation — only that they share a common stochastic trend
• Test using Engle-Granger or Johansen procedure
• Provides the hedge ratio directly

2. Distance method (Gatev et al. 2006):

• Normalize prices, compute sum of squared differences over formation period
• Select pairs with minimum distance (most similar price paths)
• Simple but does not guarantee mean reversion

3. Correlation-based:

• Select highly correlated pairs (> 0.80)
• Monitor for correlation breakdown
• Weaker theoretical basis than cointegration

4. Fundamental/sector-based:

• Pair companies with similar business models, market caps, factor exposures
• Use cointegration as a filter, not the sole criterion
• More robust because the economic link provides a structural reason for co-movement

Detailed Methodology

Pair Selection Pipeline

Step 1: Define universe (e.g., S&P 500 stocks within same GICS sector)
Step 2: Pre-filter by correlation (keep pairs with corr > 0.70)
Step 3: Test cointegration on formation period (12 months)
         - Engle-Granger: ADF on OLS residuals, p < 0.05
         - Use Engle-Granger critical values, NOT standard ADF
Step 4: Estimate half-life of mean reversion
         - Keep pairs with half-life between 5 and 60 days
Step 5: Check Hurst exponent of spread (H < 0.5)
Step 6: Verify economic rationale (same sector, similar business)
Step 7: Rank qualifying pairs by:
         - Cointegration test statistic (most negative = strongest)
         - Half-life (shorter = better)
         - Historical spread Sharpe ratio
Step 8: Select top N pairs (10-30 for diversification)
Step 9: Re-run selection monthly or quarterly

Spread Construction

Given pair (A, B) with cointegrating relationship:
  Price_A = alpha + beta * Price_B + spread

Hedge ratio estimation:
  Method 1: OLS regression (simple, biased)
    beta = cov(A, B) / var(B)

  Method 2: Total Least Squares (TLS/Deming regression)
    Accounts for noise in both variables
    More symmetric (A on B gives same ratio as B on A)

  Method 3: Kalman filter (dynamic, adaptive)
    Tracks time-varying hedge ratio
    Best for production use

  Method 4: Johansen cointegrating vector
    Estimated jointly, handles multiple pairs

Spread computation:
  spread_t = Price_A_t - beta * Price_B_t - alpha

Z-score:
  z_t = (spread_t - mean(spread)) / std(spread)
  Use rolling statistics (window = 2 * half_life minimum)

Trading Rules

Entry:
  Long spread:  z_t < -2.0 (spread is abnormally negative)
    → Buy A, Sell B (in ratio beta)
  Short spread: z_t > +2.0 (spread is abnormally positive)
    → Sell A, Buy B (in ratio beta)

Exit:
  Close when z_t crosses 0 (full mean reversion)
  Or close when z_t crosses +/-0.5 (partial, more conservative)
  Or time-based exit after 3 * half_life days

Stop-loss:
  Close if |z_t| > 4.0 (spread blew out — relationship may be broken)
  Close if cointegration re-test fails on recent data
  Close on corporate event (M&A announcement, earnings shock, sector re-classification)

Position sizing:
  Dollar-neutral: Long $100K of A, Short $100K * beta of B
  Beta-neutral: Adjust for beta difference to eliminate market exposure
  Volatility-sized: Each pair contributes equal risk to portfolio

Risk Management

Pair-level risks:
1. Divergence risk: Spread keeps widening instead of reverting
   - Hard stop-loss (Z > 4)
   - Time stop (3x half-life)
   - Maximum loss per pair (e.g., 2% of capital)

2. Structural break: Cointegration relationship permanently breaks
   - Re-test cointegration monthly
   - Monitor for fundamental changes (M&A, spin-offs, bankruptcies)
   - Automatic exit on corporate event flags

3. Leg risk: One leg moves sharply while the other is illiquid
   - Execute both legs simultaneously (or as close as possible)
   - Avoid pairs where one leg has low liquidity

4. Short squeeze: Borrowed stock gets recalled or borrow cost spikes
   - Monitor borrow availability and cost
   - Avoid hard-to-borrow stocks in the short leg

Portfolio-level risks:
1. Sector concentration: Many pairs from the same sector = sector bet
   - Diversify across sectors
   - Monitor net sector exposure

2. Factor exposure: Pairs may have hidden factor tilts
   - Compute portfolio-level factor exposure
   - Ensure approximate factor neutrality

3. Correlation among pairs: Pairs can become correlated in stress
   - Monitor pairwise correlation of spread returns
   - Reduce overall exposure during correlation spikes

Portfolio of Pairs

Construction:
  Select 10-30 pairs across sectors
  Equal risk weight per pair (vol-adjusted)
  Maximum 3-5 pairs per sector
  Total gross exposure: 100-300% of capital

Rebalancing:
  Re-screen pairs monthly or quarterly
  Replace broken pairs (failed cointegration re-test)
  Adjust hedge ratios (rolling OLS or Kalman filter update)

Performance expectations:
  Sharpe: 1.0-2.0 for well-constructed portfolio of pairs
  Max drawdown: 5-15%
  Market correlation: near zero (by design)
  Capacity: Limited by liquidity of pair members

Diversification benefit:
  Single pair Sharpe: ~0.5-0.8
  Portfolio of 20 pairs: Sharpe improves by sqrt(N/effective_N)
  If pair returns have 0.1 average correlation:
    Effective N ≈ N / (1 + (N-1)*rho) ≈ 7 for 20 pairs with rho=0.1
    Portfolio Sharpe ≈ single_pair_Sharpe * sqrt(7) ≈ 1.5

Templates / Examples

Pair Evaluation Report

Pair: KO (Coca-Cola) vs PEP (PepsiCo)
Sector: Consumer Staples | Formation: 2020-01 to 2022-12

--- Cointegration Tests ---
Engle-Granger ADF:   -4.12 (p = 0.001) [Cointegrated]
Johansen Trace:       r=1 confirmed
Hedge Ratio (OLS):    0.92
Hedge Ratio (TLS):    0.95
Hedge Ratio (Kalman): 0.93 (mean), range [0.85, 1.02]

--- Spread Properties ---
Half-Life:            14 days
Hurst Exponent:       0.35
Spread Std Dev:       $2.45
Mean Z-score Range:   [-3.1, +2.8]

--- Backtest (OOS: 2023-01 to 2024-12) ---
Entry: Z > 2.0 or Z < -2.0 | Exit: |Z| < 0.5 | Stop: |Z| > 4.0
Trades (round-trip):  18
Win Rate:             78%
Average P&L per trade: $1,850
Sharpe Ratio:         1.65
Max Drawdown:         -3.8%
Average Holding:      11 days

--- Risk Assessment ---
Short borrow cost:    Low (both mega-cap, widely available)
Leg liquidity:        Excellent (both > $500M ADV)
Event risk:           Low (stable businesses)
Sector concentration: Consumer Staples (monitor if adding more from sector)

Verdict: PASS — strong cointegration, reasonable half-life, good OOS performance

Pair Monitoring Dashboard Template

Active Pairs Report — [Date]

Pair    | Hedge | Current Z | Entry Z | Days Held | P&L   | Status
KO/PEP  | 0.93  | -0.8      | -2.1    | 8         | +$1.2K| Converging
XOM/CVX | 1.15  | -1.5      | -2.3    | 12        | +$0.6K| Slow convergence
JPM/BAC | 0.78  | +3.2      | +2.0    | 5         | -$1.8K| Diverging (watch)
MSFT/AAPL| 0.65 | +0.3      | +2.2    | 15        | +$2.1K| Near exit

Portfolio Summary:
  Pairs active: 14 of 20
  Net market exposure: -2.1% (approximately neutral)
  Gross exposure: 180%
  Portfolio Z-score (avg): 0.4
  MTD P&L: +$8.5K
  Pairs at stop-loss risk (|Z| > 3.5): 1 (JPM/BAC)

Pair Selection Screening Results

Universe: S&P 500, same GICS sector
Formation Period: 2022-01 to 2023-12
Pairs tested: 4,850 | Cointegrated at 5%: 312 (6.4%)

Top 10 by Cointegration Strength:
Rank | Pair        | Sector  | ADF stat | Half-Life | Spread SR
1    | KO/PEP      | Staples | -4.85    | 14 days   | 1.82
2    | XOM/CVX     | Energy  | -4.52    | 18 days   | 1.45
3    | V/MA        | Fintech | -4.31    | 12 days   | 1.68
4    | HD/LOW      | Retail  | -4.15    | 22 days   | 1.25
5    | UNH/CI      | Health  | -3.98    | 16 days   | 1.52
...

Selected: Top 20 pairs across 8 sectors (max 4 per sector)

Quality Gate

Before deploying a pairs trading strategy:

• Cointegration confirmed at 5% significance level with correct critical values
• Economic rationale for pair relationship documented
• Half-life is practical for trading frequency (5-60 days)
• Hedge ratio estimated robustly (TLS or Kalman, not just OLS)
• Out-of-sample backtest shows positive Sharpe
• Stop-loss rules defined for divergence, time, and corporate events
• Short leg is borrowable at reasonable cost
• Both legs have sufficient liquidity for target position sizes
• Portfolio diversified across sectors (no single-sector concentration)
• Re-screening schedule established (monthly or quarterly cointegration re-test)
• Execution plan handles simultaneous leg entry/exit