Tools

Cointegrated — or just correlated?

Two assets can move together for years and still be untradeable as a pair. Correlation says they wiggle in step day to day; cointegration says their spread keeps coming back. Build a pair, slide the cointegration strength, and watch the correlation stay high while the spread quietly turns into a random walk that drifts away.

What it shows: a pairs trade bets that a spread mean-reverts. That only works if the two assets are cointegrated — a stable long-run relationship — not merely correlated. This simulator estimates the hedge ratio by OLS over a formation window (Engle–Granger step 1), runs a simplified Dickey–Fuller test on the residual spread (step 2), then trades a z-score rule out-of-sample with no look-ahead. It's the intuition behind the pairs trading and statistical arbitrage guides.

All series are synthetic — nothing here is a performance figure or investment advice. The Dickey–Fuller test is simplified (no lag augmentation) and uses the Engle–Granger residual-based 5% critical value of −3.34 for the intuition; production work augments with lagged differences and MacKinnon p-values. Related tools: Backtest Overfitting Simulator · Information Coefficient Calculator · Signal Decay Calculator.

Build a pair

Two assets are built from a shared trend (so they co-move and their returns correlate strongly) plus a spread that mixes a mean-reverting part with a random-walk part. Cointegration strength sets the mix. Watch the correlation stay high while only the stationary spread stays tradeable.

0% = two independent random walks · 100% = a truly stationary spread

how fast the mean-reverting part pulls back to the mean

open a trade when the spread is this many σ from its mean

close the trade when the spread returns inside this band

3.0 years · first half = formation, second half = out-of-sample trading

a break shifts the hedge ratio out-of-sample

re-rolls the random draws — the cointegration verdict barely moves; the P&L jumps around