Record for Tracking Errors and Volatility in Different Types of Leveraged ETF

The purpose of this work is to identify tracking errors on different investment horizons and modeling the volatility of commodity Leveraged Exchange Traded Funds (LETF). The subject of the study are 25 ETFs that track and multiply returns of silver, gold, WTI crude oil, natural gas, as well as the oil and gas sector and the basic material industry. Tracking errors were measured using regression analysis. Several mathematical and statistical approaches were also applied. Volatility modeling was performed using the ARMA-GARCH econometric model. The study was carried out between January 2007 and April 2019. It was found that, on average, with the growth of the investment horizon, the tracking error increases. Statistical analysis showed that the most optimal period of investing in LETF, in which the shift from the target level is negligible – one week. It is important to note that funds that track indices on futures contracts allow for higher divergences than funds which follow industry indices. Simulation of the annual volatility of the LETF showed that its growth increases the probability of tracking errors in LETF. It was also found that the risks of LETF exceed the risks of the respective benchmarks approximately in proportion to their leverage.