  We study the profitability of optimal mean reversion trading strategies in
the US equity market. Different from regular pair trading practice, we apply
maximum likelihood method to construct the optimal static pairs trading
portfolio that best fits the Ornstein-Uhlenbeck process, and rigorously
estimate the parameters. Therefore, we ensure that our portfolios match the
mean-reverting process before trading. We then generate contrarian trading
signals using the model parameters. We also optimize the thresholds and the
length of in-sample period by multiple tests. In nine good pair examples, we
can see that our pairs exhibit high Sharpe ratio (above 1.9) over the in-sample
period and out-of-sample period. In particular, Crown Castle International
Corp. (CCI) and HCP, Inc. (HCP) achieve a Sharpe ratio of 2.326 during
in-sample period and a Sharpe ratio of 2.425 in out-of-sample test. Crown
Castle International Corp. (CCI) and Realty Income Corporation (O) achieve a
Sharpe ratio of 2.405 and 2.903 respectively during in-sample period and
out-of-sample period.
