Inverse futures P&L: calculate profit and collateral value

Inverse futures P&L formula: profit and loss in the base coin

For this hypothetical inverse long, let D be the fixed USD face amount, including the contract multiplier, E the entry price and P the comparison price in USD/BTC. Coin P&L is D × (1/E − 1/P). The reciprocal-price difference has units BTC/USD; multiplying by D therefore produces BTC, not USD. Reversing the contract direction reverses this result.

Translate coin P&L at P when reporting its value at the comparison point. Keep full precision until presentation. A venue's displayed unrealized P&L, margin valuation and eventual execution can use different price inputs; record which one you are using rather than calling every observation the current price.

USD equity: contract P&L plus collateral revaluation

If starting collateral is C BTC, theoretical equity at the comparison point is C + coin P&L. Its USD value is that total multiplied by P. The change from starting USD equity splits into contract P&L valued at P plus C × (P − E), the revaluation of the original collateral. For this reconciliation, the original BTC collateral is valued at E initially and at P later, using the same prices as the contract calculation. If the collateral valuation price and the contract price differ, use separate prices; the USD hedge identity in the exercise no longer follows automatically.

The exercise excludes fees, funding, deposits, withdrawals, borrowing, other positions and liquidation before the comparison point. It describes hypothetical endpoint values, not a guarantee that a venue would keep the account open along the intervening path. Recognized collateral and withdrawable funds may also differ from this equity measure.

Example: 6,000 USD inverse long with 0.10 BTC collateral

Assume D = 6,000 USD, E = 60,000 USD/BTC and C = 0.10 BTC. Starting equity is 6,000 USD. At P = 50,000, contract P&L is −0.02 BTC, worth −1,000 USD at that same price. The original collateral also loses 1,000 USD of value.

Equity is therefore 0.08 BTC, worth 4,000 USD: the account change is −2,000, not −1,000. At 70,000 the two USD contributions are each +1,000. Equal USD price moves here produce unequal coin P&L amounts; the reporting convention matters.

Mistake: treating the USD face amount as a BTC quantity

6,000 × (50,000 − 60,000) is not this contract's payoff: it treats the USD face amount like a base-asset quantity. Adding −0.02 BTC directly to −1,000 USD is another unit error. Both can survive a spreadsheet review if column headings omit currencies.