Adverse Selection & Stale Reference Prices

A maker order does not receive a random sample of market states. It waits until another trader chooses to trade against it. That choice is often most attractive after information has moved fair value against the resting order.

Conditional value at fill #

The relevant quantity is not unconditional edge $q-p$, but

$$EV_{fill}=E[Y\mid order\ filled,\ I_{fill}]-p-costs.$$

$I_{fill}$ is information available at the actual fill time. If fills select bad states, $E[Y\mid filled]$ can be below the probability estimated when the order was posted.

Stale-reference timeline #

Suppose a maker computes $fair=0.65$ and bids 0.60. News lowers fair value to 0.50 on the fast reference venue. Before cancellation reaches the maker venue, a trader sells into 0.60. The order appeared to have five cents of edge when posted but has roughly -0.10 before costs at fill.

Life example #

A used-car dealer's standing offer is accepted fastest by owners who just learned about a serious defect. Acceptance itself contains information about the asset.

Why spread is not edge #

A five-cent quote discount does not guarantee five cents of informational advantage. It may merely compensate for latency, toxic flow, inventory risk, and the fact that good orders remain unfilled while bad orders execute.

Application to no-hedge #

Measure reference age at order creation and fill, cross-venue clock uncertainty, cancellation latency, and reference movement immediately after fills. Calibrate $q$ on filled orders, not all quotes. When required reference freshness or semantic identity is unavailable, do not quote.