# Inverse vs Linear Contracts

### Inverse vs Linear Contracts

A linear payout is the simplest to describe and is used for many swaps. The price of a linear contract is expressed as the price of the underlying against the base currency. ETHUSDT is a linear perpetual and is quoted in Tether, with margin and PNL calculations denominated in Tether.

An inverse contract is worth a fixed amount of the quote currency. In the case of the ETHUSD perpetual, each contract is worth $1 of Ethereum at any price. ETHUSD is an inverse contract because it is quoted as ETH/USD but the underlying is USD/ETH or 1 / (ETH/USD). It is quoted as an inverse to facilitate hedging US Dollar amounts while the spot market convention is to quote the number of US Dollars per Ethereum.

### Convexity Implications

Convexity (also known as Gamma) refers to the second derivative of a contract's value with respect to price, and in the case of inverse perpetual futures, it can differ from the relationship suggested by a linear move in price.

While the payoff for a linear contract is just the Contract Multiplier\*(Entry Price-Exit Price), the payoff for an inverse contract is Contract Multiplier\*(1/Entry Price - 1/Exit Price), introducing convexity.

**Example**

A trader goes long 50,000 contracts of ETHUSD at a price of 10,000. \
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A few days later the price of the contract increases to 11,000.

The trader’s profit will be: 50,000 \* 1 \* (1/10,000 - 1/11,000) = 0.4545 ETH

If the price had in fact dropped to 9,000, the trader’s loss would have been: 50,000 \* 1 \* (1/10,000 - 1/9,000) = -0.5556 ETH. \
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The loss is greater because of the inverse and non-linear nature of the contract. \
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Conversely, if the trader was short then the trader’s profit would be greater if the price moved down than the loss if it moved up.