Pairs Trading & Cointegration
Estimate a hedge ratio, test the spread for stationarity and half-life, then backtest a z-score strategy honestly with costs and an out-of-sample split.
The scenario
A stat-arb pod hands you two price series and asks whether they can be traded as a mean-reverting pair. Estimate the hedge ratio, test the spread for stationarity, measure its half-life, then build and honestly backtest a z-score mean-reversion strategy with costs and an out-of-sample split.
Where this shows up
Testing a pair for cointegration and backtesting a mean-reversion signal is a classic statistical-arbitrage take-home at firms of this type.
Firms such as Two Sigma, Citadel, Man Group.
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Task brief
# Pairs Trading & Cointegration **Role relevance:** Quant research / statistical arbitrage take-home **Estimated time:** 75 minutes **Difficulty:** Advanced **Format:** Jupyter notebook (.ipynb) ## What you are given - pairs_trading_starter.ipynb - a guided notebook that runs end to end even before you fill it in - prices.csv - 750 business days of two price series - Validation targets in the final cell, so you can grade your own work ## What you must deliver 1. The hedge ratio, fitted on the in-sample window only 2. An ADF stationarity test and the spread's half-life 3. A causal z-score signal with the position lagged one day 4. A cost-aware backtest reporting in-sample and out-of-sample separately, plus a written verdict ## Constraints & assumptions The hedge ratio is fitted on the first 500 rows only. The z-score must be rolling, not full-sample. Positions must be lagged before they earn PnL. Costs are 5bp on turnover. ## Submission note Complete the starter file, then compare your work against the mark scheme.
Your tasks
- 01Estimate the hedge ratio by regressing one series on the other and form the spread.
- 02Test the spread for stationarity (ADF) and estimate its half-life of mean reversion.
- 03Build a z-score strategy: enter when the spread is beyond an entry threshold, exit near zero, with no lookahead.
- 04Backtest with transaction costs and an in-sample / out-of-sample split, and report the Sharpe and whether the edge survives.
How you're assessed
The full points-based mark scheme is included with the pack.
What you'll learn
- The difference between correlation and cointegration, and why a pair needs the latter.
- How the half-life sets a sensible holding period and z-thresholds.
- Why costs and an out-of-sample split separate a real pair from an overfit.