Model predictive control for optimal portfolios with cointegrated pairs of stocks

In this paper, we demonstrate a model predictive control (MPC) approach to constructing an optimal portfolio consisting of multiple spreads of cointegrated pairs of stocks. It is shown that a conditional mean-variance (MV) optimization problem with any given prediction horizon may be solved efficiently when the spreads of stocks follow a vector autoregressive (VAR) model. Based on the solution to the conditional MV problem, we can apply an MPC strategy that calculates the conditional MV optimal portfolio with a given prediction horizon at each rebalancing period. We also perform out-of-sample simulations using empirical stock price data from Japan, and examine the effects of the length of the prediction horizon, rebalance intervals, and transaction costs.