A stationary spread is the engine of pairs trading, but locating one is the first and most costly step. A universe of 5,000 stocks produces roughly 12 million candidate pairs; running a full cointegration test on all of them is computationally prohibitive. Practitioners therefore use a two-stage funnel: a fast, cheap screening step that scores pairs by their historical co-movement and discards obvious non-candidates, followed by rigorous statistical testing on the shortlist. Once a pair passes those tests, three distinct approaches have emerged for constructing the spread itself and calibrating its dynamics: the empirical distance method (Gatev et al.), the econometric cointegration framework (Engle-Granger, Johansen), and the adaptive Kalman filter method (state-space).
This topic covers all three estimation approaches end-to-end, then closes with the trading design problem: given an estimated stationary spread, how do you choose the entry and exit thresholds that maximize expected profit per unit of time?
By the end of this topic you should be able to:
- normalize a price series and compute the sum-of-squared-deviations distance used in empirical pair screening;
- state the Engle-Granger and Johansen cointegration tests, run them, and interpret their output;
- construct the common-trends representation of two cointegrated series and identify the cointegrating vector ;
- link APT factor exposure profiles to the necessary conditions for cointegration;
- set up the state-space model for a dynamic hedge ratio and compute the Kalman filter update in scalar form;
- derive the optimal entry threshold for a white-noise spread and adapt it to OU dynamics;
- explain the convergence trap and design a stop-loss rule that bounds worst-case loss.
In this lesson
- Contents
- The big picture
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