Optimal Trading with Cointegrated Pairs of Stocks

In general, stock prices are believed to evolve according to a random walk and thus the prices of the stock market cannot be predicted. However, in some stock markets, we can observe that there are pairs of stocks whose movements look similar, characterized as "cointegration of pairs of stocks." In this paper, we demonstrate how to search for cointegrated pairs of stocks and construct optimal portfolios based on the following two techniques: (1) Mean-variance optimization which solves a single period problemand (2) Expected utility maximization in the terminal wealth at a specified time in the future. We perform out-of-sample simulations using empirical stock price data in Japan, and then examine the effects of parameter estimation periods and transaction costs.