多元化收益组合的Optimization模型研究
An Optimization Study of Diversification Return Portfolios
摘要：
多元化收益率（DR）的概念是由Booth和Fama在20世纪90年代提出的，在金融文献中已经得到了很好的研究，主要集中在它可能产生的各种来源上。然而，与Markowitz的经典均值-方差（MV）模型不同，DR投资组合缺乏优化理论来证明其通常出色的经验表现。在本文中，我们首先解释了DR标准试图实现的投资组合中心性。这种解释的一个后果是，实际施加的规范约束，实际上隐含地执行DR的约束。然后，我们得出的最大DR组合下给定的风险，并获得有效的DR边界。我们进一步发展了一个分离定理，这个前沿和建立DR前沿和Markowitz MV有效前沿之间的关系。在方差向量与底层资产的预期收益向量成比例的特定情况下，两个边界产生相同的有效投资组合。证明技术在很大程度上依赖于最近开发的最大DR组合的几何解释。最后，我们使用DAX 30股票数据来说明所获得的结果，并展示了一个有趣的链接到Choueifaty和Coignard研究的最大多元化比率的投资组合。
英文摘要：
The concept of Diversification Return (DR) was introduced by Booth and Fama in 1990s and it has been well studied in the finance literature mainly focusing on the various sources it may be generated. However, unlike the classical Mean-Variance (MV) model of Markowitz, DR portfolios lack optimization theory for justifying their often outstanding empirical performance. In this paper, we first explain what the DR criterion tries to achieve in terms of portfolio centrality. A consequence of this explanation is that practically imposed norm constraints in fact implicitly enforce constraints on DR. We then derive the maximum DR portfolio under given risk and obtain the efficient DR frontier. We further develop a separation theorem for this frontier and establish a relationship between the DR frontier and Markowitz MV efficient frontier. In the particular case where the variance vector is proportional to the expected return vector of the underlining assets, the two frontiers yield same efficient portfolios. The proof techniques heavily depend on recently developed geometric interpretation of the maximum DR portfolio. Finally, we use DAX30 stock data to illustrate the obtained results and demonstrate an interesting link to the maximum diversification ratio portfolio studied by Choueifaty and Coignard.
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