Beyond Volatility Decay: Correcting Relative Expected Return Estimates for Leveraged Exchange Traded Funds

Leveraged exchange traded funds (LETFs) magnifying popular index daily returns by up to +/- 3.0x are often assumed to belong in the domain of sophisticated traders with short-term horizons. Despite this, eight of the top ten performing funds over the last 10 years are LETFs. This study shows why the standard method used to calculate LETF long-run expected returns relative to an underlying index produces estimates that significantly deviate from realized returns given a particular index return and standard deviation. A statistically exact equation is derived which demonstrates how current methods lead to underestimating LETF expected returns by over one hundred percentage points annually for bullish LETFs during high return/high volatility environments and equally overstate bearish LETFs performance during negative return/low volatility environments. This new method is then applied to monthly and quarterly reset LETFs showing they outperform daily LETFs in average to high volatility environments while daily LETFs tend to outperform in high return low volatility environments.