Copula的条件以及对股票投资组合的合理措施

Copula的条件以及对股票投资组合的合理措施(中文4300字,英文3100字)    
摘要
 基于多元正态分布的传统投资组合理论认为投资者可以通过相关性较低的投资资产从多元化中受益。然而，这是不是在现实中发生的事情，因为它是很容易看到金融市场有不同的相关关系，但市场的崩溃几乎相同的性质（如果我们定义市场大跌的时候回报他们的最低百分位） 。以类似的方式，最近的实证研究表明，在动荡时期的金融市场往往产生不同的水平比发生在平静期的依赖。为了考虑到这一现实，我们采取的Copula理论及其条件的依赖的措施，如Kendall的头和尾的依赖。前者满足大多数的依赖的措施必须有，它可以检测出非线性协会的相关所需性能无法看到。尾部相关性是指，从极端的观测随机变量之间产生的依赖性。我们认为，由在美国的市场实际成交的五个最重要的期货合约的投资组合，我们考虑到在过去十年中最不稳定的时期，也就是2000年3月13日之间，直到2000年6月9日。我们将展示如何将这些条件依赖的措施既可以在传统的均值 - 方差框架，并在多变量的估计很容易实现，具有显著的改善了传统的多元相关分析。

 Copula’s Conditional Dependence Measures for Portfolio Management and Value at Risk
Abstract
Traditional portfolio theory based on multivariate normal distribution assumes that investors can benefit from diversification by investing in assets with lower correlations. However, this is not what happens in reality, since it is quite easy to see financial markets with different correlations but almost the same numbers of market crashes (if we define market crash as when returns are in their lowest percentile). In a similar fashion, recent empirical studies show that in volatile periods financial markets tend to be characterized by different level of dependence than occurs in quiet periods. In order to take into account this reality, we resort to copula theory and its conditional dependence measures, like Kendall’s Tau and Tail dependence. The former satisfies most of the desired properties that a dependence measure must have and it can detect non-linear association that correlation cannot see. Tail dependence refers to the dependence that arises between random variables from extreme observations. We consider a portfolio made up of the five most important future contracts actually traded in American markets and we take into consideration the most volatile period of the last decade, that is between March 13th 2000 until June 9th 2000. We show how these conditional dependent measures can be easily implemented both in the traditional mean-variance framework and in multivariate estimation, with a significant improvement over traditional multivariate correlation analysis.