Compounding Effects in Leveraged ETFs: Beyond the Volatility Drag Paradigm

A common belief is that leveraged ETFs (LETFs) suffer long-term performance decay due to \emph{volatility drag}. We show that this view is incomplete: LETF performance depends fundamentally on return autocorrelation and return dynamics. In markets with independent returns, LETFs exhibit positive expected compounding effects on their target multiples. In serially correlated markets, trends enhance returns, while mean reversion induces underperformance. With a unified framework incorporating AR(1) and AR-GARCH models, continuous-time regime switching, and flexible rebalancing frequencies, we demonstrate that return dynamics -- including return autocorrelation, volatility clustering, and regime persistence -- determine whether LETFs outperform or underperform their targets. Empirically, using about 20 years of SPDR S\&P~500 ETF and Nasdaq-100 ETF data, we confirm these theoretical predictions. Daily-rebalanced LETFs enhance returns in momentum-driven markets, whereas infrequent rebalancing mitigates losses in mean-reverting regimes.