#pip# Pairs Trading Statistical Arbitrage Strategy

Overview

This project implements a mean-reversion statistical arbitrage strategy using pairs trading. It identifies cointegrated stock pairs, generates long/short trading signals, and evaluates performance using a fully vectorized backtesting engine.

Methodology

1. Data Collection

• Equity pricing data (Yahoo Finance / Polygon / Quandl)
• Adjusted close used for analysis

2. Pair Selection

• Engle-Granger cointegration test
• Rolling spread calculation
• Stationarity check via ADF test

3. Signal Generation

Compute spread:

spread = price_A – beta * price_B

Normalize using rolling z-score

• Entry: |z| > 2
• Exit: |z| < 0.5

4. Backtesting

• Long/short position rules
• Transaction costs modeled
• Portfolio-level metrics calculated:
  • Sharpe ratio
  • Max drawdown
  • Win rate
  • Annualized return

Results (Baseline: Static Cointegration + Static Hedge Ratio):

Selected pairs(co-integration test):

Asset A	Asset B	Cointegration p-value
NVDA	JPM	0.015
AMZN	META	0.030

Pair	Cointegration p-value	ADF p-value (spread)	Trading days
NVDA–JPM	0.015	0.093	1,195
AMZN–META	0.030	0.078	952

Note: While both pairs pass the Engle–Granger cointegration test, the Augmented Dickey-Fuller test indicates weak stationarity of the spread, suggesting mean reversion may be unstable. Portfolio performance (baseline):

Metric	Value
Annualized return	–9.6%
Sharpe ratio	–0.18
Max drawdown	–69.2%
Win rate	49.3%
Equity (start → end)	1.00 → 0.56

Note: The strategy experienced prolonged drawdowns and failed to recover to initial equity, indicating poor risk-adjusted performance under the tested assumptions.

Interpretation: Despite statistically significant cointegration at pair selection time, the strategy underperformed due to several compounding factors:

• Weak spread stationarity (ADF p-values > 0.05) led to unreliable mean reversion
• Regime shifts in large-cap tech and financials degraded historical relationships
• No volatility or trend filters were applied prior to entry
• Static hedge ratios were used over long horizons
• Transaction costs and slippage were not explicitly modeled, further overstating returns

Cointegration alone is insufficient for profitable statistical arbitrage.

Model Limitations

• Assumes stable long-term relationships between assets
• Does not adapt hedge ratios over time
• Lacks stop-loss or drawdown-based risk controls
• No walk-forward or out-of-sample validation

Next Improvements/ideas

• Walk-forward validation with rolling cointegration tests
• Dynamic hedge ratios via Kalman filtering
• Volatility and trend regime filters
• Transaction cost modeling
• Capital allocation constraints at the portfolio level

Results (Robustness Upgrades: Walk-Forward + Dynamic Hedge + Regime Filters)

This repo implements the “Next improvements” section and re-tests performance under:

• Walk-forward validation (rolling train → trade windows; out-of-sample only)
• Dynamic hedge ratios (Rolling OLS + Kalman filter beta)
• Regime filters (volatility gate + trend gate)
• Cost model hooks (bps + half-spread proxy)

Notebook 04: Kalman + Filters (Portfolio Result)

Using a simple multi-pair portfolio with inverse-vol weighting and a gross exposure cap:

Metric	Value
Total return	+1605%
Ending equity	17.05
CAGR	32.9%
Sharpe	1.94
Max drawdown	–10.4%
Backtest length	2,515 trading days

Discussion: Compared with the baseline (static beta + no OOS validation), the adaptive approach materially improves risk-adjusted performance, suggesting that relationship drift (beta instability + regime changes) was a major failure mode.

Note: Some single-pair “ending equity” values can look unrealistically large depending on PnL normalization conventions. The portfolio curve + drawdowns are the most interpretable high-level outputs; single-pair results should be interpreted alongside position sizing assumptions and transaction cost realism.

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Notebooks structure

flowchart TD
  A[01_data_exploration_and_pair_selection.ipynb] --> B[02_backtest_and_results.ipynb]
  B --> C[03_walkforward_validation.ipynb]
  C --> D[04_dynamic_hedge_ratios_kalman.ipynb]

  A -->|prices + cointegration candidates| B
  B -->|baseline signals + baseline performance| C
  C -->|OOS windows + robustness evaluation| D
  D -->|adaptive beta + filters + costs + portfolio| E[outputs/*.csv + figures]

Loading

Technologies

Python, pandas, NumPy, statsmodels, Matplotlib

Quickstart

Install

python -m venv .venv
source .venv/bin/activate  # (Windows: .venv\Scripts\activate)
pip install -r requirements.txt
pip install -e .

Notebook roles

• 01: data sanity checks + candidate universe + cointegration screening
• 02: baseline backtest + failure analysis (cointegration ≠ tradable)
• 03: walk-forward (rolling cointegration) + out-of-sample trading
• 04: dynamic hedge ratios (rolling OLS, Kalman beta) + regime filters + costs + portfolio constraints

Key Limitations & Future Work

Limitations

• Costs/slippage are simplified; real execution frictions can dominate returns
• No hard risk controls (stop-loss, max-hold, circuit breakers)
• Kalman filter is 1D beta-only (no alpha/intercept state)
• Results are sensitive to z-score lookbacks, thresholds, and sizing assumptions
• Survivorship / selection bias risk in small universes

Future Work

• Full walk-forward around Kalman + filters (not just baseline)
• 2D Kalman state '[alpha_t , beta_t] + parameter calibration (q/r)'
• Market-impact model + spread-based slippage estimates
• Portfolio optimizer (risk parity sizing, exposure constraints, correlation control)
• Stronger regime models (HMM / volatility clustering / macro features)