Understanding the mechanics behind your LP position
Impermanent loss is not a bug — it's a structural property of Automated Market Makers. Every time you provide liquidity to an AMM pool, you accept a specific payoff profile that differs from simply holding. The five charts below break down the mathematics, the geometry, and the capital dynamics so you can enter positions with full clarity. All charts are interactive — drag the sliders to model real scenarios.
What is the constant product curve?
Every Uniswap V2-style pool enforces a single invariant: the product of the two token reserves must remain constant — x · y = k. This constraint creates a hyperbola. As traders buy Token A, the pool's A reserve decreases and B reserve increases — moving the price along the curve.
When you deposit liquidity, you enter at a specific point on this curve. If prices change, the AMM automatically rebalances your holdings by moving your position along the hyperbola to the new price point.
Where does impermanent loss come from?
If you had simply held your tokens instead of providing liquidity, your portfolio would move along a straight tangent line — not the curve. The dashed green line shows this HODL trajectory. The red shaded area between the two paths is impermanent loss: value you gave up to the arbitrageurs who kept the pool price accurate.
Use the slider to shift the price ratio and observe how the gap widens. IL is always zero at the original entry price, and grows with any price divergence in either direction.
Reading the IL curve
The IL formula is IL = 1 − 2√r / (1+r) where r is the final-to-initial price ratio. The curve is symmetric around the entry price and accelerates non-linearly at extremes.
The three colored bands act as a practical decision grid. If your expected price range sits mostly in the green zone (below 5% IL), fee APR can realistically offset it. The amber zone (5–20%) demands high-fee pools or short durations. The red zone (above 20%) requires exceptional fee yields or a deliberate directional view to be viable.
The concavity cost of liquidity provision
The HODL value is linear in price — it rises or falls proportionally. The LP value follows a square-root curve — it captures gains more slowly in bull markets and loses value faster in bear markets. This asymmetry is a fundamental structural disadvantage of LPing vs holding.
The red shaded gap between the two curves represents your impermanent loss in dollar terms at any given price. The gap is always zero at the original entry price and widens in both directions. Fees earned must exceed this gap over your holding period to make the LP position worthwhile.
How V3 concentrates your capital
Uniswap V3 lets LPs select a specific price band instead of providing liquidity across the entire 0→∞ curve. The highlighted blue segment of the hyperbola is where your capital is deployed — only this section of the curve is active, earning trading fees whenever the market price is within range.
The trade-off is severe: if the market price exits your range, fee accrual immediately stops, and your position becomes 100% denominated in the cheaper token. A tighter range delivers higher capital efficiency (more fees per dollar) but dramatically higher exposure to this out-of-range risk.
Capital efficiency in practice
This chart shows how much trading depth (protection against price impact) exists at each price tick. In Uniswap V2, every dollar of liquidity is spread uniformly across all possible prices from zero to infinity — most of it sitting uselessly at price levels that are never traded.
V3 lets LPs stack all their capital near the current price. The result is 5–100× more depth near the active market price — and therefore 5–100× more fees earned per dollar of capital. The flip side: those concentrated LPs also absorb 5–100× more impermanent loss when price moves significantly. This is the central V3 risk/reward trade-off every LP must understand before deploying capital.
| Component | Token A Qty | Token A Value | Token B Qty | Token B Value | Total Value |
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