Statistical Analysis of Portfolio Characteristics for Different Risk Measures

在Markowitz(1952)的开创性工作中，对于给定的投资组合收益率，通过最小化投资组合的方差来获得最优投资组合。虽然同时也有许多其他方法被引入来构造最优投资组合，但Markowitz(1952)的均值方差分析仍然是实践中最流行的方法。长期以来，推导最优投资组合权重的关键假设之一是，潜在收益过程的参数是已知的。建议通过历史数据估计这些数量。最近，几位作者开始从统计学的角度分析这一问题。已经提出了最优投资组合权重和投资组合特征的各种估计器和检验方法，并进行了相互比较(例如，Okhrin和Schmid(2006)，Bodnar和Schmidd(2008a/b，2009))。在这些论文中，选择方差作为投资组合的风险度量。然而，在过去的几年里，几篇论文表明，方差不是一个好的风险衡量标准，应该采用其他衡量标准(例如，Artzner等人)。(1999))。这个项目的目的是通过使用更合适的风险度量来考虑投资组合选择问题。将得到相应的最优投资组合权重和投资组合特征的估计值和检验。

In the pioneering work of Markowitz (1952) an optimal portfolio is obtained by minimizing the portfolio variance for a given value of the portfolio return. Although in the meantime many other approaches for constructing an optimal portfolio have been introduced, the meanvariance analysis of Markowitz (1952) is still the most popular method in practice. For a long time one of the crucial assumptions for the derivation of the optimal portfolio weights was that the parameters of the underlying return process are known. It was recommended to estimate these quantities by historical data. Recently several authors started to analyze this problem from a statistical point of view. Various estimators and tests of optimal portfolio weights and portfolio characteristics have been proposed and compared with each other (e.g., Okhrin and Schmid (2006), Bodnar and Schmid (2008a/b, 2009)). In these papers the variance is chosen as a risk measure of the portfolio. In the last years, however, it has been shown in several papers that the variance is not a good risk measure and other measures should be favored (e.g., Artzner et al. (1999)). The aim of this project is to consider the portfolio selection problem by using more suitable risk measures. Estimators and tests for the corresponding optimal portfolio weights and portfolio characteristics will be derived.