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Robust long-term growth rate of expected utility for leveraged ETFs

Author

Listed:
  • Tim Leung

    (University of Washington)

  • Hyungbin Park

    (Seoul National University
    Seoul National University)

  • Heejun Yeo

    (Seoul National University)

Abstract

This paper analyzes the robust long-term growth rate of expected utility and expected return from holding a leveraged exchange-traded fund. When the Markovian model parameters in the reference asset are uncertain, the robust long-term growth rate is derived by analyzing the worst-case parameters among an uncertainty set. We compute the growth rate and describe the optimal leverage ratio maximizing the robust long-term growth rate. To achieve this, the worst-case parameters are analyzed by the comparison principle, and the growth rate of the worst-case is computed using the Hansen–Scheinkman decomposition. The robust long-term growth rates are obtained explicitly under a number of models for the reference asset, including the geometric Brownian motion, Cox–Ingersoll–Ross, 3/2, and Heston and 3/2 stochastic volatility models. Additionally, we demonstrate the impact of stochastic interest rates, such as the Vasicek and inverse GARCH short rate models. This paper is an extended work of Leung and Park (Int J Theor Appl Finance 20(6):1750037, 2017).

Suggested Citation

  • Tim Leung & Hyungbin Park & Heejun Yeo, 2024. "Robust long-term growth rate of expected utility for leveraged ETFs," Mathematics and Financial Economics, Springer, volume 18, number 5, February.
    • Handle: RePEc:spr:mathfi:v:18:y:2024:i:4:d:10.1007_s11579-024-00371-1
    DOI: 10.1007/s11579-024-00371-1
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    References listed on IDEAS

    as
    1. Anis Matoussi & Dylan Possamaï & Chao Zhou, 2015. "Robust Utility Maximization In Nondominated Models With 2bsde: The Uncertain Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 258-287, April.
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    7. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230, arXiv.org, revised May 2018.
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    13. Tim Leung & Hyungbin Park, 2017. "LONG-TERM GROWTH RATE OF EXPECTED UTILITY FOR LEVERAGED ETFs: MARTINGALE EXTRACTION APPROACH," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-33, September.
    14. Hyungbin Park & Heejun Yeo, 2022. "Dynamic and static fund separations and their stability for long-term optimal investments," Papers 2212.00391, arXiv.org, revised Mar 2023.
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    More about this item

    Keywords

    Robustness; Long-term growth rate; Expected utility; Leveraged exchange-traded fund;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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