# Linear vs Inverse Perpetuals

A Linear Perpetual Future Contract is a type of derivative where the contract is quoted in a stable currency, typically USDT, and the margin, funding payments, as well as profit and loss (PnL), are also settled in this currency. This setup makes it straightforward as all financial calculations remain in the same currency. The payout to a linear perpetual future is: (Entry - Exit) * Contract Size

An Inverse Perpetual Future Contract operates differently. These contracts are quoted in one currency (such as USD), but the margin, funding payments, and PnL are calculated in another currency (such as ETH). This introduces a non-linear relationship between the contract price and the PnL. The payout to an inverse perpetual future is: (1/Entry - 1/Exit) * Contract Size

Consider a Long ETH position in both the linear and inverse perpetual contract for the same nominal amount.

Time | Linear Perp Position Sz | Inverse Perp Position Sz | Close Price Perp | Scenario#1Long Linear Perp UPNL(USDT) | Scenario#2 Long Inverse Perp UPNL(ETH) |

T0 | 20 ETH | $100,000 | $5,000 | $0 | $0 |

T+1 | 20 ETH | $100,000 | $8,000 | $60,000 | 7.5 |

T+2 | 20 ETH | $100,000 | $2,000 | -$60,000 | -30 |

Scenario#1:

**Linear Perpetual Contract-**If the price of ETH increases from $5,000 to $8,000, the PnL is $60,000 USDT. If the price decreases from $5,000 to $2,000, the PnL is -$60,000 USDT. The PnL change is symmetric for price increases and decreases.Scenario#2:

**Inverse Perpetual Contract-**If the price of ETH increases from $5,000 to $8,000, the PnL is 7.5 ETH. If the price decreases from $5,000 to $2,000, the PnL is -30 ETH. The PnL change is asymmetric, showing a larger impact for price decreases than increases.

This non-linear relationship in inverse contracts means that traders need to account for **convexity** when managing their positions, as losses can be larger than gains for the same magnitude of price movement in the opposite direction.

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