Leverage and exposure

Leverage in Butter comes from how scalar long and short tokens translate conditional USDC into exposure to the asset’s price inside a branch.

This page explains how exposure is measured, how leverage is defined, why it differs for long and short positions, and how it behaves as prices move without requiring liquidations.

Exposure, notional, and collateral

Every position in a branch has three key quantities:

  • Size, measured in units of the asset (for example, 2 BTC). I.e. how many units of the asset you have exposure to. 2 BTC of long exposure means you profit $2 for every $1 increase in BTC price, and you lose $2 for every $1 decrease in BTC price.

  • Notional value, which is size multiplied by the branch price (for example, 2 BTC times 65,000 USD = 130,000 USD notional).

  • Collateral, which is how much conditional USDC backs the long or short tokens in that branch.

The leverage of a position is:

Leverage=NotionalCollateral\text{Leverage} = \frac{\text{Notional}}{\text{Collateral}}

Collateral is determined by the value of the long or short tokens that make up the position at the current AMM price in that branch.

When you increase position size in a branch, your size and notional grow, and so does the amount of conditional USDC used to back your position.

How leverage arises from scalar bounds

Scalar bounds define how quickly a long or short token’s value responds to changes in the asset’s price.

For a branch with lower bound lowerBoundPrice\text{lowerBoundPrice} and upper bound upperBoundPrice\text{upperBoundPrice}:

  • A change of 1 USD in the asset price inside the bounds changes each long token’s value by 1upperBoundPrice−lowerBoundPrice\frac{1}{\text{upperBoundPrice} - \text{lowerBoundPrice}} USDC.

  • The same 1 USD change changes each short token’s value by 1upperBoundPrice−lowerBoundPrice\frac{1}{\text{upperBoundPrice} - \text{lowerBoundPrice}} USDC in the opposite direction.

The wider the bounds, the smaller this per‑token price change is, so you need more tokens to achieve a given amount of exposure.

The narrower the bounds, the larger the per‑token price change is, so you need fewer tokens to achieve the same exposure.

This is why bounds cannot be arbitrarily wide or arbitrarily narrow:

  • Very wide bounds make leverage low and the market less capital efficient.

  • Very narrow bounds make leverage very high but leave a high chance that the asset’s price jumps outside the bounds, which leads to many markets settling at clamped prices, degrading trader experience.

How leverage depends on the conditional price

Even though your exposure in asset units is fixed once you have opened a position, the leverage of that position depends on where the branch’s conditional price sits between the bounds.

For a long position with conditional branch price branchPrice\text{branchPrice}, lower bound lowerBoundPrice\text{lowerBoundPrice}, and upper bound upperBoundPrice\text{upperBoundPrice}:

  • The loss per unit of exposure is capped by the distance from the current conditional price to the lower bound.

  • The closer the conditional price is to the lower bound, the smaller the worst‑case loss per unit of exposure and the higher the leverage you can obtain for a given amount of collateral.

  • The further the conditional price is from the lower bound, the larger the worst‑case loss per unit of exposure and the lower the leverage.

For a short position with the same conditional branch price branchPrice\text{branchPrice}, lower bound lowerBoundPrice\text{lowerBoundPrice}, and upper bound upperBoundPrice\text{upperBoundPrice}:

  • The loss per unit of exposure is capped by the distance from the current conditional price to the upper bound.

  • The closer the conditional price is to the upper bound, the smaller the worst‑case loss per unit of exposure and the higher the leverage you can obtain for a given amount of collateral.

  • The further the conditional price is from the upper bound, the larger the worst‑case loss per unit of exposure and the lower the leverage.

In formula form, with the conditional branch price denoted by branchPrice\text{branchPrice}:

  • Long leverage is equal to:

    • branchPricebranchPrice−lowerBoundPrice\frac{\text{branchPrice}}{\text{branchPrice} - \text{lowerBoundPrice}}

  • Short leverage is equal to:

    • branchPriceupperBoundPrice−branchPrice\frac{\text{branchPrice}}{\text{upperBoundPrice} - \text{branchPrice}}

The denominators here are the distances to the bounds, measured in the same price units as branchPrice\text{branchPrice}.

When the branch price is close to the lower bound, branchPrice−lowerBoundPrice\text{branchPrice} - \text{lowerBoundPrice} is small, so long positions can obtain high leverage while short positions obtain low leverage.

When the branch price is close to the upper bound, upperBoundPrice−branchPrice\text{upperBoundPrice} - \text{branchPrice} is small, so short positions can obtain high leverage while long positions obtain low leverage.

In the extreme, if the lower bound is 0 and the branch price is at the upper bound, the worst‑case loss per unit of long exposure is equal to the current price and the best you can do is approximately 1× leverage as a long.

For shorts, there is no symmetric lower bound on leverage: if the lower bound is 0 and the branch price is very low relative to the upper bound, the distance to the upper bound is very large, so the maximum leverage available to a short position can approach 0.

Worked examples for long and short

Consider a BTCUSD conditional with:

  • Lower bound lowerBoundPrice=60,000\text{lowerBoundPrice} = 60{,}000 USD.

  • Upper bound upperBoundPrice=110,000\text{upperBoundPrice} = 110{,}000 USD.

  • Current branch price branchPrice=80,000\text{branchPrice} = 80{,}000 USD.

The bounds are 50,000 USD wide, so 50,000 long or short tokens give 1 BTC of conditional exposure in this branch.

Long position example

Suppose you open a 1 BTC long position in this branch at 80,000 USD using long tokens:

  • Size is 1 BTC.

  • Notional is 80,000 USD.

  • The worst‑case loss per BTC is 20,000 USD if the price falls from 80,000 USD to the 60,000 USD lower bound.

To make that worst‑case loss equal to your collateral, you would need to post 20,000 USDC of conditional USDC, which corresponds to 4× leverage (80,000 USD notional divided by 20,000 USDC of collateral).

If instead the branch price were much closer to the lower bound, the distance to the lower bound would be smaller, so the worst‑case loss per BTC would be smaller and you could obtain higher leverage for the same collateral.

Short position example

Now consider a 1 BTC short position in the same branch at 80,000 USD:

  • Size is −1 BTC.

  • Notional magnitude is still 80,000 USD.

  • The worst‑case loss per BTC is 30,000 USD if the price rises from 80,000 USD to the 110,000 USD upper bound.

You need 30,000 USDC of collateral to cover this worst‑case loss, so the leverage is around 2.67× (80,000 USD notional divided by 30,000 USDC of collateral).

If instead the branch price were very close to the upper bound, the distance to the upper bound would be small and you would be able to achieve higher leverage for shorts and lower leverage for longs.

No liquidations

Unlike margin trading or perpetual futures, positions in Butter do not have liquidations.

Every long and short token is backed by conditional USDC in the branch, and each matched long–short pair always pays 1 USDC in total at settlement, regardless of where the asset price lands inside or outside the bounds.

This structure means that:

  • You never owe more than the collateral already committed to your position in that branch.

  • Adverse price moves reduce the value of your tokens and can take your position’s value to zero, but they cannot create a negative balance or a margin call.

In effect, leverage comes from how far the price can move against you within the fixed bounds, and not from borrowing additional capital.

This is similar in spirit to trading fully collateralized options or structured products rather than leveraged perpetual futures, even though the payoff profile is defined by scalar long and short tokens rather than options.

Implications for traders

Although leverage changes as the branch price moves, your exposure (e.g. in # of BTC) stays constant once your position is opened, until you modify or close it. Leverage only changes due to the value of your long/short tokens changing as the conditional price fluctuates.

Leverage is only relevant to you when opening your position, as it determines how much USDC collateral you need to commit to achieve a target exposure. Once the position is open, you can just focus on whether you still want that level of asset exposure in the branch.

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