# Statistical foundations for assessing the difference between the classical and weighted-Gini betas

## TL;DR

This paper develops statistical methods to compare the classical CAPM beta with the weighted-Gini beta from the insurance model, providing tools for portfolio design and risk allocation.

## Contribution

It introduces large-sample inference techniques for testing the equality of classical and weighted-Gini betas, aiding financial and insurance risk assessment.

## Key findings

- Confidence intervals for beta differences
- Hypothesis tests for beta equality
- Implications for portfolio and risk management

## Abstract

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.