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A Dynamic Mean-Variance Analysis for Log Returns

Author

Listed:
  • Min Dai

    (Department of Mathematics, Risk Management Institute, and Suzhou Research Institute, National University of Singapore, Singapore 119076)

  • Hanqing Jin

    (Oxford-Nie Financial Big Data Laboratory, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom)

  • Steven Kou

    (Department of Finance, Questrom School of Business, Boston University, Boston, Massachusetts 02215)

  • Yuhong Xu

    (Center for Financial Engineering, Math Center for Interdiscipline Research, and School of Mathematical Sciences, Soochow University, Suzhou 215006, P.R. China)

Abstract

We propose a dynamic portfolio choice model with the mean-variance criterion for log returns. The model yields time-consistent portfolio policies and is analytically tractable even under some incomplete market settings. The portfolio policies conform with conventional investment wisdom (e.g., richer people should invest more absolute amounts of money in risky assets; the longer the investment time horizon, the more proportional amount of money should be invested in risky assets; and for long-term investment, people should not short-sell major stock indices whose returns are higher than the risk-free rate), and the model provides a direct link with the constant relative risk aversion utility maximization in a complete market. This paper was accepted by Kay Giesecke, finance.

Suggested Citation

  • Min Dai & Hanqing Jin & Steven Kou & Yuhong Xu, 2021. "A Dynamic Mean-Variance Analysis for Log Returns," Management Science, INFORMS, vol. 67(2), pages 1093-1108, February.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:2:p:1093-1108
    DOI: 10.1287/mnsc.2019.3493
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    8. Mengge Li & Shuaijie Qian & Chao Zhou, 2023. "Robust Equilibrium Strategy for Mean-Variance Portfolio Selection," Papers 2305.07166, arXiv.org, revised May 2023.
    9. Ma, Shuai & Ma, Xiaoteng & Xia, Li, 2023. "A unified algorithm framework for mean-variance optimization in discounted Markov decision processes," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1057-1067.
    10. Yuchen Li & Zongxia Liang & Shunzhi Pang, 2022. "Continuous-Time Monotone Mean-Variance Portfolio Selection," Papers 2211.12168, arXiv.org, revised Jan 2024.
    11. Min Dai & Yuchao Dong & Yanwei Jia & Xun Yu Zhou, 2023. "Learning Merton's Strategies in an Incomplete Market: Recursive Entropy Regularization and Biased Gaussian Exploration," Papers 2312.11797, arXiv.org.
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    14. Kristoffer Andersson & Cornelis W. Oosterlee, 2023. "D-TIPO: Deep time-inconsistent portfolio optimization with stocks and options," Papers 2308.10556, arXiv.org, revised Sep 2023.

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