Forming combinations of comoving assets is a critical step in pairs trading that has only been addressed either manually or through enumerative procedures. Both approaches fail in the multivariate case and do not consider conflicting objectives in the problem structure. This paper is the first attempt to address these novel problems by presenting an intelligent system that recommends profitable pair combinations through a Mixed Integer Programming (MIP) formulation and solving the NP-Hard optimization problem with a multi-objective genetic algorithm (NSGA-II) containing problem specific modifications. Combinations of assets are optimized on two conflicting objectives of risk (mean-reversion) and return (spread variance) to form sets of profitable multivariate pairs trading opportunities. Promising results support the superiority of multi-objective and multivariate pairs trading strategies over their traditional single objective and univariate counterparts. The findings should motivate new directions for pairs trading research and also expand the applications of evolutionary multi-objective optimization for hard problems in finance and other industries.

Introduction

Expert and intelligent systems have already made a profound impact on the financial industry. From “robo advisers” making automated asset allocation decisions to high frequency trading algorithms, the market has become ever-more dynamic, efficient, and competitive. Research in the pairs trading space has in some ways kept pace with these advancements, although there still lacks a sophisticated approach to forming profitable pair combinations. Deteriorating profitability of traditional approaches to the strategy have mostly been attributed to increased market efficiency so an advancement of an intelligent selection procedure should be a welcome innovation. Existing techniques for selecting pairs remain dependent on either expert intuition or computationally intensive enumerative procedures. Not only does this restrict the trading opportunities to univariate pairs, but the usual selection procedures fail to consider conflicting objectives properly. The problem draws similarities from Markowitz portfolio theory (1952) for systematic asset selection that optimizes a trade-off between conflicting risk and return objectives. Forming pairs of multiple assets under multiple objectives can not be done using existing approaches. The proposed methodology automatically generates a frontier of efficient multivariate pair combinations that satisfy multiple conflicting objectives. The problem is formulated as a mixed integer programming (MIP) model and, due to the non-convex constraints and exponential solution space, a genetic algorithm (GA) is employed to obtain profitable pair combinations. GA is also easily extended to handle multiple objectives, such as the Non-dominating Sorting Genetic Algorithm II (NSGA-II) used in this paper. We show how multivariate pairs from S&P 500 constituents generate excess returns over their univariate or single-objective benchmarks.