# Delta-Neutral Examples

Based on Arthur Hayes' example in his article: Dust on Crust.

A Bitcoin inverse perpetual swap (e.g., Ticker: XBTUSD on BitMEX) 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

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

We have 1 BTC

The total equity balance with the exchange is 1 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

The PNL of BTCUSD Position = 0.01 BTC

The total equity balance with the exchange is 1 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.

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