A market maker quotes a price to buy and a price to sell, and earns the gap between them. Described like that it sounds like a toll booth. In practice the spread is the smaller part of the job. The larger part is the inventory that every fill leaves behind, and the uncomfortable fact that the clients most eager to trade with you are often the ones who know something you do not.
Where a spread comes from
The classic decomposition has three parts, and each points at a different lever:
| Component | What it pays for | What moves it |
|---|---|---|
| Order processing | Fees, infrastructure, people | Scale and automation |
| Inventory | Carrying a position you did not choose | Volatility, position size, time to unwind |
| Adverse selection | Trading against better-informed flow | Who the counterparty is, and how fast prices move after the fill |
Ho and Stoll formalised the inventory part in 1981; Glosten and Milgrom the adverse-selection part in 1985. Neither is new. What changes in a real system is that all three are measured continuously, per instrument and per client segment, rather than assumed.
Skew before you widen
When a market maker accumulates a long position the instinct is to widen both sides. That is usually the wrong move. Widening makes you less competitive on the side that would reduce your risk as well as on the side that would add to it.
The better move is to skew: shift both quotes down, so your offer becomes more attractive — someone buys your inventory from you — and your bid less attractive, so fewer people sell you more. The spread can stay the same width while its centre moves away from the market mid.
Avellaneda and Stoikov (2008) made this precise. Their reservation price — the price at which the market maker is indifferent to holding one more unit — is the mid adjusted for inventory:
r = s − q · γ · σ² · (T − t)
where s is the mid, q the signed inventory, γ risk aversion, σ the
volatility and T − t the time left to carry the position. Quotes are then
placed around r, not around s.
A worked illustration, with round numbers rather than market ones: mid 100.00,
long 10 units, γ = 0.01, σ = 2 per square-root day, half a day left.
The adjustment is 10 × 0.01 × 4 × 0.5 = 0.20, so the reservation price is
99.80 and both quotes slide twenty cents down. Double the position and the skew
doubles. Double the volatility and it quadruples — which is the formula's way
of saying that inventory in a fast market is much more expensive than the same
inventory in a slow one.
The same paper gives the optimal total spread:
δ = γ · σ² · (T − t) + (2 / γ) · ln(1 + γ / k)
where k measures how quickly the chance of a fill falls away with distance
from the mid. The spread widens with volatility and with the time left to carry
the position, and narrows as k rises — when competition for flow is fierce,
quoting wide simply stops getting filled. Risk aversion is less obvious than it
looks: it raises the first term and lowers the second, so a more cautious market
maker skews harder but does not necessarily quote wider.
Adverse selection, measured
You cannot see a counterparty's information. You can see what the market did after you traded with them. That is a markout: the move in the mid, from your side of the trade, at a set horizon after the fill.
- Buy at 99.98, mid is 99.90 a second later: −8 ticks at one second.
- The same at ten seconds and sixty seconds gives a curve.
Average those curves by client segment, venue or order type, and the toxic flow identifies itself. Benign flow has markouts that hover around zero. Informed flow has markouts that fall steadily against you, and the horizon at which they stop falling tells you how fast the information was.
Markouts are the single most useful number a dealing desk computes, because they turn an argument ("this client is too smart for us") into a measurement, and because they separate two problems that look the same in P&L: quoting too tight, and quoting the wrong people.
Hold, net or hedge
Every fill leaves exposure, and there are three things to do with it:
- Hold it and let the skew work it off. Cheapest, if the market cooperates.
- Net it against opposing client flow. A dealer facing many clients often finds that buyers and sellers offset each other for much of the day, and only the residual needs managing.
- Hedge it externally — in the underlying, a future, or a correlated instrument. This costs a spread and carries basis risk, but caps the loss.
The decision is a limit structure, not a judgement call made trade by trade: position limits per instrument and per correlated group, a loss limit, and rules for when the residual is hedged automatically. A hedging algorithm then decides how — slicing the hedge, choosing venues and managing its own market impact — which is the problem the execution note covers.
Options make it two-dimensional
An options market maker carries the same problem with more axes. The inventory is not a quantity but a set of Greeks: delta, which is hedged continuously in the underlying, and gamma and vega, which can only be reduced by trading other options. Skew then applies to the volatility surface rather than to a price: a book that is long vega lowers the implied volatility it quotes, across the strikes and expiries where it is long.
The cost of carrying that gamma is exactly what the dynamic hedging note simulates: the premium collected for an option is the price of the hedging it is about to require.
What breaks in practice
- Stale inputs. Quoting off a price that has stopped updating is the fastest way to be picked off. Every quoting engine needs a staleness kill switch — see the market data note.
- Correlated inventory. Ten small positions in instruments that move together are one large position. Limits set per instrument miss it.
- Feedback loops. Your own hedging moves the market your quotes are built on. A hedge that is too aggressive shows up as worse markouts on your own next fills.
- Regime change. Parameters fitted on a quiet month are wrong on the day it stops being quiet, which is the day they matter.
None of this needs exotic maths. It needs every number — spread, skew, markout, residual — to be visible to the people accountable for the book, live, with the age of the data beside it.