A Levered ETF Anomaly Explained

Battle Count: 56

Highly relevant for any quantitative strategy involving levered ETFs. The decomposition provides a clear framework for understanding why daily-rebalanced levered ETFs underperform over long horizons beyond simple volatility drag. The covariance term is a novel and practically important component that must be estimated for accurate forecasting. Directly applicable to portfolio construction, risk budgeting, and the decision of whether to hold levered ETFs for multi-day/multi-month horizons. Less relevant for pure ML-based trading models but critical for any strategy that uses levered ETFs as building blocks.

The core methodology is straightforward: compute daily returns, form return ratios (ETF return / index return), estimate arithmetic mean and volatility, apply the Taylor approximation formula, and compute the covariance between return ratio and index return. All calculations are basic statistics and arithmetic. The main practical challenge is obtaining clean daily price-based return data for the ETFs and index. No complex optimization, model fitting, or programming beyond basic data manipulation is required.

The mathematical framework (Formula 1, covariance decomposition) is fully specified and derivable. However, the empirical analysis relies on CRSP daily ETF return data, which requires a subscription. The specific time window (Jan 3, 2022 – Dec 29, 2023) and tickers (VOO, SSO, UPRO) are clearly stated. Appendix C provides the full derivation of the geometric-arithmetic approximation. Winsorization procedure is described but the exact implementation details are minimal.