Choosing How Wide to Quote

Ask a market-making candidate to quote a two-sided price on some quantity, and the number that decides whether they make or lose money isn't the midpoint — it's the spread around it. Quote too tight, and anyone who knows more than you do will only ever trade with you when they're right, bleeding you slowly. Quote too wide, and ordinary customers who'd have traded with you (and paid you a small, reliable edge) go elsewhere. The width is the whole game.

The two kinds of counterparty

Flow arriving at your quote splits, roughly, into two buckets. Uninformed flow trades for reasons unrelated to the true value — hedging, rebalancing, liquidity needs — and on average pays you the spread as pure profit. Informed flow trades because it knows something you don't, and it only takes your price when your price is wrong in its favor, so on average it costs you the gap between your quote and the true value. Your spread has to be wide enough that the profit from uninformed flow outweighs the losses from informed flow, on average, across everyone who trades with you.

Worked example

You're quoting a coin-flip-style game: the true value is 50 or 60 with equal probability, revealed only to informed players. You quote 52/58 (bid/ask around your best guess of 55). Suppose 40% of traders who approach you are informed and 60% are uninformed (trading randomly, 50/50 buy or sell regardless of true value). An informed trader only buys your 58 offer when the true value is 60 (buying at 58, worth 60, is a 2-point gain for them, a 2-point loss for you), and only sells into your 52 bid when the true value is 50 (symmetric loss for you). So every informed trade costs you 2. Uninformed trades, being random, are equally likely to hit either side regardless of true value: half the time they buy your 58 offer when the true value is only 50, netting you a healthy 8, and half the time they buy when the true value is 60, costing you 2 — averaging $3 profit per uninformed trade (and symmetrically on the sell side). Blending: $0.4 \times (-2) + 0.6 \times (3) = -0.8 + 1.8 = 1.0$. You expect to net $1 per trade at this width — thin, but positive. Narrow the quote to 54/56 and the informed loss stays roughly the same per trade while the uninformed profit shrinks toward zero, and the blend can flip negative.

What this means in practice

Real desks estimate the informed/uninformed mix from historical fill data, order size, venue, and counterparty identity, then set spreads (and skew them per side) to keep the blended expected value positive with a margin of safety. Widening isn't free either — it loses uninformed volume to tighter competitors, so the optimum is rarely obvious and shifts constantly with market conditions.