Volatility Decay

A Cryptoswap LP position's value scales as $\sqrt{p}$ in the volatile asset price. That shape is concave, which means on any round-trip price move the LP underperforms a linear hold. Wrapping the LP in 2x leverage turns the exponent into one, cancelling the drag at the yb-LP depositor level. The cost of cancelling impermanent loss lives in LEVAMM's rebalancing and crvUSD interest.

Before you read this

This page assumes some background on AMM geometry and leverage. For the basics in one place, see Concepts.

Bonding-curve value functions. Each AMM family has a value-vs-price curve. For constant-product (Uniswap v2), that curve is $\sqrt{p}$ . Sublinearity in price is where impermanent loss comes from.
What compounding leverage means. Debt held as a fixed fraction of collateral value, rebalanced as price moves. See Compounding Leverage.
LVR (loss-versus-rebalancing). The block-by-block dollar cost LPs pay to arbitrageurs as price moves. Covered in the section below.
Why "rebalance cost" differs from "impermanent loss". IL is a property of the bonding curve measured at a single price point. Rebalance cost is the realised slippage paid on the path between prices. IL exists even if no trade has happened; rebalance cost only accumulates when price moves.

Derivations for the $\sqrt{p}$ law, $L=2$ cancellation, and APR decomposition live in Math Primer §1, §2, §4.

Quick answer

If the price of the volatile asset in a Cryptoswap pool moves, an LP token's value moves with it, but not proportionally:

Price up 4x: LP value up 2x, not 4x. Half the upside is forgone.
Price down 4x: LP value down 2x, not 4x. Half the loss is absorbed.
Round-trip back to $p$ : LP value is unchanged in nominal terms; accrued fees leave the LP ahead.

The forgone upside and the absorbed loss are symmetric consequences of the same concavity. The term impermanent loss refers to this underperformance versus a linear hold. It is bonding curve geometry, not a fee, not caused by trades, not removable at the AMM level.

With constant leverage $L$ held in the limit of instantaneous rebalancing, the leveraged value scales as $V^* \propto p^{L/2}$ . At $L = 2$ : linear in price, drag-free against the asset. See Math Primer §2.

Who pays for the cancellation

The drag does not disappear; it is offset by the payoff of the leveraged position, but the leveraged position itself has costs:

Rebalance slippage. Maintaining $L = 2$ requires continuous trades on LEVAMM (initiated by arbitrageurs; see Compounding Leverage). Also, Cryptoswap periodically rebalances its price_scale, which has a cost partially subsidised by donations.
Borrower interest on crvUSD. The leveraged position holds crvUSD debt. Interest accrues on the debt, but it does not subtract from LP value directly. All of it is swept to LT and donated back to Cryptoswap, where it becomes rebalance reserve (see Refueling & Donations). Borrower interest and rebalance-cost offset are a closed loop.

The explicit APR formulas, whitepaper-clean (Eq 4.3 and 4.4) and realised-under-implementation (Eq 4.8), live in Math Primer §4. In summary:

Whitepaper: $\text{APR}_{\text{net}} \approx 2 r_{\text{pool}} - r_{\text{borrow}} - r_{\text{releverage}}$ .
Realised: $\text{APR}_{\text{net}} \approx L \cdot r_{\text{pool,realised}} - (r_{\text{releverage}} - r_{\text{refuel}})$ , where $r_{\text{pool,realised}}$ is reduced by the Cryptoswap 50/50 fee split and $r_{\text{refuel}} \approx r_{\text{borrow}}$ at steady state.

When the net is positive (gross fee capture outpaces residual rebalancing drag after refuel offsets interest), the position earns. When it is not, the drag shows up as slow PPS growth.

Who bears the drag when APR goes negative

Two distinct cases arise, covered in detail under Fee Mechanics and Watermark & Recovery:

Staked LPs absorb it first. Drag reduces the staked bucket value: staked drops below ideal_staked. Forward admin-fee flow then routes to the staked bucket preferentially until parity. This is the "first funds volatility decay and rebalancing loss" step in fee routing. During the drawdown, the staker's compensation is YB emissions. Parity recovery is forward-fee-dependent and can take days to weeks.
Unstaked LPs see the drag as slow PPS growth. Because admin fees route to staked first during recovery, unstaked LPs receive $(1 - f_a) \times$ remainder only after watermark has closed. PPS does not go negative (unstaked only receives positive remainder), but it can grow slowly through an adverse regime.