THE IMPACT CURVE

//01_ WHY A HAIRCUT

Paperhands charges no spread, no funding and nothing to open a position. The house is the only counterparty and it starts at zero. Its edge is a haircut applied to gains and never to losses, which is why the curve is called asymmetric.

The haircut is heaviest on small moves, where a gain is most likely to be noise or a timing edge, and lightest on large moves, where it approaches its floor of 10%. It depends on the market and on the size of the move. It does not depend on your position size or your leverage: two traders who close the same move on the same market keep the same fraction of their gain.

//02_ THE FORMULA

scale    = (1 - baseRate) / (1 + term1 + term2)
term1    = 1 / (move x rateMultiplier)
term2    = referenceNotional / (1,000,000 x move x positionMultiplier)
adjusted = g x scale

g is the gain after the deadband, move is the price move after the deadband as a fraction (0.01 for 1%), and referenceNotional is in dollars. With the launch parameters the formula reduces to:

scale = 0.9 / (1 + 1 / (15,000 x move) + 0.1 / (positionMultiplier x move))

The contract computes it in 18-decimal fixed point. Both terms round up, the scale rounds down and the adjusted gain rounds down, so rounding always favours the house, by at most one base unit of USDG.

//03_ PARAMETERS

A lower position multiplier makes the second term larger and the haircut heavier on small moves. The owner can change these values within bounds (the base rate can never exceed 20%), and a change only applies to positions opened after it. See admin powers.

//04_ THE WORKED TABLE

Fraction of the deadbanded gain you keep, before the profit cap and the win fee:

Computed with the formula above at exactly these moves. Three checks by hand, BTC:

move 1%     term1 = 1 / 150         = 0.006667
            term2 = 0.1 / 8.14598   = 0.012276
            scale = 0.9 / 1.018943  = 0.883

move 0.1%   term1 = 1 / 15          = 0.066667
            term2 = 0.1 / 0.814598  = 0.122760
            scale = 0.9 / 1.189427  = 0.757

move 5%     term1 = 1 / 750         = 0.001333
            term2 = 0.1 / 40.7299   = 0.002455
            scale = 0.9 / 1.003789  = 0.897

//05_ READING THE TABLE

• A BTC long that gains 1% on $1,000 of notional has a deadbanded gain of $9.98 and keeps $8.814691 of it. The full calculation is in wins and losses.
• Very small moves pay very little. At a 0.01% move the BTC scale is 0.311, the ETH scale 0.241 and the equity scale 0.270.
• Very large moves approach 0.9 without reaching it. At 10% the BTC scale is 0.898; at 20% it is 0.899.

//06_ THE DEADBAND

Before the haircut, the exit is made less favourable by entry / 50,000, which is 0.2 bps of the entry price: $2.00 on a BTC entry of $100,000.00, $0.0036 on an equity entry of $180.00. The move that enters the formula is the move after that adjustment. A win that the deadband reduces to zero or less returns the margin and nothing else: no fee and no paper.