Buying YES versus Buying NO

If YES and NO are true complements, knowing one probability determines the other. But trading still requires comparing each side with its own executable price.

Probability translation #

If your YES estimate is $q_Y$, then

$$q_N=1-q_Y.$$

For $q_Y=0.70$, fair value of YES is 0.70 and fair value of NO is 0.30. If their buy prices are $p_Y$ and $p_N$,

$$EV_Y=q_Y-p_Y, \qquad EV_N=(1-q_Y)-p_N.$$

Numeric example #

Suppose $q_Y=0.70$, YES ask is 0.74, and NO ask is 0.27. Buying YES has EV -0.04. Buying NO has EV $0.30-0.27=+0.03$. NO is the less likely settlement but the better-priced purchase.

Executable asks may sum above 1 because both include spread; executable bids may sum below 1. Comparing one side's bid with the other side's ask without tracking what transaction each quote supports mixes different actions.

Life example #

Two insurance policies can cover opposite outcomes but charge different premiums. Complementary events do not imply equal profit margins or symmetric transaction costs.

Application to no-hedge #

When a reference quote represents the opposite side, transform its probability scale with $1-referenceVWAP$ only after verifying identical event, deadline, resolution source, invalidation policy, and payout currency. Then compare the transformed fair value with the maker-side executable buy price.