Optimizing Minimum Profit Boundaries for Cointegration Pairs Trading

Summary

This document explains a method for choosing entry boundaries in a cointegration-based pairs trade. The strategy fades a spread when it crosses a preset upper or lower threshold, then closes when it returns to its mean. With position weights set by the cointegration coefficient, the boundary corresponds to a minimum profit per completed trade under the stated model. The proposed objective is to choose the threshold that maximizes estimated minimum total profit over a trading horizon, balancing profit per trade against the expected number of trades.

The estimates rely on mean first-passage times for a stationary Gaussian AR(1) spread, computed numerically through a discretized integral equation. The method assumes a stable cointegration relationship in and out of sample, symmetric spread behavior, feasible short sales, and no trading costs or short-borrow charges. These assumptions limit practical interpretation: costs, changing relationships, asymmetric behavior, and model error can erode the estimated profit. The supplied text is also truncated in the optimization section, and it gives no complete empirical performance results.

Key ideas

• The strategy enters paired positions when a cointegration spread crosses a preset boundary and exits at the mean.
• The boundary sets a modeled minimum profit per trade when pair weights follow the cointegration coefficient.
• An AR(1) first-passage-time calculation estimates trade duration and the wait until another entry.
• The method selects a boundary to balance profit per trade against estimated trade frequency.
• Its assumptions include stable cointegration, symmetric spread behavior, short-sale access, and zero trading costs.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.