Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/325715 
Year of Publication: 
2022
Citation: 
[Journal:] Operations Research Perspectives [ISSN:] 2214-7160 [Volume:] 9 [Article No.:] 100216 [Year:] 2022 [Pages:] 1-13
Publisher: 
Elsevier, Amsterdam
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).
Subjects: 
Dynamic Programming
Investment analysis
GARCH models
Closed-form solutions
Expected Utility theory
JEL: 
G11
C61
C22
C02
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by-nc-nd Logo
Document Type: 
Article

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