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Delta-Neutral Examples

Last updated 5 months ago

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Context

Based on Arthur Hayes' example in his article:

Here, we have used an inverse perpetual to explain the different payoff scenarios of a delta-neutral strategy. Ethena will utilize both inverse and linear perpetuals. The payoff outcomes on an inverse perpetual are more intricate and as a result, we focus on explaining those scenarios below.

An Ethereum inverse perpetual which is worth $1 of Ethereum paid out in Ethereum has the following payoff function:

$1 / Ethereum Price in USD

If Ethereum is worth $1, then the Ethereum value of the perpetual is 1 ETH, $1 / $1.

If Ethereum is worth $0.5, then the Ethereum value of the perpetual is 2 ETH, $1 / $0.5.

If Ethereum is worth $2, then the Ethereum value of the perpetual is 0.5 ETH, $1 / $2.

Worked Examples

1 USDe = $1 of ETH + Short 1 Ethereum / USD Inverse Perpetual

To create 1 USDe, Ethena needs to delegate 1 ETH as margin with a derivatives exchange (via "Off-Exchange Settlement" solution) and short 1 ETHUSD perpetual.

Rapid ETH Price Decrease

  • Now the Ethereum price falls from $1 to $0.1.

  • The value of ETHUSD in ETH = $1 / $0.1 = 10 ETH

  • The PNL of ETHUSD Position = 10 ETH (current value) – 1 ETH (initial value) = +9 ETH

  • We have 1 ETH delegated as margin with the exchange.

  • Ethena's total equity balance with the exchange is 1 ETH (our initial margin) + 9 ETH (profit from the ETHUSD position), and the total balance is now 10 ETH.

  • The Ethereum price is now $0.1, but the system has 10 ETH, and therefore the USD value of the total portfolio is unchanged at $1, $0.1 * 10 ETH.

Rapid ETH Price Increase

  • Now the Ethereum price rises from $1 to $100.

  • The value of ETHUSD in ETH = $1 / $100 = 0.01 ETH

  • The PNL of ETHUSD Position = 0.01 ETH (current value) – 1 ETH (initial value) = -0.99 ETH

  • Ethena's total equity balance with the exchange is 1 ETH (initial margin) – 0.99 ETH (loss from ETHUSD position), and total balance is now 0.01 ETH.

  • The Ethereum price is now $100, but Ethena has 0.01 ETH, and therefore the USD value of the total portfolio is unchanged at $1, $100 * 0.01 ETH.

Delta-neutral strategies aim to ensure the portfolio value in synthetic USD terms is unchanged despite changes in value of the underlying collateral. In certain conditions and market environments this may not hold, as is described in more detail in the Risks section.

Further Worked Examples

Dust on Crust