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Robust Long-Term Growth Rate of Expected Utility for Leveraged ETFs

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  • Tim Leung
  • Hyungbin Park
  • Heejun Yeo

Abstract

This paper analyzes the robust long-term growth rate of expected utility and expected return from holding a leveraged exchange-traded fund (LETF). 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 martingale extraction method. The robust long-term growth rates are obtained explicitly under a number of models for the reference asset, including the geometric Brownian motion (GBM), Cox--Ingersoll--Ross (CIR), 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 \citet{Leung2017}.

Suggested Citation

  • Tim Leung & Hyungbin Park & Heejun Yeo, 2023. "Robust Long-Term Growth Rate of Expected Utility for Leveraged ETFs," Papers 2310.02084, arXiv.org.
    • Handle: RePEc:arx:papers:2310.02084
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    References listed on IDEAS

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