Why your fills are worse than your quotes

Question

You quote a two-sided market that you believe is centered exactly on fair value, your bid and ask are symmetric around the true price. Yet at the end of the day your fills, on average, lose money.

Explain why even a "fair" quote gets picked off, and what this implies about where you must set your prices.

Accepted Answer

The problem is which of your quotes get hit. You don't get filled at random, you get filled selectively, on the side that's about to be wrong. Concretely, imagine the fair value is about to jump to \101 or drop to \99 (unknown to you), and you're quoting \99.50 bid / \100.50 ask around a \100 mid. A trader who knows the value is heading to \101 lifts your \100.50 ask (cheap for them); one who knows it's heading to \99 hits your \99.50 bid (expensive for them to sell to you, good for them). Either way, the informed trader always takes the side you'll regret. Your uninformed fills wash out, but…

Why your fills are worse than your quotes

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