Risk capital allocations are of central importance in performance measurement. A popular solution concept in the academic literature is the Euler rule. This paper studies the volatility of the Euler rule for capital allocation in static and dynamic empirical applications with a simulated history. The Euler rule is not continuous with respect to small changes in the underlying risk capital allocation problem. We show that, when combined with value-at-risk, the Euler rule is very sensitive to empirical measurement error. The use of a known distribution with estimated parameters helps to reduce this error. The Euler rule with an expected shortfall risk measure is less volatile, but it is still more volatile than the proportional rule.

中文翻译：

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使用欧拉规则的静态和动态风险资本分配

风险资本分配在绩效衡量中至关重要。学术文献中一个流行的解决方案概念是欧拉规则。本文在模拟历史的静态和动态经验应用中研究了欧拉规则在资本配置中的波动性。对于潜在风险资本分配问题的微小变化，欧拉规则是不连续的。我们表明，当与风险价值结合时，欧拉规则对经验测量误差非常敏感。使用具有估计参数的已知分布有助于减少这种误差。具有预期短缺风险测度的欧拉规则的波动性较小，但仍比比例规则波动性大。