Why There's a Gap Between Buy and Sell Prices: Glosten-Milgrom

Every time you trade a stock, you quietly lose a little money before the price even moves. Look closely at any quote and you'll see two numbers: the price you can sell at (the "bid") and the slightly higher price you can buy at (the "ask"). That gap, the bid-ask spread, means if you buy and immediately sell, you come out behind. It looks like a rip-off. Where does that gap come from, and why can't competition compete it away to zero?

In 1985, Lawrence Glosten and Paul Milgrom gave a stunningly clean answer: the spread exists because the market maker is afraid of you. Or more precisely, afraid that you might know something they don't.

The market maker's nightmare

A market maker is a dealer who stands ready to buy from anyone who wants to sell and sell to anyone who wants to buy. They make their living on the tiny spread. Simple enough, but they have a terrifying problem.

They don't know who they're trading with. Every so often, the person selling to them is selling because they know bad news is coming. Every so often, the person buying from them is buying because they know good news is coming. The market maker, trading against these informed people, is guaranteed to lose: they buy right before the price drops and sell right before it rises. They're always on the wrong side.

This is called adverse selection, and it's the same disease that plagues used-car dealers and insurance companies. The people most eager to trade with you are often the ones who know something you don't. In the used-car world it's the seller hiding a broken transmission. In markets it's the trader sitting on tomorrow's earnings surprise.

How the spread solves it

Here's the elegant part. The market maker can't tell informed traders from ordinary ones, they all look identical. So the maker can't just refuse to trade with the dangerous ones. Instead, they do something cleverer: they charge everyone a small toll to cover the losses the informed few will inflict.

That toll is the spread. By selling a hair above the true value and buying a hair below it, the market maker skims a little from every trade. The uninformed traders, the vast majority, pay this toll happily, because they just need to trade for their own reasons and the cost is tiny. Those small tolls, collected from everybody, exactly cover the beatings the maker takes from the informed minority.

So the spread isn't greed. It's insurance. The wider the spread, the more protection against informed traders. In fact, in Glosten and Milgrom's model, the maker earns zero profit on average, competition drives the spread down to precisely the level that covers adverse-selection losses and no more. It's a break-even toll, not a fat margin.

The spread as a truth serum

Now the truly beautiful idea. Every trade tells the market maker a little something. If someone buys, that's a whisper of "maybe good news." If someone sells, a whisper of "maybe bad news." Most whispers are just noise from uninformed traders, but the maker can't be sure, so they listen to every one.

So after each trade, the maker nudges their quotes:

• Someone bought? Maybe they know something good. Nudge both bid and ask up a touch.
• Someone sold? Maybe they know something bad. Nudge both down a touch.

Over many trades, this process acts like a truth serum. If there really is an informed trader quietly buying, the steady drip of buy orders keeps pushing the price up until it reaches the true value, at which point the informed trader stops, because there's no edge left. The market learns the secret just from the pattern of trades, without anyone ever announcing anything. Prices come to reflect information not by magic, but by this trade-by-trade updating.

This is a profound picture of how markets become "efficient." Efficiency isn't a starting assumption, it's the end product of market makers nervously watching order flow and adjusting.

A close cousin of the Kyle model

Glosten-Milgrom and the Kyle model (published the same year) are the twin pillars of market microstructure, and they're worth comparing:

• Kyle imagines one big strategic insider deciding how much to trade, and focuses on price impact and depth, how far each order moves the price.
• Glosten-Milgrom imagines a stream of small traders arriving one at a time, and focuses on the bid-ask spread, the gap the maker needs to survive adverse selection.

They're two lenses on the same underlying truth: information is the reason trading has a cost. Where there's a chance your counterparty knows more than you, someone has to be compensated for that risk, and that compensation shows up either as price impact or as the spread.

How it's used today

The paper reshaped how everyone thinks about trading costs:

• The spread has a name for its biggest ingredient. Practitioners now routinely break the bid-ask spread into pieces, and the largest piece is the "adverse selection component", the part that exists purely because of the fear of informed traders. That decomposition comes straight from this line of work.
• Market makers manage adverse selection actively. Modern electronic market makers widen their spreads exactly when informed trading seems likely, around news, at the open, during volatile stretches, and tighten them when flow looks benign. That's Glosten-Milgrom in action, running billions of times a day.
• It explains why some stocks cost more to trade. Obscure, thinly-covered stocks have wide spreads not because dealers are greedy, but because the risk of trading against someone informed is higher when less is publicly known.

The honest limitations

Like all clean models, it buys its clarity with simplifications:

• Traders arrive one at a time, trading a fixed small size. Real markets have simultaneous orders of all different sizes, which the basic model doesn't capture.
• It splits the world into "informed" and "uninformed." Reality is a spectrum, everyone has some information, and most people are somewhere in the fuzzy middle.
• It ignores the maker's inventory worries. A real market maker also cares about getting stuck holding too much of a stock, a separate source of spread that the companion Avellaneda-Stoikov tradition handles.
• It assumes fierce competition drives profit to zero. In markets with few dealers or other frictions, spreads can be wider than pure adverse selection would require.

The one-line takeaway

Glosten and Milgrom showed that the bid-ask spread is the market maker's defense against the possibility that you know something they don't, a small toll charged to everyone so the dealer can survive the informed few, and that the same nervous, trade-by-trade price adjustments are exactly how secrets end up baked into prices.