We hold inverse perpetual shorts and count the account in ETH. On a falling market we saw funding settlements credit more coin than earlier ones paid at the very same rate. Nothing about the market had become more generous. It is a property of the contract, and it is worth writing down because it decides which of two numbers a funding figure is quietly reporting.
An inverse contract has a fixed face value in dollars. On the ETH contract we use it is $10. A short of N contracts is a short of N × $10 of notional, settled in ETH. Measured in coin, that same position is
exposure in ETH = N × 10 / P
where P is the price. The position does not change when the price moves; its size in coin does. Halve the price and the same contracts are a short of twice as many coins.
Funding is charged on the position's value in coin, so a settlement at rate r credits a short
funding in ETH = N × 10 / P × r
Multiply by the price to see it in dollars and P cancels: N × 10 × r. Per contract, funding in dollars does not depend on the price at all. Funding in coin moves as 1/P.
A linear contract does the opposite. There the position is a fixed number of coins and funding is paid in dollars, so the dollar amount moves with the price and the coin amount stays put. Neither contract pays more in any absolute sense. They fix a different unit, and the other one floats.
The cleanest way to see this is to hold everything else still: the same trade, so the same number of contracts, and two settlements at the same rate. The rate on this contract lands exactly on the 0.0100 per cent constant often enough for that: in an earlier note it held in 27 per cent of 2683 settlements pooled across three contracts (we wrote about why in [Funding never paid a short more than the interest rate](/notebook/funding-never-paid-more)).
One trade on the live account held 6820 contracts from 18 September to 15 October. Two of its settlements were paid at exactly 0.0100 per cent:
| Settlement, UTC | Price | Short, ETH | Funding, ETH | Funding, $ |
|---|---|---|---|---|
| 2 Oct 08:00 | 2741.36 | 24.878 | 0.002488 | 6.82 |
| 10 Oct 08:00 | 2493.23 | 27.354 | 0.002735 | 6.82 |
The price fell 9.05 per cent. The dollar amount is identical. The coin amount rose 9.95 per cent, which is the price ratio 2741.36 / 2493.23 = 1.0995 and nothing else. No contract was added in between; the account never adds to an open position.
The same thing runs the other way. An earlier trade held 6248 contracts through a rally:
| Settlement, UTC | Price | Short, ETH | Funding, ETH | Funding, $ |
|---|---|---|---|---|
| 12 Aug 16:00 | 1890.35 | 33.052 | 0.003305 | 6.25 |
| 22 Aug 00:00 | 2501.71 | 24.975 | 0.002497 | 6.25 |
Up 32.34 per cent in price, down 24.4 per cent in coin, the same $6.25 each time.
Away from the constant the rate moves as well, and the two effects mix in a single number. That is why a column of funding in coin cannot be read as a column of rates: a rising coin amount can come from the rate, from the price, or from a larger position, and on this contract the price alone is enough to produce it.
Funding is not the only figure built on 1/P. The result of an inverse short closed at P_exit is
result in ETH = N × 10 × (1/P_exit − 1/P_entry)
so a fall earns more coin for each further dollar of decline than the one before. Funding and the result rise together on the way down because they come from the same term.
So does the size of the short against the stack, the figure on the dashboard labelled short vs stack. Our position opens at 62 per cent of the stack. With no trade placed, that share reaches 100 per cent once the price has fallen 38 per cent from entry, because 0.62 / 0.62 = 1. The room left at entry exists for exactly this: the short grows in coin by itself, and the cover rule is written against the coin, not against the dollars.
It is not extra income in dollars. The dollar amount per contract is unchanged; each coin is simply cheaper. For an account counted in coin, more coin is the thing being measured, so the gain is real on the scale we report. Converted back at the lower price, it is the same $6.82.
It works the same way against the short. When the rate turns negative the short pays, and it pays in coin at the same 1/P. On 7 October the rate settled at −0.0143 per cent and the account paid 0.0037 ETH on that one settlement, more than either credit in the first table.
Our record of it is close to the exchange's, not identical. The exchange settles on the mark price at the funding timestamp. Our account books funding at the close of the price bar that opens each eight hour period, from public data. We have not compared the two settlement by settlement, so we would not lean on the fourth significant digit.
We can only check the last three months. The exchange publishes about three months of funding history. Earlier settlements in our records were computed when that window still reached them, and today there is nothing public left to recompute them against. The two trades shown here sit inside the window, and their funding, recomputed from the public series, matches what the account recorded to within 0.1 per cent.