Three L1 based nonconvex methods in constructing sparse mean reverting portfolios

Xiaolong Long Knut Solna University of California at Irvine Jack Xin University of California at Irvine

Information Theory mathscidoc:1802.19002

Journal of Scientific Computing, 2017.10
We study the problem of constructing sparse and fast mean revert- ing portfolios. The problem is motivated by convergence trading and formu- lated as a generalized eigenvalue problem with a cardinality constraint [6]. We use a proxy of mean reversion coefficient, the direct Ornstein-Uhlenbeck (OU) estimator, which can be applied to both stationary and nonstationary data. In addition, we introduce three different methods to enforce the sparsity of the solutions. One method uses the ratio of l1 and l2 norms and the other two use l1 norm. We analyze various formulations of the resulting non-convex opti- mization problems and develop efficient algorithms to solve them for portfolio sizes as large as hundreds. By adopting a simple convergence trading strat- egy, we test the performance of our sparse mean reverting portfolios on both synthetic and historical real market data. In particular, the l1 regularization method, in combination with quadratic program formulation as well as differ-ence of convex functions and least angle regression treatment, gives fast and robust performance on large out-of-sample data set. To appear in Journal of Scientific Computing (JOMP).
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@inproceedings{xiaolong2017three,
  title={Three L1 based nonconvex methods in constructing sparse mean reverting portfolios},
  author={Xiaolong Long, Knut Solna, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180214111936837728926},
  booktitle={Journal of Scientific Computing},
  year={2017},
}
Xiaolong Long, Knut Solna, and Jack Xin. Three L1 based nonconvex methods in constructing sparse mean reverting portfolios. 2017. In Journal of Scientific Computing. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180214111936837728926.
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