We propose a new backtesting framework for expected shortfall (ES) that can be used by regulators. Instead of looking at estimated capital reserve and realized cashflow separately, one can bind them into a secured position, for which risk measurement is much easier. Using this simple concept combined with monotonicity of ES with respect to its target confidence level, we introduce a natural and efficient backtesting framework. Our test statistics is given by the biggest number of worst realizations for the secured position that adds up to a negative total. Surprisingly, this simple quantity can be used to construct an efficient backtesting framework for unconditional coverage of ES in a natural extension of the regulatory traffic-light approach for value-at-risk. While being easy to calculate, the test statistic is based on the underlying duality between coherent risk measures and scale-invariant performance measures.

中文翻译：

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回测预期不足：一个简单的方法？

我们提出了一个新的预期短缺（ES）回溯测试框架，可供监管机构使用。无需分别查看估计资本储备和已实现现金流，您可以将它们绑定到一个有担保的位置，这样风险衡量要容易得多。使用这个简单的概念，结合 ES 在其目标置信水平方面的单调性，我们引入了一个自然而有效的回测框架。我们的测试统计数据是由安全头寸的最差实现的最大数量给出的，加起来为负总数。令人惊讶的是，这个简单的数量可用于构建一个有效的回溯测试框架，用于无条件覆盖 ES，这是监管交通灯方法的自然扩展，用于风险价值。虽然容易计算，