Analysis of Leveraged ETF Compounding Difference

Abstract

This thesis studies leveraged exchange-traded funds (ETFs). Because leveraged ETFs track the daily returns of their underlying indices, the performance of leveraged ETFs can deviate from their underlying indices over time due to compounding. This paper assumes perfect tracking and defines compounding difference as the difference between the return of a leveraged ETF and the return of its underlying index, after adjusting for leverage. This paper analyzes the distribution of compounding difference under different volatility conditions using the leveraged ETF model proposed by Avellaneda and Zhang (2010). Findings show that the distribution of compounding difference under the constant volatility model is a positively skewed and right heavytailed distribution with no left tail. Under the mean-reverting stochastic volatility model, the distribution is positively skewed and has a light left tail and a heavy right tail. The negative correlation between stock shocks and volatility shocks reduces the range of compounding difference. Under both models, results indicate that the most negative median compounding difference occurs when there is a small positive drift. In addition, an increase in investment horizon widens the range of compounding difference.