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Optimal consumption and investment in general affine GARCH models

Author

Listed:
  • Marcos Escobar-Anel

    (University of Western Ontario)

  • Ben Spies

    (Technical University of Munich)

  • Rudi Zagst

    (Technical University of Munich)

Abstract

Our paper presents the first optimal analytical solution for an investor maximizing both consumption and terminal wealth within expected utility theory in the realm of GARCH models. Working in a general family of affine GARCH models, we derive an affine GARCH optimal wealth process, providing analytical representations for optimal allocation, consumption and value functions. In particular, the optimal consumption ratio avoids the undesirable scenario of investors consuming all wealth prior to maturity. Our numerical study highlights the importance of formally accounting for consumption as it disrupts the level of optimal risky allocations. It also shows a larger impact of stochastic conditional variance (heteroscedasticity) on risky allocations in comparison to the impact of non-Gaussianity. We find, in a numerical study based on S&P 500 index data over a 5-years horizon, that an investor following a Gaussian GARCH strategy can achieve 10% more total consumption and at the same time 8% more terminal wealth than another investor following a constant variance (homoscedastic) strategy.

Suggested Citation

  • Marcos Escobar-Anel & Ben Spies & Rudi Zagst, 2024. "Optimal consumption and investment in general affine GARCH models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 987-1026, September.
    • Handle: RePEc:spr:orspec:v:46:y:2024:i:3:d:10.1007_s00291-024-00749-z
    DOI: 10.1007/s00291-024-00749-z
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    References listed on IDEAS

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    More about this item

    Keywords

    Dynamic portfolio optimization; Affine GARCH models; Consumption; IG-GARCH model; Expected utility theory;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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