> For the complete documentation index, see [llms.txt](https://docs.paragon.trade/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.paragon.trade/markets/power-perpetuals/hedging-and-risk.md). # Hedging & Risk One contract carries $$p P^{p-1} / K$$ units of the underlying in delta, $$2P / K$$ on the square, or 2 units at launch, and that delta moves with the price. A short position is hedged with a long position of that size in the underlying, and a long position with a short one. The hedge is reset often enough to keep pace. Examples on this page use the square, $$p = 2$$. ## Greeks For one contract on index $$I = P^p / K$$, with $$P$$ the underlying's price: | Greek | Formula | For the square at launch, P = K | What it means | | ------------ | ------------------------------------- | --------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------- | | Delta | $$\Delta = p P^{p-1} / K$$ | $$2P / K$$, 2 units of the underlying | Hedge size. On the square it doubles when the underlying doubles. | | Gamma | $$\Gamma = p(p-1) P^{p-2} / K$$ | $$2 / K$$ | Constant on the square: the hedge changes by $$2/K$$ units per unit move in the underlying. Grows with the price for higher powers. | | Dollar gamma | $$\Gamma P^2 = p(p-1), I$$ | $$2I$$, twice the index value | Convexity in currency; a move's second-order P\&L is half of this times the squared move. | | Vega | 0 | 0 | The index is a price, not a volatility. Volatility exposure comes through funding. | | Theta | 0 for the index; the carry is funding | $$\sigma^2$$ per period ($$\tfrac{p(p-1)}{2}\sigma^2$$ in general) plus financing | What a long pays to hold the convexity and finance the exposure. See [Funding](/markets/power-perpetuals/funding.md). | Second-order expansion of a move: $$\dfrac{\Delta I}{I} \approx p,\dfrac{\Delta P}{P} + \dfrac{p(p-1)}{2}\left(\dfrac{\Delta P}{P}\right)^{2}$$, which for the square is $$2,\dfrac{\Delta P}{P} + \left(\dfrac{\Delta P}{P}\right)^{2}$$. The first term is what the delta hedge captures; the second is what it leaves behind. Worked on the square at launch, underlying at 100 so $$K = 100$$ and the index at 100. Delta is 2 units. The underlying rises to 110: the index is 121, delta is now 2.2 units, and a hedger who was short one contract against 2 units long has to buy 0.2 more. The hedge captured 20 of the 21 points; the missing point is $$(\Delta P/P)^2 = 1%$$ of the index, the gamma loss for that move. Summed over every move, those losses are the realized variance, which is what the interest rate is set to cover. ## Leverage and liquidation distances Hyperliquid liquidates a position when its equity falls below the maintenance margin, half of the initial margin at the market's maximum leverage, charged on current notional. On a 3x market that is 16.7% of notional, whatever leverage the position was opened with. See [Risk & Liquidations](/trading/liquidations.md) and [Hyperliquid's liquidation price formula](https://hyperliquid.gitbook.io/hyperliquid-docs/trading/liquidations#computing-liquidation-price). How far the underlying has to move to liquidate a position on the square, by the collateral posted: | Collateral (leverage) | Long liquidates at (underlying move) | Short liquidates at (underlying move) | | --------------------- | ------------------------------------ | ------------------------------------- | | 100% (1x) | None | +30.9% | | 50% (2x) | −22.5% | +13.4% | | 33% (3x) | −10.6% | +6.9% | For collateral $$1/L$$ of notional and maintenance rate $$\mu$$, a long is liquidated when the index falls to $$(1 - 1/L)/(1 - \mu)$$ of its entry, and a short when it rises to $$(1 + 1/L)/(1 + \mu)$$. On the square the underlying's move is the square root of that ratio, less one. At 3x the long ratio is $$0.667/0.833 = 0.8$$, an underlying move of −10.6%. 3x on the square carries 6x the underlying's exposure, but the liquidation distance comes from the maintenance rate above, −10.6% at 3x. On cross margin the account's cross-margin equity backs the position, so the leverage setting changes the collateral drawn, not the liquidation price. Maximum leverage is listed per market in [Contract Specifications](/resources/specifications.md#market-specifications). See [Margining](/trading/margining.md). The index and its payoff are described in [Index & Payoff](/markets/power-perpetuals/index-and-payoff.md). --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation by asking a question. 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