> For the complete documentation index, see [llms.txt](https://docs.ethena.fi/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.ethena.fi/protocol-overview/underlying-derivatives/inverse-vs-linear-contracts.md). # 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. \ \ 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. \ \ The loss is greater because of the inverse and non-linear nature of the contract. \ \ 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. --- # 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. Perform an HTTP GET request on the following URL with the `ask` and `goal` query parameters: ``` GET https://docs.ethena.fi/protocol-overview/underlying-derivatives/inverse-vs-linear-contracts.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is what the user is ultimately trying to achieve, the reason they need the answer. Sharing it helps GitBook give you a better, more relevant answer. A goal is most helpful when it describes the outcome the user wants rather than restating the question. For example, with `ask=how do I create an API token`, a goal like `automate deployments from our CI pipeline` lets GitBook tailor the answer to that use case. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.