2016/12/03 by Tim Leung, Leung, Tim, Hyungbin Park +1
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1612.01013
2 figures
arxiv created 2016/12/03 · openalex publication_date 2016/12/03 · arxiv updated 2016/12/06 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28
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.