Decay across leverage
The same underlying, held daily-rebalanced at each leverage. Excess drag is what you lose beyond simply multiplying the spot's own compound return by the leverage — it grows with L×(L−1), so it accelerates fast.
| Leverage | Excess drag/yr | Expected CAGR | After horizon |
|---|
Leverage is a trend tool, not a hold tool
The reason a 3× token bleeds in a flat market is pure math: leverage triples the drift but multiplies the variance drag by nine, so the decay outruns the reward unless the trend is strong and steady. The break-even drift — about half the leverage times the variance — is the minimum trend the underlying needs just to offset the drag. Below it, a smaller unlevered position beats the leveraged one. Measure the underlying's real volatility on the volatility calculator, size the raw position on the leverage calculator, add the periodic funding cost that a real perp charges on top of this drag, and check how close a leveraged hold sits to liquidation.
The math
With annualized drift μ and volatility σ, an asset's compound (geometric) growth is μ − σ²⁄2 — the σ²⁄2 term is volatility drag. A constant-leverage position rebalanced daily has an exposure of L×, so its expected log-growth is L·μ − L²·σ²⁄2: the drift scales with L, but the drag scales with L².
A naive holder expects the leveraged product to return L× the spot's own compound return, L·(μ − σ²⁄2) = L·μ − L·σ²⁄2. The gap between that and what it really grows at is the excess drag = ½·σ²·L·(L−1) — zero at 1×, and rising fast with leverage. The break-even drift, where the leveraged growth turns positive, is μ* = ½·L·σ².
Over N days the expected value is start × e^(g·N⁄365) with g = L·μ − L²·σ²⁄2. This models the drag from daily rebalancing only — fees, funding on a perp, and the discreteness of real resets add more. It is an expectation, not a guarantee: a strong sustained trend can still make leverage pay, which is exactly the trade-off the numbers make visible.