Simulation of Leveraged ETF Volatility Using Nonparametric Density Estimation

Abstract

Leveraged Exchange Traded Funds (LETFs) are constructed to provide the indicated leverage multiple of the daily total return on an underlying index. LETFs may perform as expected on a daily basis; however, fund issuers state that there is no guarantee of achieving the multiple of the index return over longer time horizons. LETF returns are extremely volatile and funds frequently underperform their target for horizons greater than one month. In this paper, we contribute two nonparametric simulation methods for analyzing LETF return volatility and how this is related to the underlying index. First, to overcome the limited history of LETF returns data, we propose a method for simulating implied LETF tracking errors while still accounting for their dependence on underlying index returns. This allows for the incorporation of the complete history of index returns in an LETF returns model. Second, to isolate the effects of daily, leveraged compounding on LETF volatility, we propose an innovative method for simulating daily index returns with a chosen constraint on the multi-day period return. By controlling for the performance of the underlying index, the range of volatilities observed in a simulated sample can be attributed to compounding with leverage and the presence of tracking errors. Our nonparametric methods are flexible-easily incorporating any chosen number of days, leverage ratios, or period return constraints, and can be used in combination or separately to model any quantity of interest derived from daily LETF returns.