TY - JOUR
T1 - Elliptical Capital Asset Pricing Models
T2 - Formulation, Diagnostics, Case Study with Chilean Data, and Economic Rationale
AU - Leal, Danilo
AU - Jiménez, Rodrigo
AU - Riquelme, Marco
AU - Leiva, Víctor
N1 - Publisher Copyright:
© 2023 by the authors.
PY - 2023/3
Y1 - 2023/3
N2 - The capital asset pricing model (CAPM) is often based on the Gaussianity or normality assumption. However, such an assumption is frequently violated in practical situations. In this paper, we introduce the symmetric CAPM considering distributions with lighter or heavier tails than the normal distribution. These distributions are symmetric and belong to the family of elliptical distributions. We pay special attention to the family members related to the normal, power-exponential, and Student-t cases, with the power-exponential distribution being particularly considered, as it has not been explored widely. Based on these cases, the expectation-maximization algorithm can be used to facilitate the estimation of model parameters utilizing the maximum likelihood method. In addition, we derive the leverage and local influence methods to carry out diagnostics in the symmetric CAPM. We conduct a detailed case study to apply the obtained results estimating the systematic risk of the financial assets of a Chilean company with real data. We employ the Akaike information criterion to conclude that the studied models provide better results than the CAPM under Gaussianity.
AB - The capital asset pricing model (CAPM) is often based on the Gaussianity or normality assumption. However, such an assumption is frequently violated in practical situations. In this paper, we introduce the symmetric CAPM considering distributions with lighter or heavier tails than the normal distribution. These distributions are symmetric and belong to the family of elliptical distributions. We pay special attention to the family members related to the normal, power-exponential, and Student-t cases, with the power-exponential distribution being particularly considered, as it has not been explored widely. Based on these cases, the expectation-maximization algorithm can be used to facilitate the estimation of model parameters utilizing the maximum likelihood method. In addition, we derive the leverage and local influence methods to carry out diagnostics in the symmetric CAPM. We conduct a detailed case study to apply the obtained results estimating the systematic risk of the financial assets of a Chilean company with real data. We employ the Akaike information criterion to conclude that the studied models provide better results than the CAPM under Gaussianity.
KW - CAPM
KW - expectation-maximization algorithm
KW - financial asset valuation
KW - generalized leverage
KW - local influence diagnostics
KW - symmetric or univariate elliptical distributions
KW - systematic risk
UR - http://www.scopus.com/inward/record.url?scp=85151510241&partnerID=8YFLogxK
U2 - 10.3390/math11061394
DO - 10.3390/math11061394
M3 - Article
AN - SCOPUS:85151510241
SN - 2227-7390
VL - 11
JO - Mathematics
JF - Mathematics
IS - 6
M1 - 1394
ER -