Dynamic Portfolio Choice with Linear Rebalancing Rules

Abstract

We consider a broad class of dynamic portfolio optimization problems that allow for complex models of return predictability, transaction costs, trading constraints, and risk considerations. Determining an optimal policy in this general setting is almost always intractable. We propose a class of linear rebalancing rules and describe an efficient computational procedure to optimize with this class. We illustrate this method in the context of portfolio execution and show that it achieves near optimal performance.We consider another numerical example involving dynamic trading with mean-variance preferences and demonstrate that our method can result in economically large benefits.

Fairness and Efficiency in Multiportfolio Optimization

“…The former requirement reflects that the marginal market impact cost increases with the size of the trade, whereas the latter reflects the natural feature that more trading results in larger costs (for instance, due to reduced "at-the-money" liquidity). This is a commonly made assumption in the literature and is well aligned with empirical observations and practice (e.g., see Bertsimas and Lo 1998, Bertsimas et al 1999a, Almgren and Chriss 2000, O'Cinneide et al 2006, Brown et al 2010, Lim and Wimonkittiwat 2011, Moallemi and Saglam 2012.…”

“…For simplicity of exposition, we furthermore assume that the trading activity in a particular asset does not affect market impact costs associated with trading other assets (see, e.g., O'Cinneide et al 2006, Brown et al 2010, Fabozzi et al 2010, Moallemi and Saglam 2012. In other words, t is separable across assets and can be expressed as…”

“…Because of market impact, short-term return predictability, and/or potential constraints on trading, the problem of finding an optimal execution schedule is nontrivial and has received considerable attention in the literature (see, e.g., Bertsimas and Lo 1998, Almgren and Chriss 2000, Moazeni et al 2010, Tsoukalas et al 2012, and references therein). The setting that we adopt here is most closely aligned with that in Moallemi and Saglam (2012), to which we direct the interested reader for details and discussions of underlying assumptions. We first describe the single portfolio model in the former paper and then extend it to the MPO setting.…”

“…As in Moallemi and Saglam (2012), we assume that the manager is risk neutral, and his objective is to maximize the total expected excess profits from trading, net of transaction costs.…”

Performance Bounds and Suboptimal Policies for Multi-Period Investment

“…In [70], the authors describe a class of linear rebalancing policies for the discrete-time portfolio optimization problem. They develop several bounds, including a bound based on a clairvoyant investor and a bound obtained by solving an unconstrained quadratic problem.…”