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Volatility decay

A yb-LP position keeps full price exposure to BTC or ETH. A yb-LP share is a claim on a Curve Cryptoswap pool position held at 2× leverage. LEVAMM, the market's leveraged automated market maker, holds that pool position and owes crvUSD debt against it. The position pays borrow interest on that debt. To stay at 2× leverage as the price moves, it also pays a rebalancing cost to arbitrageurs.

Volatility decay is the YieldBasis name for the net rebalancing cost that LEVAMM pays to arbitrageurs as the price moves, partly offset by refueling. Refueling is the donation of borrower interest to the Curve pool. The sections below show where the cost comes from, compare volatility decay with impermanent loss (IL) and loss-versus-rebalancing (LVR), and show who bears the cost when costs exceed fee income.

LP value after a price move​

If the volatile asset's price quadruples, a Cryptoswap liquidity provider (LP) position only doubles in value. The position's value scales as p\sqrt{p} in the volatile asset price. That shape is concave, so the position underperforms a hold when the price moves.

An LP token's value moves with the price, but not proportionally:

  • Price up 4×: LP value up 2×, not 4×. The LP gives up half the upside.
  • Price down 4×: LP value down 2×, not 4×. The LP absorbs only half the loss.
  • Round-trip back to pp: LP value is unchanged in nominal terms. Accrued fees leave the LP ahead.

The forgone upside and the absorbed loss come from the same concave LP value curve. For the derivation of the p\sqrt{p} law (Eq 1.6 to 1.9), read Constant-product LP value in Math primer.

How 2× leverage straightens the curve​

Suppose the protocol holds constant leverage LL and rebalances instantly. Then V∗V^*, the value of the leveraged position, scales as V∗∝pL/2V^* \propto p^{L/2}. At L=2L = 2, the value is linear in price, like holding the asset. So a 2× leverage wrapper turns the exponent into one, and a yb-LP share keeps full price exposure to BTC or ETH, up and down. For the derivation of the L=2L = 2 case (Eq 2.5 to 2.7), read Compounding leverage in Math primer.

Who pays for the straight curve​

The concave LP value curve stays in the pool. The leveraged position offsets it and pays two costs. It pays a rebalancing cost to the arbitrageurs who keep it at L=2L = 2. It also pays borrow interest on its crvUSD debt.

LT, the market's vault contract, donates the borrower interest to the Curve pool as refueling. There, the interest funds moves of price_scale, the pool's internal price, so borrower interest and rebalancing form a closed loop. For each cost and who receives it, read What you pay in Compounding leverage.

Volatility decay, impermanent loss, and loss-versus-rebalancing​

Three related terms describe LP underperformance at different layers:

  • Impermanent loss (IL). The shortfall of the LP position compared with holding the deposited assets. The concave LP value curve causes it. IL exists when price moves away from the start, whether or not any trade has occurred.
  • Loss-versus-rebalancing (LVR). The cost of the arbitrage trades that rebalance the pool as price moves. LVR depends on the price path. In classic models, it scales with σ2⋅t\sigma^2 \cdot t, where σ\sigma is the volatility of the price and tt is the elapsed time. It is the dollar amount that LPs pay to arbitrageurs block by block.
  • Volatility decay in YieldBasis. Closest in meaning to LVR. It is the net rebalance cost that LEVAMM pays to arbitrageurs as price moves. The refueling subsidy from crvUSD borrower interest offsets part of it.

Net return of the position​

The model's net annual percentage rate (APR) for an unstaked yb-LP position is a simple yearly rate. It is the fee income of the 2× position minus its costs. The whitepaper form (Eq 4.3 and 4.4) subtracts borrow interest and the rebalancing cost. The realized form (Eq 4.8) starts from the fee income left after the pool's profit split (Eq 4.6). It then subtracts the rebalancing cost left after refueling.

The position earns when gross fee income is larger than the rebalancing drag that remains after refueling. The measured rate is Fundamental yield: Fundamental Value growth of unstaked yb-LP over a trailing 7-day or 30-day window, compounded. Fundamental Value is the value of one yb-LP share on the vault's books. For each rate symbol and the full equations, read Net APR and cost terms in Math primer.

Losses when costs exceed fees​

The position loses value in any period when the rebalancing cost left after refueling exceeds fee income. The net APR of Eq (4.8) is then negative for that period.

The following example uses the canonical position: 1 cbBTC deposited at a BTC price of $100,000. In one volatile week, the rebalancing cost left after refueling exceeds the week's fees by $100. The position loses 0.1% ($100 / $100,000). Compounded like Fundamental yield, a trailing 7-day window annualizes this loss to about −5.1%: (1 − 0.001)^(365/7) − 1. A trailing 30-day window that holds the loss week, with no gain or loss on its other days, shows about −1.2%: (1 − 0.001)^(365/30) − 1. Neither number predicts the next year.

How LT shares a loss​

LT splits a loss pro rata by balance between the staked and unstaked sides. After losses, a staked position can sit below its watermark. While the gauge holds at least 0.01 yb-LP (MIN_STAKED_FOR_FEES), LT charges no admin fee until gains close the gap. YB emissions are the staker's compensation during the drawdown. Recovery depends on future fee income, so the recovery time varies. Unstaked LPs see the loss as slow or negative Fundamental Value growth.

For the equations, including the small-stake case, read Admin-fee curve and staked accounting in Math primer (Eq 5.2a to 5.6). For how the watermark shortfall opens and closes, read Watermark and recovery.