Sparse mean-reverting portfolios via penalized likelihood optimization

An optimization approach is proposed to construct sparse portfolios with mean-reverting price behaviors. Our objectives are threefold: (i) design a multi-asset long-short portfolio that best fits an Ornstein-Uhlenbeck process in terms of maximum likelihood, (ii) select portfolios with desirable characteristics of high mean reversion through penalization, and (iii) select a parsimonious portfolio using to-regularization, i.e. find a small subset of a larger universe of assets that can be used for long and short positions. We present the full problem formulation, and develop a provably convergent algorithm for the nonsmooth, nonconvex objective based on partial minimization and projection. We demonstrate model functionalities on simulated and empirical price data, and include comparison with a pairs trading algorithm. (C) 2019 Elsevier Ltd. All rights reserved.