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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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