Optimizing Sparse Mean-Reverting Portfolio

Mean-reverting behavior of individuals assets is widely known in financial markets. In fact, we can construct a portfolio that has mean-reverting behavior and use it in trading strategies to extract profits. In this paper, we show that we are able to find the optimal weights of stocks to construct portfolio that has the fastest mean-reverting behavior. We further add minimum variance and sparsity constraints to the optimization problem and transform into Semidefinite Programming (SDP) problem to find the optimal weights. Using the optimal weights, we empirically compare the performance of contrarian strategies between non-sparse mean-reverting portfolio and sparse mean-reverting portfolio to argue that the latter provides higher returns when we take into account of transaction costs.