Cointegration and Pairs Trading AI Prompt

Test for cointegration between two assets and build a pairs trading model.

Asset 1: {{asset_1}}
Asset 2: {{asset_2}}
Price series: {{price_series}}

1. Cointegration testing:

   Engle-Granger two-step approach:
   Step 1: Run OLS: P1_t = α + β × P2_t + ε_t
   Step 2: Test residuals ε_t for stationarity using ADF
   - If residuals are stationary: the pair is cointegrated
   - Cointegrating coefficient β: the hedge ratio (how much of asset 2 to hold per unit of asset 1)
   - Limitation: only tests one cointegrating vector; sensitive to which asset is on the left-hand side

   Johansen test (preferred for robustness):
   - Tests for multiple cointegrating relationships
   - Trace statistic and Max-Eigenvalue statistic
   - Null H₀(r=0): no cointegrating vectors. Reject at p < 0.05.
   - Reports the cointegrating vector and loading coefficients (speed of adjustment)

2. Spread construction:
   Spread_t = P1_t - β × P2_t
   - Plot the spread over time: should look mean-reverting if cointegrated
   - Compute: mean of spread, std of spread, half-life of mean reversion
   - Half-life: from Ornstein-Uhlenbeck fit: dS = κ(μ - S)dt + σdW
     Half-life = ln(2) / κ
   - Very short half-life (<5 days): crowded, may not survive transaction costs
   - Very long half-life (>120 days): too slow, requires significant capital commitment

3. Trading signals:
   Standardized spread (z-score): z_t = (Spread_t - μ) / σ
   - Entry long: z < -2 (spread below mean by 2σ: buy asset 1, sell asset 2)
   - Entry short: z > +2 (spread above mean: sell asset 1, buy asset 2)
   - Exit: z crosses zero (or ±0.5)
   - Stop-loss: z > ±3 or ±4 (spread has diverged beyond tolerable levels)

4. Backtest the pairs strategy:
   - Signal generation as above
   - Dollar-neutral: equal dollar value in each leg
   - Transaction costs: round-trip spread + market impact
   - Report: Sharpe ratio, Calmar, turnover, avg holding period, win rate, drawdown

5. Stability checks:
   - Is the cointegrating relationship stable over time? Rolling Engle-Granger test
   - Does the hedge ratio drift? Rolling OLS hedge ratio over 252-day window
   - Structural break tests (CUSUM, Bai-Perron): has the relationship broken down?

Return: cointegration test results, spread construction and statistics, OU parameter estimates, backtest performance, and stability analysis.