The Grossman-Miller Model

Why does a market maker agree to buy shares from a seller who showed up at a random moment, before knowing whether a buyer will show up any time soon? The Grossman-Miller model, a foundational result in market microstructure theory, answers this by treating liquidity provision as a service with a price: market makers bridge the gap in time between sellers who arrive now and buyers who arrive later, charging for bearing the risk of that gap.

Liquidity as insurance against bad timing

The model's setup is simple: suppose buyers and sellers don't arrive at the same moment — a wave of sellers might show up at 10 a.m. and a wave of buyers not until 2 p.m. Without anyone willing to stand in the middle, the 10 a.m. sellers would have to wait, unable to trade, or accept a much worse price. Market makers solve this by buying from the 10 a.m. sellers and holding that inventory until the 2 p.m. buyers arrive. The price they pay sellers and later charge buyers has to compensate for the risk taken in between — exposure to the price moving against their inventory during the hours it sits unhedged — and the bid-ask spread in this model is exactly that compensation.

The key insight is that the spread isn't primarily about the market maker's cost of doing business — it's compensation for inventory risk over the window until an offsetting trade arrives. The longer that expected window, the more compensation required, and the wider the spread needs to be. If more market makers compete, they share the inventory risk among themselves, and the model predicts the equilibrium spread narrows — more risk-bearing capacity means each unit of temporary imbalance is less costly to absorb.

Worked example: spread as a function of imbalance and risk-bearing capacity

Suppose sellers show up wanting to sell 100,000 shares at 10 a.m., and the market maker expects offsetting buy interest of roughly the same size to arrive by 2 p.m. — a four-hour holding period. If the stock's volatility implies a one-standard-deviation price move over four hours of $0.30, a single market maker bearing all that risk alone might require a spread wide enough to compensate, quoting perhaps 50 cents wide. If four market makers instead share the inventory — each absorbing 25,000 shares — each one's risk exposure drops roughly in proportion, and competition pushes the equilibrium spread down toward 15 cents, since no single market maker needs compensating for the full risk. This is the model's central prediction in miniature: spreads compensate for inventory risk, and more risk-bearing capacity competing to provide liquidity narrows spreads for everyone.

What this means in practice

The Grossman-Miller framework explains a pattern seen throughout real markets: spreads widen exactly when order-arrival imbalances are expected to be large or slow to offset — around scheduled news, at the open, or in stocks with sparse, lumpy trading — and narrow in stocks with dense, well-balanced two-sided flow. It also explains why block trades often move through the upstairs market: a single large imbalance is exactly the kind of event this model says should command a wider effective spread if absorbed all at once by limited risk-bearing capacity, part of why brokers price block liquidity at a discount to compensate for taking on that concentrated risk themselves.