  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.
