pair-trade-screener

$29

When to Use This Skill

Use this skill when:

• User asks for "pair trading opportunities"

• User wants "market-neutral strategies"

• User requests "statistical arbitrage screening"

• User asks "which stocks move together?"

• User wants to hedge sector exposure

• User requests mean-reversion trade ideas

• User asks about relative value trading

Example user requests:

• "Find pair trading opportunities in the tech sector"

• "Which stocks are cointegrated?"

• "Screen for statistical arbitrage opportunities"

• "Find mean-reversion pairs"

• "What are good market-neutral trades right now?"

Analysis Workflow

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:

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 (ρ)

• Calculate rolling correlation (90-day window) for stability check

• Filter pairs with ρ >= 0.70 (strong positive correlation)

Correlation Interpretation:

• ρ >= 0.90: Very strong correlation (best candidates)

• ρ 0.70-0.90: Strong correlation (good candidates)

• ρ 0.50-0.70: Moderate correlation (marginal)

• ρ < 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 × 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 (★★★)

• p-value 0.01-0.05: Moderate cointegration (★★)

• 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:

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 × 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 ≥ ±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

→ 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

→ Action: Short Stock A, Buy Stock B (hedge ratio = beta)

Aggressive Approach (Z ≥ ±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)

→ Close both legs simultaneously

Secondary Exit: Partial Profit Take

Exit 50% when z-score reaches ±1.0

Exit remaining 50% at z-score = 0

Stop Loss:

Exit if z-score extends beyond ±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 = β:

Equal Dollar Exposure:

If portfolio size = $10,000 allocated to this pair:

- Long $5,000 of Stock A

- Short $5,000 × β of Stock B

Example (β = 1.2):

- Long $5,000 Stock A

- Short $6,000 Stock B

→ 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 > ±3.0 or -5% loss on spread

• Portfolio-level risk: Sum of all pair risks ≤ 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

Quality Standards

Statistical Rigor

Minimum Requirements for Valid Pair:

• ✓ Correlation ≥ 0.70 over 2-year period

• ✓ Cointegration p-value < 0.05 (ADF test)

• ✓ Spread stationarity confirmed

• ✓ Half-life < 90 days

• ✓ No structural breaks in recent 6 months

Red Flags (Exclude Pair):

• Correlation dropped >0.20 in recent 6 months

• Cointegration p-value > 0.05

• Half-life increasing over time (mean-reversion weakening)

• Significant corporate events (merger, spin-off, bankruptcy risk)

• Liquidity concerns (avg volume < 500K shares/day)

Practical Considerations

Transaction Costs:

• Assume 0.1% round-trip cost per leg

• Total cost per pair = 0.4% (entry + exit, both legs)

• Minimum z-score threshold should exceed transaction costs

Short Selling:

• Verify stock is shortable (not hard-to-borrow)

• Factor in short interest costs (borrow fees)

• Monitor short squeeze risk

Execution:

• Enter/exit both legs simultaneously (avoid leg risk)

• Use limit orders to control slippage

• Pre-locate shorts before entry

Available Scripts

scripts/find_pairs.py

Purpose: Screen for cointegrated pairs within a sector or custom list.

Usage:

# Sector-based screening

python scripts/find_pairs.py --sector Technology --min-correlation 0.70

# Custom stock list

python scripts/find_pairs.py --symbols AAPL,MSFT,GOOGL,META --min-correlation 0.75

# Full options

python scripts/find_pairs.py \

  --sector Financials \

  --min-correlation 0.70 \

  --min-market-cap 2000000000 \

  --lookback-days 730 \

  --output pairs_analysis.json

Parameters:

• --sector: Sector name (Technology, Financials, etc.)

• --symbols: Comma-separated list of tickers (alternative to sector)

• --min-correlation: Minimum correlation threshold (default: 0.70)

• --min-market-cap: Minimum market cap filter (default: $2B)

• --lookback-days: Historical data period (default: 730 days)

• --output: Output JSON file (default: stdout)

• --api-key: FMP API key (or set FMP_API_KEY env var)

Output:

[

  {

    "pair": "AAPL/MSFT",

    "stock_a": "AAPL",

    "stock_b": "MSFT",

    "correlation": 0.87,

    "beta": 1.15,

    "cointegration_pvalue": 0.012,

    "adf_statistic": -3.45,

    "half_life_days": 42,

    "current_zscore": -2.3,

    "signal": "LONG",

    "strength": "Strong"

  }

]

scripts/analyze_spread.py

Purpose: Analyze a specific pair's spread behavior and generate trading signals.

Usage:

# Analyze specific pair

python scripts/analyze_spread.py --stock-a AAPL --stock-b MSFT

# Custom lookback period

python scripts/analyze_spread.py \

  --stock-a JPM \

  --stock-b BAC \

  --lookback-days 365 \

  --entry-zscore 2.0 \

  --exit-zscore 0.5

Parameters:

• --stock-a: First stock ticker

• --stock-b: Second stock ticker

• --lookback-days: Analysis period (default: 365)

• --entry-zscore: Z-score threshold for entry (default: 2.0)

• --exit-zscore: Z-score threshold for exit (default: 0.0)

• --api-key: FMP API key

Output:

• Current spread analysis

• Z-score calculation

• Entry/exit recommendations

• Position sizing

• Historical z-score chart (text)

Reference Documentation

references/methodology.md

Comprehensive guide to statistical arbitrage and pair trading:

• Pair Selection Criteria: How to identify good pair candidates

• Statistical Tests: Correlation, cointegration, stationarity

• Spread Construction: Price difference vs price ratio approaches

• Mean Reversion: Half-life calculation and interpretation

• Risk Management: Position sizing, stop losses, diversification

• Common Pitfalls: Survivorship bias, look-ahead bias, overfitting

references/cointegration_guide.md

Deep dive into cointegration testing:

• What is Cointegration?: Intuitive explanation

• ADF Test: Step-by-step procedure

• P-Value Interpretation: Statistical significance thresholds

• Half-Life Estimation: AR(1) model approach

• Structural Breaks: Testing for regime changes

• Practical Examples: Case studies with real pairs

Integration with Other Skills

Sector Analyst Integration:

• Use Sector Analyst to identify sectors in rotation

• Screen for pairs within outperforming sectors

• Pairs in leading sectors may have stronger trends

Technical Analyst Integration:

• Confirm pair entry/exit with individual stock technicals

• Check support/resistance levels before entry

• Validate trend direction aligns with spread signal

Backtest Expert Integration:

• Feed pair candidates to Backtest Expert for validation

• Test historical z-score entry/exit rules

• Optimize threshold parameters (entry z-score, stop loss)

• Walk-forward analysis for robustness

Market Environment Analysis Integration:

• Avoid pair trading during extreme volatility (VIX > 30)

• Correlations break down in crisis periods

• Prefer pair trading in sideways/range-bound markets

Portfolio Manager Integration:

• Track multiple pair positions

• Monitor overall market-neutral exposure

• Calculate portfolio-level pair trading P/L

• Rebalance hedge ratios periodically

Important Notes

• All analysis and output in English

• Statistical foundation: No discretionary interpretation

• Market neutral focus: Minimize directional beta exposure

• Data quality critical: Garbage in, garbage out

• Requires FMP API key: Free tier sufficient for basic screening

• Python dependencies: pandas, numpy, scipy, statsmodels

Common Use Cases

Use Case 1: Technology Sector Pairs

User: "Find pair trading opportunities in tech stocks"

Workflow:

1. Screen Technology sector for stocks with market cap > $10B

2. Calculate all pairwise correlations

3. Filter pairs with correlation ≥ 0.75

4. Run cointegration tests

5. Identify current z-score extremes (|z| > 2.0)

6. Generate top 10 pairs report

Use Case 2: Specific Pair Analysis

User: "Analyze AAPL and MSFT as a pair trade"

Workflow:

1. Fetch 2-year price history for AAPL and MSFT

2. Calculate correlation and beta

3. Test for cointegration

4. Calculate current spread and z-score

5. Generate entry/exit recommendation

6. Provide position sizing guidance

Use Case 3: Regional Bank Pairs

User: "Screen for pairs among regional banks"

Workflow:

1. Filter Financials sector for industry = "Regional Banks"

2. Exclude banks with <$5B market cap

3. Calculate pairwise statistics

4. Rank by cointegration strength

5. Focus on pairs with half-life < 45 days

6. Report top 5 mean-reverting pairs

Troubleshooting

Problem: No cointegrated pairs found

Solutions:

• Expand universe (lower market cap threshold)

• Relax cointegration p-value to 0.10

• Try different sectors (Utilities often cointegrate well)

• Increase lookback period to 3 years

Problem: All z-scores near zero (no trade signals)

Solutions:

• Normal market condition (pairs in equilibrium)

• Check back later or expand universe

• Lower entry threshold to ±1.5 instead of ±2.0

Problem: Pair correlation broke down

Solutions:

• Check for corporate events (earnings, guidance changes)

• Verify no M&#x26;A activity or restructuring

• Remove pair from watchlist if structural break confirmed

• Monitor for 30 days before re-entering

API Requirements

• Required: FMP API key (free tier sufficient)

• Rate Limits: ~250 requests/day on free tier

• Data Usage: ~2 requests per symbol for 2-year history

• Upgrade: Professional plan ($29/mo) recommended for frequent screening

Resources

• FMP Historical Price API: https://site.financialmodelingprep.com/developer/docs/historical-price-full

• Stock Screener API: https://site.financialmodelingprep.com/developer/docs/stock-screener-api

• Statsmodels Documentation: https://www.statsmodels.org/stable/index.html

• Cointegration Paper: Engle &#x26; Granger (1987) - "Co-Integration and Error Correction"

Version: 1.0

Last Updated: 2025-11-08

Dependencies: Python 3.8+, pandas, numpy, scipy, statsmodels, requests