§1.3 — Trading
Statistical Arbitrage Backtester
Pairs-trading backtester across S&P 500 constituents using cointegration and inverse-volatility sizing.
2018-01-02 to 2023-12-29: +121% (5x, top 5 pairs) vs. +96% SPY · Sharpe 0.73 · max drawdown -60%
backtest only — never traded live, not connected to any broker
1. top 10 cointegrated pairs — S&P 500, 2018–2023
Screened ~1,225 pairs from 50 large-caps for correlation >0.8, then Engle-Granger cointegration p<0.01. Each row is its own independent backtest of the strategy's real entry/exit z-score rules.
2. portfolio — top 5 pairs, inverse-volatility weighted, 5x leverage
drawdown
Real weights: PM-UNH 19% · ABT-QCOM 18% · ABT-TXN 22% · MA-WMT 19% · JNJ-TMO 22%. Beats SPY on raw return over this window, but at a much larger drawdown — -60% vs. a much milder SPY decline in the same March 2020 stretch, the cost of 5x leverage on a concentrated 5-pair book.
3. the signal — one pair's real z-score
The single best pair by Sharpe (PM–UNH): real hedge-ratio-adjusted spread z-score, 2018–2023. Crossing ±2 opens a full position, ±0.5 a half position, back toward 0 exits.
4. sensitivity — slippage assumptions, not volatility, drive the result
rows: liquidity_factor · cols: volatility_factor · cell: portfolio Sharpe
Re-ran the full top-5 portfolio at every combination of the two slippage-model knobs. Sharpe is flat across volatility_factor but drops from 0.83 to 0.36 as liquidity_factor alone rises 20x — this backtest's edge lives or dies on how expensive trading is assumed to be, not on how volatile the market is.
honest limitations
No borrow costs, no market-impact modeling beyond the linear slippage terms above, and pair selection uses the full 2018–2023 window rather than a walk-forward split — so the same data that picked the top 10 pairs also backtested them. A real deployment would need out-of-sample pair selection before this Sharpe means anything predictive.