A capital asset pricing model based on the value at risk under asymmetric Laplace distribution

Abstract

Purpose

Financial asset return series usually exhibit nonnormal characteristics such as high peaks, heavy tails and asymmetry. Traditional risk measures like standard deviation or variance are inadequate for nonnormal distributions. Value at Risk (VaR) is consistent with people's psychological perception of risk. The asymmetric Laplace distribution (ALD) captures the heavy-tailed and biased features of the distribution. VaR is therefore used as a risk measure to explore the problem of VaR-based asset pricing. Assuming returns obey ALD, the study explores the impact of high peaks, heavy tails and asymmetric features of financial asset return data on asset pricing.

Design/methodology/approach

A VaR-based capital asset pricing model (CAPM) was constructed under the ALD that follows the logic of the classical CAPM and derive the corresponding VaR-β coefficients under ALD.

Findings

ALD-based VaR exhibits a minor tail risk than VaR under normal distribution as the mean increases. The theoretical derivation yields a more complex capital asset pricing formula involving β coefficients compared to the traditional CAPM.The empirical analysis shows that the CAPM under ALD can reflect the β-return relationship, and the results are robust. Finally, comparing the two CAPMs reveals that the β coefficients derived in this paper are smaller than those in the traditional CAPM in 69–80% of cases.

Originality/value

The paper uses VaR as a risk measure for financial time series data following ALD to explore asset pricing problems. The findings complement existing literature on the effects of high peaks, heavy tails and asymmetry on asset pricing, providing valuable insights for investors, policymakers and regulators.

Citation

Wu, L. and Xu, S. (2023), "A capital asset pricing model based on the value at risk under asymmetric Laplace distribution", Kybernetes, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/K-03-2023-0416