ABSTRACT

An accurate assessment of tail inequalities and tail asymmetries of financial returns is key for risk management and portfolio allocation. We propose a new test procedure for detecting the full extent of such structural differences in the dependence of bivariate extreme returns. We decompose the testing problem into piecewise multiple comparisons of Cramér–von Mises distances of tail copulas. In this way, tail regions that cause differences in extreme dependence can be located and consequently be targeted by financial strategies. We derive the asymptotic properties of the test and provide a bootstrap approximation for finite samples. Moreover, we account for the multiplicity of the piecewise tail copula comparisons by adjusting individual p-values according to multiple testing techniques. Monte Carlo simulations demonstrate the test’s superior finite-sample properties for common financial tail risk models, both in the iid and the sequentially dependent case. During the last 90 years in U.S. stock markets, our test detects up to 20% more tail asymmetries than competing tests. This can be attributed to the presence of nonstandard tail dependence structures. We also find evidence for diminishing tail asymmetries during every major financial crisis—except for the 2007–2009 crisis—reflecting a risk-return trade-off for extreme returns. Supplementary materials for this article are available online.

摘要

准确评估财务收益的尾部不平等和尾部不对称性是风险管理和投资组合分配的关键。我们提出了一种新的测试程序，以检测这种结构差异对双变量极端收益的依赖性的程度。我们将测试问题分解成尾部系膜的Cramér–von Mises距离的分段多重比较。这样，可以定位导致极端依赖差异的尾部区域，并因此将其作为财务策略的目标。我们导出测试的渐近性质，并提供有限样本的自举近似。此外，我们通过调整单个p来解决分段尾系比比较的多样性值根据多种测试技术。蒙特卡洛模拟证明了在iid和顺序依赖的情况下，该测试对于常见的金融尾部风险模型具有出色的有限样本属性。在美国股票市场的最近90年中，我们的测试检测到的尾部不对称性比竞争测试高出20％。这可以归因于非标准尾巴依赖性结构的存在。我们还发现有证据表明，在每次重大金融危机中（2007年至2009年危机除外），尾部不对称性都在降低，这反映了风险回报与极高回报之间的权衡。可在线获得本文的补充材料。