Linear Rebalancing Strategy for Multi-Period Dynamic Portfolio Optimization Under Regime Switches

Abstract

Although there is a growing interest of applying regime switching models to portfolio optimization, it has never been quite easy as yet to obtain analytical solutions under practical conditions such as self-financing constraints and short sales constraints. In this paper, we extend the linear rebalancing rule proposed in Moallemi and Saglam [17] to regime switching models and provide a multi-period dynamic investment strategy that is comprised of a linear combination of factors with regime dependent coefficients. Under plausible mathematical assumptions, the problem to determine optimal coefficients maximizing a mean-variance utility penalized for transaction costs subject to self-financing and short sales constraints can be formulated as a quadratic programming which is easily solved numerically. To suppress an exponential increase of a number of optimization variables caused by regime switches, we propose a sample space reduction method. From numerical experiments under a practical setting, we confirm that our approach achieves sufficiently reasonable performances, even when sample space reduction is applied for longer investment horizon. The results also show superior performance of our approach to that of the optimal strategy without concerning transaction costs.

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