Accounting for Volatility Decay in Time Series Models for Leveraged Exchange Traded Funds

Abstract

Leverage Exchange Traded Funds (LETF's) returns tend to deviate from their underlying assets' multiple returns as their holding period increase, a phenomenon known as volatility decay. Algebraically, it is shown that volatility decay is intensified for inverse leveraged funds and as the leverage multiplier increases. The paper uses a novel approach to account for volatility decay. The ARIMA model ability to forecast future returns is tested for three major indexes and is shown to provide more accurate estimates for S&P500. The returns of S&P500 and its corresponding LETFs are fitted to an Autoregressive Integrated Moving Average (ARIMA) model. Theoretically, the constant of the ARIMA model and the variance of their Gaussian errors captures the volatility decay effect. Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models provide more flexibility in modeling conditional variance that is non-stationary. The theoretical results are verified empirically, and the constant of the fitted model captures the intensity of the decay and its direction.