Long-Term Growth Rate of Expected Utility for Leveraged ETFs: Martingale Extraction Approach

International Journal of Theoretical & Applied Finance, Vol. 20, No. 6, 2017

30 Pages Posted: 6 Dec 2016 Last revised: 18 Feb 2019

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Hyungbin Park

Seoul National University

Date Written: December 3, 2016

Abstract

This paper studies the long-term growth rate of expected utility from holding a leveraged exchanged-traded fund (LETF), which is a constant proportion portfolio of the reference asset. Working with the power utility function, we develop an analytical approach that employs martingale extraction and involves finding the eigenpair associated with the infinitesimal generator of a Markovian time-homogeneous diffusion. We derive explicitly the long-term growth rates 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. We determine the optimal leverage ratio for the long-term investor and examine the effects of model parameters.

Keywords: LETF, Long-Term Growth Rate, Expected Utility

JEL Classification: C52, G13

Suggested Citation

Leung, Tim and Park, Hyungbin, Long-Term Growth Rate of Expected Utility for Leveraged ETFs: Martingale Extraction Approach (December 3, 2016). International Journal of Theoretical & Applied Finance, Vol. 20, No. 6, 2017, Available at SSRN: https://ssrn.com/abstract=2879976 or http://dx.doi.org/10.2139/ssrn.2879976

Tim Leung

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Hyungbin Park (Contact Author)

Seoul National University ( email )

Kwanak-gu
Seoul, 151-742
Korea, Republic of (South Korea)

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
157
Abstract Views
896
Rank
339,776
PlumX Metrics