Robust Long-Term Growth Rate of Expected Utility for Leveraged ETFs
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}.
Keywords
Cite
@article{arxiv.2310.02084,
title = {Robust Long-Term Growth Rate of Expected Utility for Leveraged ETFs},
author = {Tim Leung and Hyungbin Park and Heejun Yeo},
journal= {arXiv preprint arXiv:2310.02084},
year = {2023}
}