Closed-form portfolio optimization under GARCH models

Marcos Escobar-Anel, Maximilian Gollart and Rudi Zagst
Authors registered in the RePEc Author Service: Marcos Escobar Anel ()

Operations Research Perspectives, 2022, vol. 9, issue C

Abstract: This paper develops an approximate closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth under a Heston and Nandi (2000) GARCH (HN-GARCH) model. Based on an approximation of the log returns from Campbell and Viceira (1999), we obtain closed formulas for the optimal investment strategy, the value function and the optimal terminal wealth. We find the optimal strategy is independent of the development of the risky asset, and the solution converges to that of a continuous-time Heston stochastic volatility model (Kraft, 2005), albeit under additional conditions. For a daily trading scenario, the optimal solutions are quite robust to variations in the parameters, while the numerical wealth equivalent loss (WEL) analysis shows good performance of the Heston solution, with a quite inferior performance of the Merton solution.The solution is extended to two dimensions under the multivariate affine GARCH in Escobar-Anel et al. (2020).

Keywords: Dynamic Programming; Investment analysis; GARCH models; Closed-form solutions; Expected Utility theory (search for similar items in EconPapers)
JEL-codes: C02 C22 C61 G11 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S2214716021000300
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Closed-form portfolio optimization under GARCH models (2021)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:oprepe:v:9:y:2022:i:c:s2214716021000300

DOI: 10.1016/j.orp.2021.100216

Access Statistics for this article

Operations Research Perspectives is currently edited by Rubén Ruiz Garcia

More articles in Operations Research Perspectives from Elsevier
Bibliographic data for series maintained by Catherine Liu ().