DeFi AMM Impermanent Loss (x*y=k) & Oracle Deviation Calculator (2026)

If the relative price ratio between Token A and Token B changes by a factor of `r = (P_A_new / P_A_initial) / (P_B_new / P_B_initial)`, the percentage Impermanent Loss relative to simply holding the initial 50/50 tokens in your wallet is: `IL(r) = (2 × √r) / (1 + r) - 1`. For example, if one token doubles in price (`r = 2.0`) or halves (`r = 0.5`), `IL = (2 × 1.4142) / 3 - 1 = -5.72%`.

In a Constant Product AMM (`x × y = k`), arbitrageurs continuously buy the appreciating token from the pool and sell the depreciating token into the pool until the pool's marginal ratio `y / x` matches the external market price. Whether Token A rises `2x` relative to Token B (`r = 2`) or Token B rises `2x` relative to Token A (`r = 1/2`), the geometric mean vs arithmetic mean divergence `(2√r)/(1+r) - 1` is identical (`-5.72%`).

**Push Oracles (e.g., Chainlink Data Feeds)** push on-chain updates whenever off-chain price moves beyond a **Deviation Threshold** (such as `0.5%` on ETH/USD) OR when a maximum **Heartbeat** timer expires (such as `3,600 seconds`). **Pull Oracles (e.g., Pyth Network / Chainlink Data Streams)** stream sub-second signed prices off-chain and require the user's transaction to bundle and verify the latest cryptographic price update on-demand right before executing a swap or liquidation.

Reading the spot ratio of an AMM pool inside a single block can be manipulated at near-zero capital cost using a **Flash Loan**: an attacker borrows `$50M` in a single atomic transaction, swaps it into the AMM pool to skew the spot price by 900%, borrows all assets from the victim lending protocol against artificially inflated collateral, and repays the flash loan in the same block. Oracles must use decentralized multi-exchange aggregation or manipulation-resistant TWAPs.

While traditional Impermanent Loss compares an LP position only against the start and end prices (ignoring path dependency), **Loss-Versus-Rebalancing (LVR)** measures the cumulative arbitrage profit extracted by informed MEV searchers every time external CEX prices move before the on-chain AMM pool updates (`LVR ≈ σ² / 8` per unit of variance).