Leveraged ETF Decay: Why 3x Isn't 3x Over Time

Leveraged ETF decay is the loss a 2x or 3x fund suffers when its index moves up and down, even if the index ends where it started. It happens because these funds reset their leverage every day, so gains and losses compound on a changing base. The more the index swings and the higher the leverage, the bigger the decay, which is why 3x funds rarely deliver three times the index over months or years.

Below, we show the arithmetic step by step, give a rule of thumb for estimating the drag, and explain when decay helps instead of hurts.

Where decay comes from

A leveraged ETF promises a multiple of the index's return for one day. To keep that promise every day, it has to adjust its exposure at each close. If the fund is worth $100 and wants 3x exposure, it holds $300 of index exposure. If the index rises 10%, the exposure gains $30 and the fund is worth $130, so it raises exposure to $390. If the index then falls 10%, it loses $39 and ends at $91.

The index, over those two days, went from 100 to 110 to 99. It lost 1%. The fund lost 9%, not 3%.

The problem is not the fund's management. It is the order of operations. Percentage losses come off a bigger base after a gain, and percentage gains apply to a smaller base after a loss. Ordinary investments face this too: a 10% gain and a 10% loss leave any investment 1% down. Leverage multiplies the size of each move, and because the shortfall grows roughly with the square of the move, tripling the moves makes it about nine times larger.

Decay in numbers: four scenarios

All four examples below are made-up price paths, chosen to show the effect. They ignore fees and financing costs, which would make the leveraged results slightly worse.

The first two rows show pure decay. The index barely moved, yet the 3x fund lost roughly eight to nine times as much as the index did. The inverse fund suffered exactly the same decay, because a swinging market hurts both directions equally.

The third and fourth rows show the other side. In a smooth trend with small daily moves, the 3x fund did better than three times the index. Over 10 days of +1%, three times the index result would be about +31%, and the 3x fund made +34%. Compounding worked in its favour, and the same happened to the inverse fund in the falling trend.

So decay is not a fixed tax. It is a penalty for volatility and a bonus for steady trends. The trouble is that real markets spend much of their time in the choppy middle, and the biggest moves tend to come in clusters of wild up and down days.

A rule of thumb for estimating the drag

There is a well-known approximation for how much a daily-reset fund lags its target over a period. Ignoring fees, the drag is roughly:

drag ≈ (L × L − L) ÷ 2 × variance of the index over the period

Here L is the leverage multiple, and variance is the square of the index's volatility over that period. You do not need to calculate it precisely to learn from it. Plug in a few leverage values and the pattern is clear:

Two lessons come out of this table. First, going from 2x to 3x does not add 50% more drag; it triples it. Second, inverse funds carry more drag than long funds of the same size, so a -3x fund suffers the most of all.

As an example of the formula in use, take an index whose yearly volatility is 20%, which is in the range broad stock indexes have shown in ordinary years. Its yearly variance is 0.2 × 0.2 = 0.04. For a 3x fund the drag is about 3 × 0.04 = 12% a year, before fees. If volatility rises to 40% in a stressed year, the variance quadruples to 0.16 and the drag jumps to roughly 48% a year. That is an illustration of the formula, not a forecast, but it shows why leveraged funds can melt in turbulent markets even without a big net move.

Fees and financing add to the drag

Decay is the mathematical part. There are also plain costs. Leveraged ETFs charge expense ratios close to 1% a year, much more than plain index funds. They also pay financing on the swaps they use to get extra exposure, and that cost rises with interest rates. In a year when short-term rates are high, the financing cost alone can be several percentage points of the extra exposure.

These costs matter less for someone holding a fund for a week and a lot more for someone holding it for years. Together with volatility decay, they explain why long-term charts of many leveraged funds slope downward even when their index has risen, and why inverse leveraged funds in particular have lost most of their value over long periods.

Why leveraged funds are not safe to hold long term

Put the pieces together and the picture is clear:

• In calm, rising markets, a 3x fund can do better than three times the index.
• In volatile, sideways markets, it slowly bleeds even if the index goes nowhere.
• In crashes, it falls fast, and the decay during the rebound makes recovery harder still.
• Costs are deducted every day regardless.

Nobody can reliably know in advance which kind of market the next year will be. Holding a leveraged fund for years is therefore a bet that calm trends will dominate, with a real chance of losing most of the money if they do not. Our explainer on TQQQ shows what that looked like for one popular 3x fund in 2022.

How rule-based strategies deal with decay

Because decay depends on volatility, many rule-based strategies use leveraged funds only for limited windows and leave when conditions change. Some hold them when volatility is low and trends are steady. Others do something riskier: buy leveraged funds right after a sharp fall, betting on a fast rebound, and accept that if the rebound does not come, decay and further falls will hurt badly.

Our Market Switch strategy does a version of the second. It holds SPY when nothing unusual is happening, switches to UVXY (a volatility fund) when many markets look overheated, and switches to leveraged funds after sharp falls, expecting a rebound. In a historical backtest from November 2011 to November 2026 it returned +71.9% a year with a worst fall of 42%. Over the same period the S&P 500 (SPY) returned +15.0% a year with a worst fall of 34%, and the Nasdaq 100 (QQQ) returned +19.2% a year with a worst fall of 35%. Its deepest fall ran from March 9 to March 24, 2020, and it recovered by June 11, 2020, about 3 months after the bottom.

This was a computer test on past prices. Nobody earned it, and future results will differ. Its caveat is serious: nearly half of its tested profit came from UVXY, and it failed outside the US.

The longer history is even more sobering. In a simulated three-fund version run through the 2007-2009 financial crisis, the historical backtest fell 96%, compared with 55% for the S&P 500, and took 73 months to return to its pre-crash value against 53 months for the index. That is what leverage plus decay can do when a crisis keeps going instead of bouncing. You can read more about how these numbers are calculated in our guide to max drawdown.

How to check decay yourself

You do not need special software to see decay. Three simple checks work for any leveraged fund:

1. Compare multi-month returns. Look up the index's return over the last six months and multiply by the leverage. Then look up the fund's actual return. The gap, after allowing for fees, is mostly decay or trend bonus.
2. Look at volatile months. Pick a month when the index ended roughly flat but had big daily moves. The leveraged fund will usually be down.
3. Watch it on paper. Follow a leveraged fund in a paper trading account for a few weeks of choppy trading and compare it with three times the index's move. Seeing it happen in real prices makes the arithmetic stick.

Key takeaways

• Leveraged ETF decay is the shortfall caused by daily resets when an index swings up and down; it is a property of the maths, not a fund error.
• The drag grows with volatility and grows much faster than leverage. Going from 2x to 3x roughly triples it, and -3x funds carry the most.
• Smooth trends can produce better than 3x results, so decay is a penalty for choppiness rather than a fixed fee.
• Fees and swap financing add a steady extra cost, which matters most for long holding periods.
• Leveraged and inverse funds are not designed to be held for years, and strategies that use them, even with rules, can suffer very deep historical falls.

This article is general education, not personal advice.

See decay in real prices, on paper

The quickest way to understand decay is to watch it. AlgolaneBots lets you run all five strategies, including ones that hold leveraged funds, on a $10,000 paper account during a free 90-day trial with no card required. Sign up and start on paper, and compare what the funds do with what the index did.