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LONG-TERM GROWTH RATE OF EXPECTED UTILITY FOR LEVERAGED ETFs: MARTINGALE EXTRACTION APPROACH

Author

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  • TIM LEUNG

    (Department of Applied Mathematics, Computational Finance & Risk Management Program, University of Washington, Seattle, WA 98195, USA)

  • HYUNGBIN PARK

    (Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-Gu, Seoul 08826, Republic of Korea)

Abstract

This paper studies the long-term growth rate of expected utility or expected return from holding a leveraged exchanged-traded fund (LETF), which is a constant proportion portfolio of the reference asset. We develop a martingale extraction approach to tackle the path-dependence in the expectation and determine the long-term growth rate through the eigenpair associated with the infinitesimal generator of a time-homogeneous Markovian diffusion. The long-term growth rates are derived explicitly under a number of models for the reference asset, including the geometric Brownian motion model, GARCH model, inverse GARCH model, extended CIR model, 3/2 model, quadratic model, as well as the Heston and 3/2 stochastic volatility models. We also investigate the impact of stochastic interest rate such as the Vasicek model and the inverse GARCH short rate model. Additionally, we determine the optimal leverage ratio that maximizes the long-term growth rate, and examine the effects of model parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:06:n:s0219024917500376
    DOI: 10.1142/S0219024917500376
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    Cited by:

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