Identifying small mean-reverting portfolios

Given multivariate time series, we study the problem of forming portfolios with maximum mean reversion while constraining the number of assets in these portfolios. We show that it can be formulated as a sparse canonical correlation analysis and study various algorithms to solve the corresponding sparse generalized eigenvalue problems. After discussing penalized parameter estimation procedures, we study the sparsity versus predictability trade-off and the significance of predictability in various markets.