The daily returns on leveraged and inverse-leveraged exchange-traded funds (LETFs) are a multiple of the daily returns of a reference index. Because LETFs rebalance their leverage daily, their holding period returns can deviate substantially from the returns of a leveraged investment. While about half of LETF investors hold their investments for less than a month, the standard analysis of these investments uses a continuous time framework that is not appropriate for analyzing short holding periods, so the true effect of this daily rebalancing has not been properly ascertained.
In this paper, we model tracking errors of LETFs compared to a leveraged investment in discrete time. For a period lasting a month or less, the continuous time model predicts tracking errors to be small. However, we find that in a discrete time model, daily portfolio rebalancing introduces tracking errors that are not captured in the continuous time framework. On average, portfolio rebalancing accounts for approximately 25% of the total tracking error, and in certain scenarios the rebalancing tracking error could rise to as high as 5% in 3 weeks and can dominate the total tracking error. Since investors in LETFs have short average holding periods and high average turnover ratios, the effects of portfolio rebalancing must be accurately accounted for in the analysis of LETF returns.