Constant Rebalanced Portfolio Optimization Under Nonlinear Transaction Costs

Abstract

In this paper, we study a multi-period portfolio optimization where conditional value-atrisk (CVaR) is controlled as well as expected return, and the so-called constant rebalancing strategy is employed under nonlinear transaction costs. In general, the optimization of this strategy itself is, however, difficult to attain a globally optimal solution because of the nonconvexity. In addition, nonlinearity of the transaction cost and CVaR functions makes things worse, and even a locally optimal solution may not be reached via a state-of-the-art nonlinear programming solver when the size of the problem is large. In order to provide a practical solution to the highly complex problem, we propose a local search algorithm where linear approximation problems and nonlinear equations are iteratively solved. Computational results are presented, showing that the proposed algorithm attains a good solution in practical time even when a revised version of an existing global optimization approach cannot return any feasible solutions.

Multiportfolio optimization with CVaR risk measure

“…CVaR has been used as risk measure in different portfolio optimization problems, such as, V-shaped transaction cost in rebalancing model with self-finance strategy (Wang et al 2014), multi-period portfolio optimization (Takano and Gotoh 2011, Zhang and Zhang 2009, Meng et al 2011, Najafi and Mushakhian (2015), two-stage stochastic portfolio (Fabian 2008).…”

A polynomial optimization approach to constant rebalanced portfolio selection

“…However, the constant rebalancing strategy generally leads to nonconvex optimization. Because of its difficulty, most studies (e.g., [5,26]) have focused on approximately solving the constant rebalanced portfolio optimization problem. To the best of our knowledge, only Maranas et al [19] approached it through global optimization by developing a specialized branch-and-bound algorithm.…”