Step 1: Define Pair Universe
Objective: Establish the pool of stocks to analyze for pair relationships.
Option A: Sector-Based Screening (Recommended)
Select a specific sector to screen:
- Technology
- Financials
- Healthcare
- Consumer Discretionary
- Industrials
- Energy
- Materials
- Consumer Staples
- Utilities
- Real Estate
- Communication Services
Option B: Custom Stock List
User provides specific tickers to analyze:
```
Example: ["AAPL", "MSFT", "GOOGL", "META", "NVDA"]
```
Option C: Industry-Specific
Narrow focus to specific industry within sector:
- Example: "Software" within Technology sector
- Example: "Regional Banks" within Financials
Filtering Criteria:
- Minimum market cap: $2B (mid-cap and above)
- Minimum average volume: 1M shares/day (liquidity requirement)
- Active trading: No delisted or inactive stocks
- Same exchange preference: Avoid cross-exchange complications
Step 2: Retrieve Historical Price Data
Objective: Fetch price history for correlation and cointegration analysis.
Data Requirements:
- Timeframe: 2 years (minimum 252 trading days)
- Frequency: Daily closing prices
- Adjustments: Adjusted for splits and dividends
- Clean data: No gaps or missing values
FMP API Endpoint:
```
GET /v3/historical-price-full/{symbol}?apikey=YOUR_API_KEY
```
Data Validation:
- Verify consistent date ranges across all symbols
- Remove stocks with >10% missing data
- Fill minor gaps with forward-fill method
- Log data quality issues
Script Execution:
```bash
python scripts/fetch_price_data.py --sector Technology --lookback 730
```
Step 3: Calculate Correlation and Beta
Objective: Identify candidate pairs with strong linear relationships.
Correlation Analysis:
For each pair of stocks (i, j) in the universe:
- Calculate Pearson correlation coefficient (Ο)
- Calculate rolling correlation (90-day window) for stability check
- Filter pairs with Ο >= 0.70 (strong positive correlation)
Correlation Interpretation:
- Ο >= 0.90: Very strong correlation (best candidates)
- Ο 0.70-0.90: Strong correlation (good candidates)
- Ο 0.50-0.70: Moderate correlation (marginal)
- Ο < 0.50: Weak correlation (exclude)
Beta Calculation:
For each candidate pair (Stock A, Stock B):
```
Beta = Covariance(A, B) / Variance(B)
```
Beta indicates the hedge ratio:
- Beta = 1.0: Equal dollar amounts
- Beta = 1.5: $1.50 of B for every $1.00 of A
- Beta = 0.8: $0.80 of B for every $1.00 of A
Correlation Stability Check:
- Calculate correlation over multiple periods (6mo, 1yr, 2yr)
- Require correlation to be stable (not deteriorating)
- Flag pairs where recent correlation < historical correlation by >0.15
Step 4: Cointegration Testing
Objective: Statistically validate long-term equilibrium relationship.
Why Cointegration Matters:
- Correlation measures short-term co-movement
- Cointegration proves long-term equilibrium relationship
- Cointegrated pairs mean-revert predictably
- Non-cointegrated pairs may diverge permanently
Augmented Dickey-Fuller (ADF) Test:
For each correlated pair:
- Calculate spread:
Spread = Price_A - (Beta Γ Price_B) - Run ADF test on spread series
- Check p-value: p < 0.05 indicates cointegration (reject null hypothesis of unit root)
- Extract ADF statistic for strength ranking
Cointegration Interpretation:
- p-value < 0.01: Very strong cointegration (β
β
β
)
- p-value 0.01-0.05: Moderate cointegration (β
β
)
- p-value > 0.05: No cointegration (exclude)
Half-Life Calculation:
Estimate mean-reversion speed:
```
Half-Life = -log(2) / log(mean_reversion_coefficient)
```
- Half-life < 30 days: Fast mean-reversion (good for short-term trading)
- Half-life 30-60 days: Moderate speed (standard)
- Half-life > 60 days: Slow mean-reversion (long holding periods)
Python Implementation:
```python
from statsmodels.tsa.stattools import adfuller
# Calculate spread
spread = price_a - (beta * price_b)
# ADF test
result = adfuller(spread)
adf_stat = result[0]
p_value = result[1]
# Interpret
is_cointegrated = p_value < 0.05
```
Step 5: Spread Analysis and Z-Score Calculation
Objective: Quantify current spread deviation from equilibrium.
Spread Calculation:
Two common methods:
Method 1: Price Difference (Additive)
```
Spread = Price_A - (Beta Γ Price_B)
```
Best for: Stocks with similar price levels
Method 2: Price Ratio (Multiplicative)
```
Spread = Price_A / Price_B
```
Best for: Stocks with different price levels, easier interpretation
Z-Score Calculation:
Measures how many standard deviations spread is from its mean:
```
Z-Score = (Current_Spread - Mean_Spread) / Std_Dev_Spread
```
Z-Score Interpretation:
- Z > +2.0: Stock A expensive relative to B (short A, long B)
- Z > +1.5: Moderately expensive (watch for entry)
- Z -1.5 to +1.5: Normal range (no trade)
- Z < -1.5: Moderately cheap (watch for entry)
- Z < -2.0: Stock A cheap relative to B (long A, short B)
Historical Spread Analysis:
- Calculate mean and std dev over 90-day rolling window
- Plot historical z-score distribution
- Identify maximum historical z-score deviations
- Check for structural breaks (spread regime change)
Step 6: Generate Entry/Exit Recommendations
Objective: Provide actionable trading signals with clear rules.
Entry Conditions:
Conservative Approach (Z β₯ Β±2.0):
```
LONG Signal:
- Z-score < -2.0 (spread 2+ std devs below mean)
- Spread is mean-reverting (cointegration p < 0.05)
- Half-life < 60 days
β Action: Buy Stock A, Short Stock B (hedge ratio = beta)
SHORT Signal:
- Z-score > +2.0 (spread 2+ std devs above mean)
- Spread is mean-reverting (cointegration p < 0.05)
- Half-life < 60 days
β Action: Short Stock A, Buy Stock B (hedge ratio = beta)
```
Aggressive Approach (Z β₯ Β±1.5):
- Lower threshold for more frequent trades
- Higher win rate but smaller avg profit per trade
- Requires tighter risk management
Exit Conditions:
Primary Exit: Mean Reversion (Z = 0)
```
Exit when spread returns to mean (z-score crosses 0)
β Close both legs simultaneously
```
Secondary Exit: Partial Profit Take
```
Exit 50% when z-score reaches Β±1.0
Exit remaining 50% at z-score = 0
```
Stop Loss:
```
Exit if z-score extends beyond Β±3.0 (extreme divergence)
Risk: Possible structural break in relationship
```
Time-Based Exit:
```
Exit after 90 days if no mean-reversion
Prevents holding broken pairs indefinitely
```
Step 7: Position Sizing and Risk Management
Objective: Determine dollar amounts for market-neutral exposure.
Market Neutral Sizing:
For a pair (Stock A, Stock B) with beta = Ξ²:
Equal Dollar Exposure:
```
If portfolio size = $10,000 allocated to this pair:
- Long $5,000 of Stock A
- Short $5,000 Γ Ξ² of Stock B
Example (Ξ² = 1.2):
- Long $5,000 Stock A
- Short $6,000 Stock B
β Market neutral, beta = 0
```
Position Sizing Considerations:
- Total pair allocation: 10-20% of portfolio per pair
- Maximum pairs: 5-8 active pairs for diversification
- Correlation across pairs: Avoid highly correlated pairs
Risk Metrics:
- Maximum loss per pair: 2-3% of total portfolio
- Stop loss trigger: Z-score > Β±3.0 or -5% loss on spread
- Portfolio-level risk: Sum of all pair risks β€ 10%
Step 8: Generate Pair Analysis Report
Objective: Create structured markdown report with findings and recommendations.
Report Sections:
- Executive Summary
- Total pairs analyzed
- Number of cointegrated pairs found
- Top 5 opportunities ranked by statistical strength
- Cointegrated Pairs Table
- Pair name (Stock A / Stock B)
- Correlation coefficient
- Cointegration p-value
- Current z-score
- Trade signal (Long/Short/None)
- Half-life
- Detailed Analysis (Top 10 Pairs)
- Pair description
- Statistical metrics
- Current spread position
- Entry/exit recommendations
- Position sizing
- Risk assessment
- Spread Charts (Text-Based)
- Historical z-score plot (ASCII art)
- Entry/exit levels marked
- Current position indicator
- Risk Warnings
- Pairs with deteriorating correlation
- Structural breaks detected
- Low liquidity warnings
File Naming Convention:
```
pair_trade_analysis_[SECTOR]_[YYYY-MM-DD].md
```
Example: pair_trade_analysis_Technology_2025-11-08.md
|