Optimal multi-period transaction-cost-aware long-only portfolios and time consistency in efficiency

Abstract

This paper studies a multi-period mean–variance (MV) portfolio selection problem in a market of one risk-free asset and one risky asset traded with proportional transaction costs and no-shorting constraint. A particular interest of this study is to investigate the time consistency in efficiency (TCIE) of the optimal MV portfolio in the presence of transaction costs. To this end, we derive a semi-closed-form solution of the optimal pre-committed dynamic MV policy in the no-shorting non-frictionless market with a combination of embedding and dynamic programming techniques, as well as its several analytical properties. We show that the optimal MV policy is always TCIE when no-shorting constraint is imposed, which gives right to the long-only portfolios in dynamic settings advocated in some empirical evidences. Numerically, we conduct sensitivity analyses of the efficient frontiers and the width of the no-transaction region with respect to the rates of transaction costs and initial wealth allocations. Moreover, we show the significance of the TCIE and the intuitive rationale behind it.

Keywords:

• Portfolio optimization
• Discrete-time multi-period optimization
• Transaction costs
• No-shorting constraints
• Time consistency in efficiency

JEL Classification:

• C61
• D81
• G11

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by Ministry of Education, Singapore, AcRF Tier 2 grant (Reference No: MOE-T2EP20220-0013).