Dynamically Optimal Multi-period Mean-Variance Portfolio subject to Proportional Transaction Costs and No-shorting Constraint
23 Pages Posted: 17 Jul 2020
Date Written: June 25, 2020
This paper studies multi-period 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 and duality theory, 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. Moreover, we prove the optimal policy is always time consistent in efficiency, which also implies that imposing no-shorting constraint is a sufficient condition of making a precommitted multi-period policy consistent in efficiency. It gives rights to impose no-shorting constraint in a dynamic setting. 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 find 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.
Keywords: Portfolio selection, Discrete-time multi-period optimization, Proportional transaction costs, No-shorting constraint, Time consistency in efficiency
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