[论文解读] What is the best risk measure in practice? A comparison of standard measures

Suzanne Emmer, Marie Kratz+1 more|arXiv (Cornell University)|Dec 5, 2013

Risk and Portfolio Optimization被引用 5

一句话总结

本文评估了风险价值（VaR）、期望损失（ES）和期望分位数（Expectiles）作为风险度量，考察其一致性、可预测性、稳健性以及共单调可加性。尽管ES因缺乏可预测性而使回测复杂化，作者仍认为其是目前最优的实际风险度量，而Expectiles由于非共单调可加性等问题，尚不足以提供充分理由以完全取代ES。

ABSTRACT

Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straightforward than, e.g., backtesting for VaR. Expectiles have been suggested as potentially better alternatives to both ES and VaR. In this paper, we revisit commonly accepted desirable properties of risk measures like coherence, comonotonic additivity, robustness and elicitability. We check VaR, ES and Expectiles with regard to whether or not they enjoy these properties, with particular emphasis on Expectiles. We also consider their impact on capital allocation, an important issue in risk management. We find that, despite the caveats that apply to the estimation and backtesting of ES, it can be considered a good risk measure. As a consequence, there is no sufficient evidence to justify an all-inclusive replacement of ES by Expectiles in applications. For backtesting ES, we propose an empirical approach that consists in replacing ES by a set of four quantiles, which should allow to make use of backtesting methods for VaR. Keywords: Backtesting; capital allocation; coherence; diversification; elicitability; expected shortfall; expectile; forecasts; probability integral transform (PIT); risk measure; risk management; robustness; value-at-risk

研究动机与目标

• 评估标准风险度量——VaR、ES和Expectiles——在实际风险管理应用中的适用性。
• 评估这些度量的一致性、可预测性、稳健性以及共单调可加性等关键属性。
• 研究风险度量选择对资本配置与分散化收益的影响。
• 解决由于ES缺乏可预测性而带来的回测挑战，并提出可行的替代方案。
• 在理论优势的基础上，判断Expectiles是否足以证明其在实践中取代ES的合理性。

提出的方法

• 基于公理化属性（一致性、共单调可加性、稳健性及可预测性）对VaR、ES和Expectiles进行系统比较。
• 应用概率积分变换（PIT）和评分函数进行回测，特别关注分布预测。
• 使用蒙特卡洛模拟与线性近似方法，测试不同置信水平下ES的表现。
• 通过将ES替换为四个分位数，开发一种针对ES的实证回测方法，以实现类似VaR的测试。
• 计算风险贡献与分散化指数，以评估资本配置与投资组合收益。
• 使用非参数检验（如Diebold-Mariano检验）以及PIT值的均匀性检验，验证预测性能。

实验结果

研究问题

• RQ1 尽管ES缺乏可预测性，导致回测困难，它是否仍为更优的风险度量？
• RQ2 VaR、ES和Expectiles在一致性、稳健性及共单调可加性方面的表现如何比较？
• RQ3 Expectiles能否作为ES在实际风险管理中可行的、一致且可预测的替代方案？
• RQ4 风险度量选择对投资组合资本配置与分散化收益有何影响？
• RQ5 当无法直接获得可预测性时，有哪些可行的ES回测方法？

主要发现

• 尽管缺乏可预测性，ES在一致性和尾部风险覆盖方面优于VaR。
• ES的估计与回测所需数据量大于VaR，方能达到相同的统计置信水平。
• Expectiles具有一致性与可预测性，但不满足共单调可加性，限制了其识别风险集中程度的能力。
• 所提出的ES回测方法——以四个分位数替代ES——使得标准VaR回测技术得以应用。
• 尚无充分证据支持在所有实际应用中以Expectiles完全取代ES。
• VaR因结构简单且对尾部分布行为不敏感而保持稳健，但其缺乏次可加性与尾部覆盖能力。