Realized PnL of a Binary Contract

PnL is accounting, not belief. Once you know the price paid and the settlement outcome, your probability estimate no longer enters the realized result.

One-share formula #

For a YES share bought at $p$ and settlement $Y\in\{0,1\}$,

$$PnL=Y-p.$$

Therefore

$$PnL_{YES}=1-p, \qquad PnL_{NO}=-p.$$

For $N$ shares before fees, multiply by $N$.

Running prices #

Paying more reduces winning profit and increases losing loss. The estimated $q=0.65$ changes how likely the rows are, not either row's realized number.

Life analogy #

Buying an item for 60 and reselling it for either 100 or 0 creates profit +40 or -60. Your confidence before resale does not change the invoice.

Application to no-hedge #

An unhedged maker fill realizes no locked spread at execution. Cash leaves at the buy price; final PnL remains $Y-p$ minus costs until resolution or a real closing sale. A displayed reference difference is estimated edge, not booked profit.