Loss-Versus-Rebalancing (LVR)

An AMM pool holds two assets and prices them by a formula, not by watching the outside market. When the outside price moves, the pool's price doesn't move with it until someone trades against it — and the first trader to show up is almost always an arbitrageur, buying whatever the pool is now underpricing and selling whatever it's overpricing, pocketing the difference. LVR is the metric that quantifies exactly that leak: the value an arbitrageur extracts by trading against a pool that's stale relative to the true market price.

Why it's a cleaner number than impermanent loss

Impermanent loss compares an LP position to simply holding the two assets — but that comparison mixes together ordinary price risk (which the LP knowingly took on) with the specific cost of being picked off by arbitrageurs. LVR isolates just the second piece: it assumes a benchmark portfolio that rebalances perfectly and instantly with the market, with no trading cost, so any gap left over is purely the toll arbitrageurs extract because the pool can only react to a price change after someone trades against it, never before.

Worked example

An ETH/USDC pool holds $1 million split 50/50 when ETH is $2,000. ETH's true market price jumps to $2,100 on outside exchanges. Before the pool's price adjusts, an arbitrageur buys ETH from the pool at the stale, cheaper price implied by the pool's formula — say the pool ends up selling ETH at an average effective price of $2,050 across the trade, $50 below the new market price of $2,100.

If the arbitrageur buys 5 ETH this way, they capture roughly 5 \times (2100 - 2050) = \250 of value that came directly out of the pool's assets — that \250 (scaled up across every such price move over a day, week, or month) accumulates into the pool's total LVR. A continuously-rebalancing benchmark portfolio, by contrast, would have already been holding fewer ETH by the time the price hit $2,100, and would not have handed that $250 to anyone.

What this means in practice

LVR gives LPs and protocol designers a rate — often expressed as an annualized percentage of pool value — that can be compared directly against the fee income the pool earns, making it possible to ask a concrete question: is this pool's fee tier high enough to compensate for the arbitrage toll it's paying, given the asset's volatility?