What a fill actually earns
A market maker quotes a spread but keeps much less than it. Each fill is worth half the spread against the mid, the price then tends to move against you, and the exchange gives a little back. What is left is the edge.
- Convert a quoted spread into basis points and into gross edge per share
- Net the half-spread against adverse selection and the maker rebate
- Find the narrowest spread that still breaks even, and the volume a P&L target needs
- Decide whether to match a competitor's tighter quote
The intuition
You quote a stock 4 cents wide: bid 2 cents below the mid, offer 2 cents above. Someone sells to you on the bid. You have not made 4 cents, and not even 2: you own a share worth the mid, bought 2 cents cheaper. You will earn the other 2 cents only if someone buys it from you on the offer before the mid moves. So the honest unit of account is half the spread per share filled, against the mid at that instant.
Then the mid does move, and not randomly. The people who trade with you sometimes know something, so you are sold to just before the price falls and bought from just before it rises. Measured over thousands of fills, the mid drifts against you by some average number of cents. That is adverse selection, and it comes straight out of the half-spread. Add back the rebate the exchange pays for posting liquidity, and you have the edge you keep. Multiply by the shares you fill and you have the day.
Net edge per share = half-spread − adverse selection + rebate. Daily P&L = shares filled × net edge. Break-even spread = 2 × (adverse selection − rebate). A tighter spread wins volume but thins the edge, and below break-even every extra share loses money.
Why it works
- The conventions here: quotes symmetric around the mid; each share filled earns half the quoted spread against the mid at the moment of the fill; adverse selection is the average move in the mid against the desk after a fill, in cents a share; the exchange pays a maker rebate per share; inventory is flattened at the mid for free. Spreads and per-share figures in cents, the day's P&L in dollars.
- Half, not whole. The whole spread is earned only on a complete round trip, bid then offer, with the mid unmoved in between. Counting half per fill is what makes the arithmetic honest when the two sides do not pair up.
- Adverse selection is measured, not assumed. Mark each fill against the mid a short time later and average the move, signed so that a move against you is positive. The half-spread minus that is the realized spread, what you actually kept.
- Basis points make spreads comparable. Four cents on a $20 stock is 20 bps; on a $150 stock it is under 3 bps. Desks compare spreads across stocks in basis points, and quote in cents.
- Run it backwards. Set the net edge to zero and the break-even spread falls out: twice the adverse selection less the rebate. Divide a dollar target by the net edge and you have the shares the day needs.
- The competitor question. Matching a tighter quote cuts the net edge on every share and raises the share count. The P&L goes up only if the extra volume outweighs the thinner edge, and never if the new edge is zero or below.
| Spread in basis points: $0.04 ÷ $50 × 10,000 | 8 bps |
| Gross edge: 500,000 × 2 cents | $10,000 |
| Net edge: 2 − 1.25 adverse selection + 0.25 rebate | 1 cent a share |
| Daily P&L: 500,000 × 1 cent | $5,000 |
| Share of the half-spread kept: 1 ÷ 2 | 50% |
| Break-even spread: 2 × (1.25 − 0.25) | 2 cents |
Quoting 2 cents wide would break even on every share, so winning more volume at that spread earns nothing.
The formulas
Each fill earns half the spread against the mid; basis points make spreads comparable across prices.
What you keep after the mid drifts against you and the exchange pays you.
Cents a share times shares, in dollars.
The spread at which the net edge is exactly zero.
A dollar target divided by what each share keeps.
Worked example
Start from the half-spread, subtract the average move against you, add the rebate, multiply by the shares. The follow-up asks what share of the half-spread survived.
See it move
Same stock and desk. Change the spread you quote, what the flow costs you, what the exchange pays, and how many shares you fill.
- Raise adverse selection. The net edge, the share kept and the P&L all fall, and the break-even spread rises. Raise the rebate and each reverses.
- Widen the spread. The half-spread, the net edge and the P&L rise; the break-even spread does not move, because it depends only on the flow and the rebate.
- Fill more shares. The gross edge rises, and the P&L is multiplied up: larger when the net edge is positive, and a bigger loss when it is negative. Volume never rescues a quote inside break-even.
Run it backwards
You know the flow's adverse selection and the rebate. What is the narrowest spread you can quote without losing money on average?
Set the net edge to zero: half-spread = adverse selection − rebate. Double it for the spread. Anything tighter loses on every share; anything wider is the room you have against a competitor.
The same idea sizes a day: a dollar target divided by the net edge per share is the shares you must be filled on. If the flow is worse than you measured, both answers move against you at once.
Traps
Say it in the interview
“You quote a stock 4 cents wide and fill 500,000 shares. What did you make?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- A fill earns half the spread against the mid, not the spread.
- Net edge = half-spread − adverse selection + rebate; the day is shares × net edge.
- Break-even spread = 2 × (adverse selection − rebate). Volume cannot fix a quote inside it.
- Compare spreads in basis points, quote them in cents.