Optimal Dynamic Mean-Variance Portfolio subject to Proportional Transaction Costs and No-shorting Constraint (with Appendix)

TLDR: A semi-closed form solution of the optimal dynamic investment policy with the boundaries of buying, no-transaction, selling, and liquidation regions is derived, which proves the optimal policy is always time consistent in efficiency.

Abstract: This paper studies mean-variance portfolio selection problem subject to proportional transaction costs and no-shorting constraint We do not impose any distributional assumptions on the asset returns By adopting dynamic programming, duality theory, and a comparison approach, we manage to derive a semi-closed form solution of the optimal dynamic investment policy with the boundaries of buying, no-transaction, selling, and liquidation regions Numerically, we illustrate the properties of the optimal policy by depicting the corresponding efficient frontiers under different rates of transaction costs and initial wealth allocations We nd that the efficient frontier is distorted due to the transaction cost incurred We also examine how the width of the no-transaction region varies with different transaction cost rates Empirically, we show that our transaction-cost-aware policy outperforms the transaction-cost-unaware policy in a realistic trading environment that incurs transaction costs