# Delta-Neutral Examples Based on Arthur Hayes' example in his article: [Dust on Crust](https://blog.bitmex.com/dust-on-crust/#the-satoshi-nakamoto-dollar-nakadollar-nusd). > A Bitcoin inverse perpetual swap (e.g., Ticker: [XBTUSD on ](https://www.bitmex.com/app/trade/XBTUSD)[BitMEX](https://bitmex.com)) which is worth $1 of Bitcoin paid out in Bitcoin has the following payoff function: > > $1 / Bitcoin Price in USD > > If Bitcoin is worth $1, then the Bitcoin value of the perpetual swap is 1 BTC, $1 / $1. > > If Bitcoin is worth $0.5, then the Bitcoin value of the perpetual swap is 2 BTC, $1 / $0.5. > > If Bitcoin is worth $2, then the Bitcoin value of the perpetual swap is 0.5 BTC, $1 / $2. Here, Arthur used an inverse perpetual to explain the different payoff scenarios of a delta-neutral strategy. usdx.money intends to utilize both inverse and linear perpetuals. Due to the complex nature of payoff results from inverse perpetuals, our explanation is centered on those scenarios previously detailed. ## Worked Example ``` 1 USDX = $1 of Bitcoin + Short 1 Bitcoin / USD Inverse Perpetual Swap ``` To create 1 *USDX*, we need to delegate 1 *BTC* as margin with a derivatives exchange (via our "Off-Exchange Settlement" provider) and short 1 BTCUSD perpetual. **Suppose Bitcoin price drops significantly** * Now the BTC price falls from $1 to $0.1. * The value of BTCUSD in BTC = $1 / $0.1 = 10 BTC * The PNL of BTCUSD Position = 10 BTC (current value) – 1 BTC (initial value) = +9 BTC * We have 1 BTC delegated as margin with the exchange. * The total equity balance with the exchange is 1 BTC (our initial margin) + 9 BTC (our profit from our BTCUSD position), and our total balance is now 10 BTC. * The BTC price is now $0.1, but we have 10 BTC, and therefore the USD value of our total portfolio is **unchanged** at $1, $0.1 \* 10 BTC. **Suppose Bitcoin price rises significantly** * Now the BTC price rises from $1 to $100. * The value of BTCUSD in BTC = $1 / $100 = 0.01 BTC * The PNL of BTCUSD Position = 0.01 BTC (current value) – 1 BTC (initial value) = -0.99 BTC * The total equity balance with the exchange is 1 BTC (our initial margin) – 0.99 BTC (our loss from our BTCUSD position), and our total balance is now 0.01 BTC. * The BTC price is now $100, but we have 0.01 BTC, and therefore the USD value of our total portfolio is **unchanged** at $1, $100 \* 0.01 BTC. Delta-neutral strategies aim to ensure the portfolio value in synthetic USD terms is **unchanged** despite changes in value of the underlying collateral. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://docs.usdx.money/a-synthetic-usd/delta-neutral-examples.md?ask= ``` The question should be specific, self-contained, and written in natural language. 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.