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Naive Markowitz Policies

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  • Lin Chen
  • Xun Yu Zhou

Abstract

We study a continuous-time Markowitz mean-variance portfolio selection model in which a naive agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naive policies through the limit of discretely naive policies that are committed only in very small time intervals, and derive them analytically and explicitly. We compare naive policies with pre-committed optimal policies and with consistent planners' equilibrium policies in a Black-Scholes market, and find that the former are mean-variance inefficient starting from any given time and wealth, and always take riskier exposure than equilibrium policies.

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  • Lin Chen & Xun Yu Zhou, 2022. "Naive Markowitz Policies," Papers 2212.07516, arXiv.org.
    • Handle: RePEc:arx:papers:2212.07516
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    References listed on IDEAS

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    1. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    2. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.
    3. Jianming Xia, 2005. "Mean–Variance Portfolio Choice: Quadratic Partial Hedging," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 533-538, July.
    4. Tomasz R. Bielecki & Hanqing Jin & Stanley R. Pliska & Xun Yu Zhou, 2005. "Continuous‐Time Mean‐Variance Portfolio Selection With Bankruptcy Prohibition," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 213-244, April.
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