The ‘beta’ is one of the key quantities in the capital asset pricing model (CAPM). In statistical language, the beta can be viewed as the slope of the regression line fitted to financial returns on the market against the returns on the asset under consideration. The insurance counterpart of CAPM, called the weighted insurance pricing model (WIPM), gives rise to the so-called weighted-Gini beta. The aforementioned two betas may or may not coincide, depending on the form of the underlying regression function, and this has profound implications when designing portfolios and allocating risk capital. To facilitate these tasks, in this paper we develop large-sample statistical inference results that, in a straightforward fashion, imply confidence intervals for, and hypothesis tests about, the equality of the two betas.

中文翻译：

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评估经典基尼和加权基尼贝塔系数之间差异的统计基础

“ beta”是资本资产定价模型（CAPM）中的关键数量之一。用统计语言来说，贝塔值可以看作是拟合市场价格和资产收益率的回归线的斜率。CAPM的保险同行，称为加权保险定价模型（WIPM），产生了所谓的加权基尼系数beta。取决于潜在回归函数的形式，上述两个beta可能相同也可能不同，这在设计投资组合和分配风险资本时具有深远的意义。为了方便执行这些任务，在本文中，我们开发了大样本统计推断结果，以直接的方式暗示了两个beta的相等性的置信区间和假设检验。