Published
Say BTC goes up 20% and then comes straight back down to the exact price it started at. Net move: zero. Now model a daily-reset 3x leveraged BTC token through the same two days. Day one, the token compounds 3x of a +20% move: a 1.60 multiplier. Day two, the token compounds 3x of whatever percentage move brings BTC back to its starting price — which isn't -20%, it's -16.67%, because a bigger base needs a smaller percentage to reverse it. 3x of -16.67% is a 0.50 multiplier. Multiply the two days together: 1.60 x 0.50 = 0.80. The token is down 20%. On a round-trip. To the exact same underlying price.
The mismatch that causes it
A daily-reset leveraged token doesn't track a fixed multiple of the underlying's total price change — it tracks a fixed multiple of each day's percentage return, then compounds those days together. And a percentage up-move and the percentage down-move that reverses it are never equal in size. Going from $100 to $120 is +20%. Going from $120 back to $100 is only -16.67%. That asymmetry gets multiplied by leverage on both sides, and the product lands below 1.0 no matter which direction you check it from. This is pure math, not an exchange fee or a funding cost — it would happen even with zero trading costs, on a chain with free transactions.
Same round-trip, five leverage levels
I held the round-trip size fixed at +20% / back-to-even and only changed the leverage multiplier on the token:
| Leverage | Day 1 factor | Day 2 factor | Round-trip result |
|---|---|---|---|
| 1x (spot) | 1.2000 | 0.8333 | 0.00% |
| 2x | 1.4000 | 0.6667 | -6.67% |
| 3x | 1.6000 | 0.5000 | -20.00% |
| 5x | 2.0000 | 0.1667 | -66.67% |
| 10x | 3.0000 | wiped out mid-day | fund = $0 |
At 3x, the round-trip's own size (20%) and the decay it causes (20%) happen to match — that's a coincidence of this particular number, not a rule. What isn't a coincidence is the direction: every leverage level above 1x bleeds on this round-trip, and the bleed accelerates faster than the leverage multiplier does. Going from 3x to 5x is a 1.67x increase in leverage, but the decay goes from 20% to 66.67% — a 3.3x increase in damage. At 10x, day two's required -16.67% move, multiplied by 10, is a -166.7% day — the token's value formula goes negative before the day is even over, which in practice means the fund is liquidated and reset to zero well before BTC finishes its round-trip.
Same 3x leverage, four round-trip sizes
Leverage isn't the only variable. I held leverage fixed at 3x and changed how big the round-trip itself was:
| Round-trip size | Required reversal | 3x token result |
|---|---|---|
| +5% | -4.76% | -1.43% |
| +10% | -9.09% | -5.45% |
| +20% | -16.67% | -20.00% |
| +40% | -28.57% | -68.57% |
Doubling the round-trip from 5% to 10% roughly quadruples the decay (-1.43% to -5.45%). Doubling it again from 20% to 40% more than triples it (-20% to -68.57%). Decay scales close to the square of how far the underlying swings — which is exactly why leveraged tokens are marketed as day-trading instruments and exchanges plaster "not for holding" warnings on them, and exactly why the ones that survive as products cap out around 3x-5x. Every extra unit of choppy, directionless volatility is quietly worth more than it looks, and none of it shows up if you only check the underlying's price chart.
None of this requires the token issuer to be doing anything wrong — the daily rebalancing is disclosed, and it's the only way to keep the leverage ratio constant day over day. It just means "3x BTC, held for a month of chop" is a materially different bet than "3x BTC, held for one clean trending day," even when the underlying ends up at the exact same price in both scenarios. Run your own leverage and volatility assumptions through the leveraged token decay calculator — same compounding math, any round-trip size you want to test.