Mean-Reverting Portfolio With Budget Constraint

This paper considers the mean-reverting portfolio (MRP) design problem arising from statistical arbitrage (a.k.a. pairs trading) in the financial markets. It aims at designing a portfolio of underlying assets by optimizing the mean reversion strength of the portfolio, while taking into consideration the portfolio variance and an investment budget constraint. Several specific design problems are considered based on different mean reversion criteria. Efficient algorithms are proposed to solve the problems. Numerical results on both synthetic and market data show that the proposed MRP design methods can generate consistent profits and outperform the traditional design methods and the benchmark methods in the literature.

I. Introduction

Pairs trading [2]–[5] , also known as spread trading [6]– [9], is a famous investment and trading strategy pioneered by scientists Gerry Bamberger and David Shaw, as well as the quantitative trading group led by Nunzio Tartaglia at Morgan Stanley in the mid 1980s. As indicated by the name, it is a trading strategy that focuses on a pair of assets at the same time rather than a single one. Investors or arbitrageurs embracing this strategy do not need to forecast the absolute price of every single asset within one trading pair, which by nature is difficult, but only the relative price of this pair. As a contrarian investment strategy, in order to arbitrage from the market, investors should buy the under-priced asset and short-sell the over-priced one. Profits will be locked in after the trading positions are unwound when the relative mispricing of the pair corrects itself in the future.