Elliptical Capital Asset Pricing Models: Formulation, Diagnostics, Case Study with Chilean Data, and Economic Rationale

The capital asset pricing model (CAPM) is often based on the Gaussianity or normality assumption. However, such an assumption frequently violated in practical situations. In this paper, we introduce symmetric CAPM considering distributions with lighter heavier tails than normal distribution. These are and belong to family of elliptical distributions. We pay special attention members related normal, power-exponential, Student-t cases, power-exponential distribution being particularly considered, as it has not been explored widely. Based these expectation-maximization algorithm can be used facilitate estimation parameters utilizing maximum likelihood method. addition, derive leverage local influence methods carry out diagnostics CAPM. conduct a detailed case study apply obtained results estimating systematic risk financial assets Chilean company real data. employ Akaike information criterion conclude that studied models provide better under Gaussianity.