Testing Optimal Rebalancing for Fully Invested Portfolios with Transaction Costs
Abstract
The thesis will examine the performance of various rebalancing strategies in portfolios with twoand four risky assets, where all capital is committed to risky assets. The primary objectiveis to demonstrate that portfolio rebalancing adds value for investors, even in the presence oftransaction costs. We provide a comprehensive analysis identifying the optimal rebalancing strategyfor a multi-asset portfolio. Within the mean-variance framework, the optimal strategy withoutconsidering transaction costs is to maintain constant weights in the asset allocation, irrespective ofthe performance of the risky assets. This necessitates rebalancing to restore the portfolio to its targetweights, unlike a passive portfolio where weights remain unchanged throughout the investmentperiod. The scarcity of analytical solutions for the optimal portfolio choice problem is largely dueto the complexities introduced by transaction costs, which necessitate the use of intricate numericalmethods within the domain of stochastic optimal control theory. Furthermore, the thesis drawsinspiration from Dichtl, Drobetz, and Wambach (2014) and examines the performance of variousrebalancing strategies for fully invested portfolios consisting of two risky assets, that incorporatetransaction costs. We employ the methodology of Zakamulin (2024) to illustrate that the optimalportfolio choice problem can be solved using a practical and easily applicable method, derived froma single-period model. Our findings are consistent with those of Dichtl et al. (2014) and Zakamulin(2024), indicating that the Buy-and-Hold strategy is sub-optimal