Leveraged ETF volatility decay, explained with numbers
A 3x ETF delivers three times its index’s return for one day. Over a month or a year, the result can be far more or far less than three times, depending on the path the market takes.
In short
Leveraged ETFs reset their leverage every day. Over longer periods, that daily compounding makes returns depend on volatility: in calm, trending markets a 3x fund can earn more than three times its index, and in choppy markets it can lose money even when the index ends flat. For a 3x fund the drag is roughly three times the variance of the index per year, before fees and financing costs.
How a leveraged ETF works
A 3x leveraged ETF aims to return three times its index’s return for a single day. To do that, it rebalances at the end of every trading day: after a gain it adds exposure, and after a loss it cuts exposure, so that it starts each day at exactly three times leverage again.
That daily reset is what makes a leveraged ETF practical to hold without margin calls. It is also why its long-run return is not simply three times the index’s long-run return.
Two days that show the problem
Suppose an index rises 10% one day and falls 10% the next.
| Index | 3x ETF | |
|---|---|---|
| Start | $100.00 | $100.00 |
| Day 1 | +10% to $110.00 | +30% to $130.00 |
| Day 2 | −10% to $99.00 | −30% to $91.00 |
| Total | −1% | −9% |
The index lost 1%. Three times that is 3%, but the 3x fund lost 9%. Now take a path where the index ends exactly flat: up 10%, then down 9.09%. The index is back at $100. The 3x fund rises to $130, then falls 27.27% to about $94.55, a loss of 5.45% on an unchanged index.
The formula
For a fund that keeps constant leverage L, a standard continuous approximation links its result to the index’s return and volatility:
ln(1 + fund return) ≈ L × ln(1 + index return) − ((L² − L) ÷ 2) × σ² × years
Here σ is the index’s annualized volatility. For a 3x fund, (L² − L) ÷ 2 equals 3, so the drag is about three times the index’s variance each year. For a −3x inverse fund it equals 6, which is why inverse leveraged funds decay even faster.
Here is what that drag means for a 3x fund whose index ends a year exactly flat:
| Index volatility | 3x fund after one flat year, approx. |
|---|---|
| 15%, a calm market | −6.5% |
| 20% | −11.3% |
| 25% | −17.1% |
| 35%, a turbulent market | −30.8% |
The other side: calm trends
Volatility decay is only half the story. When an index rises steadily, daily rebalancing adds exposure into strength, and the fund can earn more than three times the index.
If an index gains 20% in a year with 15% volatility, the formula puts a 3x fund at roughly +62%, more than three times the index. If the index gains the same 20% with 35% volatility, the 3x fund ends up near +20%, no better than the index, with far more risk along the way.
The lesson is that leverage is rewarded by trends that are both strong and orderly, and punished by markets that move a lot without going anywhere.
Volatility decay calculator
Uses the continuous-rebalancing approximation above. It ignores fund expenses, financing costs and the exact day-by-day path, so real results will differ.
What this means for investors
- Holding period matters. Fund sponsors and regulators warn that leveraged ETFs are designed for daily objectives and can diverge sharply from their stated multiple over longer periods.
- Volatility is a cost. Even with no trend at all, a leveraged fund loses value as volatility rises.
- Fees and financing add up. Leveraged ETFs charge higher expense ratios than plain index funds and pay to borrow their extra exposure.
How Levment uses this
Volatility decay is the reason Levment does not hold leverage all the time. Historically, strong uptrends have tended to come with lower volatility, and declines with higher volatility. A trend filter aims to hold leverage in the first kind of market and step aside in the second. Read how the strategy works.
Sources
- Avellaneda, M. and Zhang, S. (2010). “Path-Dependence of Leveraged ETF Returns.” SIAM Journal on Financial Mathematics 1(1).
- Cheng, M. and Madhavan, A. (2009). “The Dynamics of Leveraged and Inverse Exchange-Traded Funds.” Journal of Investment Management 7(4).
- U.S. Securities and Exchange Commission and FINRA. Investor alert, “Leveraged and Inverse ETFs: Specialized Products with Extra Risks for Buy-and-Hold Investors.”
- Calculations by Levment using the approximation shown above.
This article is educational and is not investment, tax or legal advice. Examples are illustrative and are not Levment results.