We study a continuous-time Markowitz mean–variance portfolio selection model in which a naïve agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naïve policies through the limit of discretely naïve policies that are committed only in very small time intervals, and derive them analytically and explicitly. We compare naïve policies with pre-committed optimal policies and with consistent planners' equilibrium policies in a Black–Scholes market, and find that the former achieve higher expected terminal returns than originally planned yet are mean–variance inefficient when the risk aversion level is sufficiently small, and always take strictly riskier exposure than equilibrium policies. We finally define an efficiency ratio for comparing return–risk tradeoff with the same original level of risk aversion, and show that naïve policies are always strictly less efficient than pre-committed and equilibrium policies.

中文翻译：

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天真的马科维茨政策

我们研究了一个连续时间马科维茨均值-方差投资组合选择模型，其中一个幼稚的代理不知道潜在的时间不一致，随着时间的推移不断重新优化。我们通过限制仅在非常小的时间间隔内提交的离散朴素策略来定义最终的朴素策略，并通过分析和显式推导它们。我们将朴素政策与预先承诺的最优政策以及布莱克-斯科尔斯市场中一致规划者的均衡政策进行比较，发现前者实现了比最初计划更高的预期最终回报，但当风险厌恶水平足够大时，均值方差效率低下规模较小，并且始终采取比均衡政策更高的风险敞口。我们最终定义了一个效率比，用于将回报风险权衡与相同的原始风险厌恶水平进行比较，并表明幼稚的政策总是比预先承诺的均衡政策效率低。