Bayesian Learning in an Affine GARCH Model with Application to Portfolio Optimization

Marcos Escobar-Anel (), Max Speck and Rudi Zagst
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Marcos Escobar-Anel: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
Max Speck: Department of Mathematics, Chair of Mathematical Finance, Technical University of Munich, Parkring 11/II, Garching-Hochbrück, 85748 Munich, Germany
Rudi Zagst: Department of Mathematics, Chair of Mathematical Finance, Technical University of Munich, Parkring 11/II, Garching-Hochbrück, 85748 Munich, Germany
Authors registered in the RePEc Author Service: Marcos Escobar Anel ()

Mathematics, 2024, vol. 12, issue 11, 1-27

Abstract: This paper develops a methodology to accommodate uncertainty in a GARCH model with the goal of improving portfolio decisions via Bayesian learning. Given the abundant evidence of uncertainty in estimating expected returns, we focus our analyses on the single parameter driving expected returns. After deriving an Uncertainty-Implied GARCH (UI-GARCH) model, we investigate how learning about uncertainty affects investments in a dynamic portfolio optimization problem. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize her expected utility from terminal wealth under an Affine GARCH(1,1) model. The corresponding stock evolution, and therefore, the wealth process, is treated as a Bayesian information model that learns about the expected return with each period. We explore the one- and two-period cases, demonstrating a significant impact of uncertainty on optimal allocation and wealth-equivalent losses, particularly in the case of a small sample size or large standard errors in the parameter estimation. These analyses are conducted under well-documented parametric choices. The methodology can be adapted to other GARCH models and applications beyond portfolio optimization.

Keywords: Affine GARCH; Bayesian learning; wealth equivalent loss (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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