Optimal Dynamic Mean-Variance Portfolio subject to Proportional Transaction Costs and No-shorting Constraint (with Appendix)
18 Pages Posted: 17 Jul 2020 Last revised: 13 Sep 2021
Date Written: June 25, 2020
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.
Keywords: Portfolio selection, Discrete-time multi-period optimization, Proportional transaction costs, No-shorting constraint, Time consistency in efficiency
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