Multivariate Affine GARCH in portfolio optimization. Analytical solutions and applications

Marcos Escobar-Anel, Yu-Jung Yang and Rudi Zagst
Authors registered in the RePEc Author Service: Marcos Escobar Anel ()

The North American Journal of Economics and Finance, 2025, vol. 77, issue C

Abstract: This paper develops an optimal portfolio allocation formula for multi-assets where the covariance structure follows a multivariate Affine GARCH(1,1) process. We work under an expected utility framework, considering an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth. After approximating the self-financing condition, we derive closed-form expressions for all the quantities of interest to investors: optimal allocations, optimal wealth process, and value function. Such a complete analytical solution is a first in the GARCH multivariate literature. Our empirical analyses show a significant impact of multidimensional heteroscedasticity in portfolio decisions compared to a setting of constant covariance as per Merton’s embedded solution.

Keywords: Expected utility; CRRA utility; Multivariate affine GARCH; Portfolio optimization (search for similar items in EconPapers)
JEL-codes: C22 C61 G11 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:77:y:2025:i:c:s1062940825000166

DOI: 10.1016/j.najef.2025.102376

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