Optimal Symmetric No-Trade Ranges in Asset Rebalancing Strategy with Transaction Costs

Abstract

Abstract There are many studies of optimal asset allocation with transaction costs in academic literatures. However, those are numerically solved for two-asset and three-asset cases. In contrast, the investment in five-asset classes (domestic bond and stock, international bond and stock, and cash) is at least required for practical pension fund management. Therefore, there are some real limitations to the continuous-time approach used in the previous literatures, which are the methods of solving the Hamilton-Bellman-Jacobi (HJB) equation for the stochastic control problem. In general, most investors use the rebalance rule with the no-trade ranges in practice which are constant and symmetric to the policy asset mix because it is easy to use the rule. In this paper, we propose the optimization model for the multiple asset allocation problem with transaction costs to determine the symmetric no-trade ranges of the policy asset mix using the derivative-free optimization (DFO) approach proposed by Hibiki et al. (2014). Specifically, we solve the five-asset problem with boundary constraints for cash for the Government Pension Investment Fund (GPIF) in Japan in a discrete-time and finite-period setting. We clarify the fact that we need to adjust the amounts of risky assets even within the no-trade range if the boundary constraints for cash are required, and we describe the simulation procedure in the discrete-time model. We examine the difference for various time intervals and horizons and conduct the sensitivity analysis for the various proportional transaction cost rates, the tracking error aversions, and the bounds for cash constraints. In addition, we compare the optimal time-dependent no-trade ranges with the constant no-trade ranges. The numerical results show the possibilities of applying the DFO model to the practical problem determining the symmetric no-trade ranges.