Multivariate Affine GARCH in portfolio optimization. Analytical solutions and applications

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.