Portfolio diversification and model uncertainty: A robust dynamic mean-variance approach
Portfolio diversification and model uncertainty: A robust dynamic mean-variance approach
复制标题
投资组合多元化和模型不确定性：稳健的动态均值方差方法
DOI：
10.1111/mafi.12320
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发表时间：
2022
影响因子：
1.6
通讯作者：
Zhou Chao
中科院分区：
文献类型：
--
作者：
Pham Huyen;Wei Xiaoli;Zhou Chao
本文研究了模型不确定性下的动态多资产均值-方差投资组合问题。我们建立了一个连续时间框架，考虑到模糊厌恶的预期收益率和相关矩阵的资产，并研究联合效应的投资组合多元化。动态设置允许我们考虑时变模糊集，包括在历史数据的滚动窗口上估计漂移和相关性的情况，或者投资者考虑学习模糊性的情况。在这种情况下，我们证明了一个一般的分离原则相关联的鲁棒控制问题，这使我们能够减少最优动态策略的参数计算的最小风险溢价函数的确定。我们的研究结果为多元化不足提供了合理性，正如实证研究和静态模型所证明的那样。此外，我们明确量化的相关性界限和夏普比率的接近程度的多样化不足，并强调漂移和相关性模糊引起的不同功能。特别是，我们表明，投资者的信心差的预期收益估计不持有任何风险资产，另一方面，交易只有一个风险资产时，相关矩阵的模糊程度是大的。我们还提供了三资产情况下最优稳健投资组合多样化的完整图景。
This paper focuses on a dynamic multi‐asset mean‐variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and correlation matrix of the assets, and for studying the join effects on portfolio diversification. The dynamic setting allows us to consider time varying ambiguity sets, which include the cases where the drift and correlation are estimated on a rolling window of historical data or when the investor takes into account learning on the ambiguity. In this context, we prove a general separation principle for the associated robust control problem, which allows us to reduce the determination of the optimal dynamic strategy to the parametric computation of the minimal risk premium function. Our results provide a justification for under‐diversification, as documented in empirical studies and in the static models. Furthermore, we explicitly quantify the degree of under‐diversification in terms of correlation bounds and Sharpe ratios proximities, and emphasize the different features induced by drift and correlation ambiguity. In particular, we show that an investor with a poor confidence in the expected return estimation does not hold any risky asset, and on the other hand, trades only one risky asset when the level of ambiguity on correlation matrix is large. We also provide a complete picture of the diversification for the optimal robust portfolio in the three‐asset case.