Dynamically Optimal Multi-period Mean-Variance Portfolio subject to Proportional Transaction Costs and No-shorting Constraint

23 Pages Posted: 17 Jul 2020

See all articles by Chi Seng Pun

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Zi Ye

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Date Written: June 25, 2020

Abstract

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

Suggested Citation

Pun, Chi Seng and Ye, Zi, Dynamically Optimal Multi-period Mean-Variance Portfolio subject to Proportional Transaction Costs and No-shorting Constraint (June 25, 2020). Available at SSRN: https://ssrn.com/abstract=3635361 or http://dx.doi.org/10.2139/ssrn.3635361

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

SPMS-MAS-05-22
21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://personal.ntu.edu.sg/cspun/

Zi Ye

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

S3 B2-A28 Nanyang Avenue
Singapore, 639798
Singapore

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