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Sparse Mean-Reverting Portfolios via Penalized Likelihood Optimization

Jize Zhang (jizez***at***uw.edu)
Tim Leung (timleung***at***uw.edu)
Aleksandr Aravkin (saravkin***at***uw.edu)

Abstract: 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 and low variance though penalization, and (iii) select a parsimonious portfolio using l0-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. The problem requires custom analysis because the objective function does not have a Lipschitz-continuous gradient. Through our experiments using simulated and empirical price data, the proposed algorithm significantly outperforms standard approaches that do not exploit problem structure.

Keywords: portfolio optimization, OU process, sparsity constraints

Category 1: Applications -- OR and Management Sciences (Finance and Economics )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 10/31/2018
Entry Accepted: 11/01/2018
Entry Last Modified: 11/02/2018

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