LETFs: Strategy to Harvest Decay
[WITH CODE] Backtesting a strategy to capture the intrinsic decay in leveraged ETFs
Reviewed and updated 20 July 2026
Hello!
Welcome back. Today, we will be building off of the concepts and research in the last post.
We will cover the sources of return for our strategy, potential filters to use in the strategy, and an initial historical iteration of the strategy.
We will likely have a third post on this topic, due to the interest from paid subscribers. A research companion is now included below for paid members.
Let’s get into it.
Volatility Decay Recap
Our first post establishes the mathematical foundation for understanding volatility decay and optimal leverage in the U.S. equity markets. It begins by distinguishing between Arithmetic Mean (simple average) and Geometric Growth (compounded wealth), noting that while statistical models often prefer the former, investors care about the latter.
I used the second-order approximation ln(1+x) ≈ x - x²/2 to connect simple returns with compounded growth. For small returns, expected log growth is approximately the arithmetic mean minus half the second raw moment; the familiar mean-minus-half-variance expression also treats the squared mean as negligible. Extending that framework to leverage produces an idealized quadratic growth function. One set of historical inputs gave an illustrative unconstrained optimum of about 2.13x, not a forecast or leverage recommendation.
I also shared a research paper that covered a simple, high-Sharpe strategy to harvest this decay.
Implications of Kurtosis and Skew
In the previous post, I made a convenient approximation: treating returns as normally distributed. Black–Scholes assumes normally distributed continuously compounded returns under its model, not normally distributed simple returns. Real equity returns also show skewness, fat tails, volatility clustering, and jumps, so the normal approximation can understate extreme-move risk.
To extend the leverage approximation beyond its first two terms, we can include the third and fourth raw moments, which are related to skewness and kurtosis. In the last post, I stopped after the second-order term to focus on the core concepts of volatility decay and LETF behavior.
When we retain the next two terms, the approximation becomes:
Skewness measures the asymmetry of returns. While a normal distribution has zero skew, equity returns often exhibit negative skew, meaning large downside moves are more pronounced than large upside moves. In the Taylor expansion, the cubic raw-moment term enters with a positive coefficient; when that third moment is negative, it lowers the approximation, all else equal.
Kurtosis describes tail weight. Equity returns are often leptokurtic, with more extreme observations than a normal model predicts. The fourth raw-moment term is subtracted in the truncated expansion, although fat tails also make a low-order Taylor approximation less reliable for large moves.
These higher-order terms scale nonlinearly when leverage is applied.
If x is replaced by fx in the truncated series, its second-, third-, and fourth-order terms scale with f², f³, and f⁴. At 3x leverage, those coefficients are multiplied by 9, 27, and 81. That is a property of the approximation, not a literal claim that every dimension of risk is multiplied by those amounts; large moves, fees, financing, tracking, and insolvency constraints also matter.
This is one reason a low-order optimal-leverage calculation can overstate usable leverage. Gap risk, financing, trading costs, tracking differences, and investor constraints can reduce it further.
Autocorrelation
Many simple volatility models approximate returns as independent, meaning yesterday’s return provides no information about today’s. Real markets can depart from that assumption.
Under independent, identically distributed returns, variance scales linearly with time. When returns are correlated with their past values, that scaling changes. This dependence is called autocorrelation.
Positive autocorrelation means returns tend to persist in the same direction. For a given set of one-period moves, a more directional path can be friendlier to daily-reset leverage than frequent reversals, but positive autocorrelation does not automatically mean lower risk.
Daily-reset leveraged ETFs can perform well during steady, low-volatility advances because directional gains can outweigh financing, fees, tracking differences, and compounding drag. The result still depends on the exact path.
Negative autocorrelation means returns tend to reverse. Back-and-forth paths can worsen the compounding drag of a daily-reset leveraged fund as it rebalances to maintain target exposure.
This can make path dependence more costly than an independent-return approximation suggests. The 2022 experience also combined falling prices, changing rates, and high volatility, so it is not a clean autocorrelation experiment.
LETF Swap Costs
Lastly, we need to cover the costs of setting up and managing LETFs. Many US leveraged equity ETFs obtain part of their exposure through total return swaps. The financing embedded in those swaps is one cost alongside the expense ratio, trading frictions, and tracking differences; the exact mix varies by fund and over time.
That financing component is generally smaller when short-term rates are near zero and more material when rates are high, although the actual drag depends on swap terms and spreads.
Financing, fees, and tracking differences create a hurdle that the leveraged exposure must overcome before the ETF earns a positive return.
Swap-based bull and bear funds can have different financing and collateral economics. The cited working paper reports that these non-compounding effects were positive for the US bull-side short hedge and negative for the corresponding bear-side hedge in its sample.
A short bull-LETF hedge may benefit from both compounding drag and financing-related underperformance, but it also bears borrow, margin, tracking, and tail risk.
Interest-rate conditions can affect the non-compounding return captured by a short US bull-LETF hedge. During the article’s 2022–2025 test window, the paper’s mechanism is one possible tailwind, not a separately identified effect in this backtest. Let’s dive into the backtested strategy.
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