Multivariate Affine GARCH in portfolio optimization. Analytical solutions and applications

IF 3.8 3区经济学 Q1 BUSINESS, FINANCE

North American Journal of Economics and Finance Pub Date : 2025-02-03 DOI:10.1016/j.najef.2025.102376

Marcos Escobar-Anel , Yu-Jung Yang , Rudi Zagst

引用次数: 0

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.

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投资组合优化中的多元仿射GARCH。分析解决方案和应用

本文建立了一个多资产组合的最优配置公式，其中协方差结构遵循多元仿射GARCH（1,1）过程。我们在预期效用框架下工作，考虑一个具有恒定相对风险厌恶（CRRA）效用的投资者，他希望从终端财富中最大化预期效用。在逼近自融资条件后，我们推导出投资者所有利益量的封闭表达式：最优配置、最优财富过程和价值函数。如此完整的解析解在GARCH多变量文献中尚属首次。我们的实证分析表明，与默顿嵌入解决方案中恒定协方差的设置相比，多维异方差对投资组合决策的影响显著。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

North American Journal of Economics and Finance Multiple-

CiteScore

7.30

自引率

8.30%

发文量

168

期刊介绍： The focus of the North-American Journal of Economics and Finance is on the economics of integration of goods, services, financial markets, at both regional and global levels with the role of economic policy in that process playing an important role. Both theoretical and empirical papers are welcome. Empirical and policy-related papers that rely on data and the experiences of countries outside North America are also welcome. Papers should offer concrete lessons about the ongoing process of globalization, or policy implications about how governments, domestic or international institutions, can improve the coordination of their activities. Empirical analysis should be capable of replication. Authors of accepted papers will be encouraged to supply data and computer programs.