{"title":"Multivariate Affine GARCH in portfolio optimization. Analytical solutions and applications","authors":"Marcos Escobar-Anel , Yu-Jung Yang , Rudi Zagst","doi":"10.1016/j.najef.2025.102376","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":47831,"journal":{"name":"North American Journal of Economics and Finance","volume":"77 ","pages":"Article 102376"},"PeriodicalIF":3.9000,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"North American Journal of Economics and Finance","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1062940825000166","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/3 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
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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.
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.
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