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Hedge LVR

Size variance units against an LP's expected loss-versus-rebalancing.

Loss-versus-rebalancing is the cost a constant-product LP pays for being arbitraged as the price moves. It is proportional to realized variance, which is exactly what a Tremor receipt pays.

The formula

For a constant-product position of value V over a horizon T (in years), with annualized vol σ:

E[LVR] ≈ V · σ² · T / 8

(Milionis, Moallemi, Roughgarden, Zhang). A receipt unit pays realized variance over its own fixed window, capped at capVariance. The following is a coarse gross sizing estimate, not replication:

hedgeUnits = (V · T / 8) / unitNotional

Both V · T / 8 and unitNotional are in USD, so the result is in receipt units. The Lens exposes the same calculation as lvrHedgeUnits(id, poolValueUsdc, horizonSeconds), and the backend serves it at GET /lvr.

In the app (/hedge)

  1. Enter pool value and horizon in days.
  2. Pick a vol source: trailing 1d / 7d / 30d realized (from the backend's Chainlink cache) or a custom vol.
  3. Read Expected LVR and the hedge notional V · T / 8.
  4. For every series with issuance open the table shows the market's quote volatility, the hedge units and the on-chain quote for that exact size as a share of the pool. Buy opens the series with ?units= pre-filled.

The allocation card shows the vol used as a share of 100% and, for each live series, how much of the remaining inventory the hedge would take.

Exact bigint math used by the UI

expectedLvr = poolUsdc · variance · horizonSec / (8 · 31_536_000 · 1e18)          USDC (6 dec)
units       = poolUsdc · horizonSec · 1e18 / (8 · 31_536_000 · unitNotional)     receipt units (18 dec)

Caveats

  • Payout is capped at capVariance; if σ ≫ cap the hedge under-pays.
  • Cost uses the on-chain integral quote, including the price impact of your own size — a large hedge moves the market's forward variance, and you pay the integral, not the opening ask.
  • The estimate is for a full-range constant-product position. Concentrated liquidity, fees, inventory, path timing and pool-specific arbitrage all change realized LP economics.
  • Series window and hedge horizon must align; otherwise basis risk remains.
  • Premium, the payout cap and available depth can dominate the gross estimate.
  • Sold units are fully collateralized, so writer default is not on this list — but the cap still truncates the tail, and that truncation is exactly where an LVR shock hurts most.