So far: People arrive one at a time. Each trades with a note already waiting, at its price, or pins one and waits, and the waiting notes stack into a book with a best bid, a best ask, a spread between them and a mid in the middle (lesson 1).
Look at any book and the best ask is above the best bid. Buy and sell again straight away, and you lose the difference. So why doesn't someone close the gap?
You run the stall
Suppose you run a stall that always quotes both sides: you'll buy a sack a little under the going price of 50 and sell one a little over. People who don't want to wait for their note to be taken come to you instead, and the difference between your two prices is how you get paid. This job is called market making.
Most of your customers just need grain, or need to sell some, and each one earns you your gap. But some have read tomorrow's newspaper. They know the price is about to move by 5 coins, and they only come to you when your price is about to be wrong. Each of them costs you the move minus your gap.
Set your gap and how many customers know tomorrow's price, then open the stall. Watch your ledger fill up.
The stall is closed. You quote 48.5 to buy and 51.5 to sell. Open the stall and watch who comes.
With nobody informed, every customer earns you your gap. Let one customer in five know tomorrow's price, and a gap of 1 only breaks even: you earn 1 from four of them and lose 4 to the fifth. The more customers know something, the wider the gap you need.
Set the gap above break-even and you make money, until another stall across the square quotes a narrower one and takes your customers. With enough competition the gap ends up where market makers just break even: wide where many customers know something, narrow where few do. Lawrence Glosten and Paul Milgrom worked this out in 1985, and it's still where economists start when they explain the spread.
Market makers also charge for holding stock they didn't want and for their own running costs, but the informed customers are why the gap widens when news is coming: everyone knows some of the people trading in the next minute know more than they do.
The maths
With a gap h either side of the price, a share π of informed customers and a news move J larger than the gap, the stall earns on average, per customer:
(1 − π) · h − π · (J − h) = h − π · J
It breaks even when the gap is h = π · J.
A better mid
The mid price treats both sides of the book as equal. They often aren't. If ten people wait to buy at 49 and two wait to sell at 51, the next trade is far more likely to clear out the two sellers than the ten buyers, and once the sellers are gone the best ask moves up.
So a better guess at the fair price leans toward the thin side. Weight each side's price by the size waiting on the other side and you get the weighted mid. Drag the queues and watch it move.
Drag the two queues. Watch the weighted mid lean toward the shorter one.
- Mid
- 50.00
- Weighted mid
- 50.67
- Imbalance
- +8
With 10 waiting to buy at 49 and 2 waiting to sell at 51, the weighted mid is 50.67: closer to 51, the side that is about to run out.
The difference between the sizes on the two sides is the book's imbalance. Martin Gould and Julius Bonart found that the imbalance at the best prices predicts the direction of the next price move.
The maths
With best bid b and best ask a, and sizes B and A waiting at them:
weighted mid = (b · A + a · B) / (A + B), imbalance = B − A
What you learned
- Market making
- Quoting a price to buy and a price to sell at once, and earning the gap between them.
- Informed customers
- Customers who know where the price is going. They trade only when the quote is about to be wrong.
- Break-even gap
- The gap where a market maker earns nothing. It grows with the share of informed customers and the size of the move.
- Weighted mid
- Each side's price weighted by the size waiting on the other side. It leans toward the thin side.
- Imbalance
- The size waiting to buy minus the size waiting to sell at the best prices.
Check yourself
1. One customer in five knows tomorrow's price, which will move by 5 coins. Which gap breaks even?
2. Ten people wait to buy at 49 and two wait to sell at 51. Where is the weighted mid?
3. News is coming, and more of the people trading know something. What happens to the spread?