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 (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.
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