Investigating the Impact of Consumption Distribution on CRRA Estimation: Quantile-CCAPM-Based Approach

Ramos Sofia B., Taamouti Abderrahim () and Veiga Helena
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Ramos Sofia B.: ESSEC Business School, Cergy, France
Taamouti Abderrahim: Department of Economics, University of Liverpool Management School, University of Liverpool, Chatham St., Liverpool L69 7ZH, UK
Veiga Helena: Department of Statistics and Instituto Flores de Lemus, Universidad Carlos III de Madrid, and BRU-UNIDE, Getafe, Spain

Studies in Nonlinear Dynamics & Econometrics, 2025, vol. 29, issue 1, 39-52

Abstract: Using quantile maximization decision theory, this paper considers a quantile-based Euler equation that states that the asset price is a function of the quantiles of the payoff, consumption growth, the stochastic discount factor, risk aversion, and the distribution of the consumption growth rate. We use a more general distribution assumption (log-elliptical distributions) than the log-normality of the consumption growth rate assumed in the literature. The simulation results show that: (1) the higher the downside risk aversion, the lower the constant relative risk aversion; (2) the heavier the tails of the Student-t distribution, the higher the risk aversion for each level of downside risk aversion; and (3) the curve of the relationship between risk aversion and downside risk aversion shifts upward when the normality assumption is dropped, and the magnitude of this shift is high even for high degrees of freedom of the Student-t distribution. Our results suggest that using normally distributed errors to model stock returns and consumption growth rates could lead to an underestimation of the risk aversion coefficient.

Keywords: CCAPM; consumption volatility; downside risk aversion; quantile-based Euler equation; risk aversion; stochastic volatility (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/snde-2023-0005

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