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Market making

See how market makers quote bids and asks, earn a spread only when trades allow it, and manage inventory, adverse selection, financing and execution costs.

Market making is the business of providing liquidity by offering to buy and sell an instrument, accepting trades and managing the positions those trades create. The market maker's bid is the price at which it buys; its ask, or offer, is the price at which it sells. The bid-ask spread is the difference between them.

The economic service is immediacy: a customer can trade against the maker without waiting for another customer with exactly the opposite requirement. In return, the maker seeks compensation for supplying that immediacy, carrying inventory and sometimes trading against better-informed counterparties. A positive quoted spread is an opportunity to earn revenue, not a guarantee of profit.

A quote is not a completed round trip

Imagine a hypothetical stock quoted at USD 99.98 bid / 100.02 ask, each for 100 shares. The midpoint is 100.00 and the full spread is 0.04 dollars per share. We will ignore fees, financing, dividends and hedging costs initially.

Two different outcomes illustrate the business:

What actually happensCash change (USD)Final sharesGross result
Buy 100 at the bid, then sell 100 at the ask−9,998 + 10,002 = +40USD 4 realised trading profit
Buy 100 at the bid; still hold them when the midpoint becomes 99.90−9,998100USD −8 marked trading P&L

In the first case, both specified fills occur. The matching quantities give

100(100.02−99.98)=4 USD.100(100.02-99.98)=4\text{ USD}.

The second case has no completed sale. The maker owns stock marked at 100×99.90=9,990100\times99.90=9{,}990 dollars after paying 9,998. Its marked profit and loss is therefore

100(99.90−99.98)=−8 USD.100(99.90-99.98)=-8\text{ USD}.

The ask quote did not force somebody to buy. A resting limit order can remain unfilled, fill partially or become unattractive as the market moves. An actual sale to unwind the stock could occur at a different price from the midpoint, with further costs.

Hypothetical 100-share market-making outcomes. A buy at USD 99.98 followed by a sale at 100.02 gives USD 4 gross at any subsequent mark. Buying only leaves marked P&L of negative USD 8 at a later midpoint of 99.90 and positive USD 2 at 100.00.
Hypothetical 100-share market-making outcomes. A buy at USD 99.98 followed by a sale at 100.02 gives USD 4 gross at any subsequent mark. Buying only leaves marked P&L of negative USD 8 at a later midpoint of 99.90 and positive USD 2 at 100.00.
Original hypothetical comparison, with USD per share on the horizontal axis and total USD P&L on the vertical axis. The solid line shows alternative later marks for the same open inventory, not a time series. The dashed line assumes both round-trip fills have already occurred; all costs are excluded.

Keep a cash ledger and an inventory ledger

For an initially flat maker, let CC be cumulative trading cash flow, qq its signed share inventory and mm the current midpoint. Before costs, the incremental marked trading result is

Π=C+qm.\Pi=C+qm.

A purchase of nn shares at bid bb reduces cash by nbnb and increases inventory by nn. A sale at ask aa adds nana to cash and reduces inventory by nn. For other instruments, contract multipliers and settlement conventions must also enter the accounting.

The stock purchase requires funding or capital even though this ledger measures changes relative to the starting position. USD 4 of spread revenue is not a return on four dollars of capital. Financing a long position, borrowing stock for a short position, margin and hedging all affect the economics. Net P&L also includes commissions, venue charges or rebates where applicable, and the cost of liquidating residual inventory. Fee arrangements depend on the venue and account; supplying liquidity does not universally earn a rebate.

This is why trading volume, spreads and net profits must be measured separately. More fills can increase revenue while increasing exposure to unfavourable price moves.

Why a fill can be bad news

The one-sided purchase initially looks favourable against the 100.00 midpoint: it buys two cents below that benchmark. Its later loss can be decomposed as

100(99.90−99.98)=100(100.00−99.98)+100(99.90−100.00)=2−10=−8 USD.\begin{aligned} 100(99.90-99.98) &=100(100.00-99.98)+100(99.90-100.00)\\ &=2-10=-8\text{ USD}. \end{aligned}
The initial USD 2 price concession is outweighed by a USD 10 inventory markdown. A maker must examine what tends to happen conditional on receiving a fill. For a passive buy evaluated at a fixed later horizon hh, the relevant gross expected mark is
E[mh−b∣bid fills],\mathbb{E}[m_h-b\mid\text{bid fills}],

per share, with the decision-time information and bid held fixed. Multiplying an unconditional average price change by an assumed number of fills misses the selection mechanism.

Adverse selection occurs when the counterparties choosing to trade are systematically more favourable to themselves than the maker's valuation allowed for. For example, a trader with faster information about a fall in value may sell into a bid that has not yet adjusted. The maker bought below the old midpoint but above the value implied by the new information.

An unfavourable markout on one trade does not prove that the seller had private information. Public news, ordinary price uncertainty and hedging activity can also produce losses. Inventory risk exists even against uninformed flow: the maker can accumulate a position and then suffer an unrelated market move.

The distinction appears in two classic models. Glosten and Milgrom show that asymmetric information can support a positive spread even for a competitive, risk-neutral specialist earning zero expected profit. Avellaneda and Stoikov instead isolate inventory risk and the trade-off between quote attractiveness and execution rates. Their models explain mechanisms under stated assumptions; neither makes every positive spread profitable. Glosten–Milgrom's original abstract and Avellaneda–Stoikov's paper provide the respective foundations.

Quote width, quote centre and size do different jobs

A maker can respond to its state along several dimensions:

  • Width: moving quotes farther apart seeks more compensation per fill, usually at the cost of less attractive prices and fewer executions. The relationship depends on competing quotes and order flow.
  • Centre: a long maker may lower both quotes to make further buying less attractive and selling more attractive. A short maker may lean the other way. New information can also move the centre independently of inventory.
  • Size: reducing the quantity offered on the side that increases an unwanted position limits additional exposure without requiring the same change in price.
None of these adjustments guarantees a fill or a safe exit. On an electronic order book, other orders may have priority at the same price. Allocation may depend on time, displayed size, pro-rata rules or other venue-specific details. A quote that was competitive when submitted can become stale before it is cancelled.
Market making is therefore more than posting symmetric prices around a midpoint. It requires a valuation, an execution policy and controls on position size, funding and loss. A hedge may reduce a chosen exposure while introducing basis risk and transaction costs. Being flat at one instant, or broadly neutral to market direction, does not eliminate information, execution or operational risk.

Explore the information problem in the quoting game

The Market-making game makes these tensions visible using a fictional contract that settles at the sum of four dice or four cards. It has eight quote rounds and lets you choose bid, ask and a size from one to five contracts. The first three items are progressively revealed; the fourth is known to an insider until settlement.
Start with Dice, size one and Calm flow. The initial public expected sum is 14. Compare your quotes with that value using Show fair value, then adjust as items are revealed. Inspect whether each fill increases or reduces your inventory. At settlement, the game separates the price concession against public fair value, the insider-information component and the remaining uncertainty, labelled “Luck”.

Then try Standard or Toxic flow: their insider-arrival probabilities are 40% and 60%, versus 25% for Calm. Wider quotes reduce the game's uninformed trading probability, so protection can also reduce business. Outcomes remain random, and changing the flow starts a new game rather than replaying identical arrivals.

Guest play is limited; a free signed-in account unlocks completion through settlement. This is an interview-style information and inventory exercise. Its contract sizes and mechanics differ from the 100-share stock ledger above; it does not model exchange queues, equity funding or a full exchange market.

For a deeper treatment of fill-conditioned losses and why order-flow patterns do not by themselves identify informed traders, see Order Flow and Adverse Selection. The linked page is a public preview; the complete Programme lesson requires membership.

Sources

  • John C. Hull, Options, Futures, and Other Derivatives, 9th edition, Global Edition, §10.5, “Trading”, subsection “Market Makers”. Used for bid/offer orientation and the intermediation role, not as a statement of current venue rules or a guarantee of continuous execution.
  • Rishi K. Narang, Inside the Black Box, 2nd edition, Chapter 7, “Aggressive versus Passive”, and Chapter 15, “Contractual Market Making”. Used for passive-order uncertainty, allocation differences and inventory intermediation. The stock scenario and figure here are original.
  • Lawrence R. Glosten and Paul R. Milgrom (1985), “Bid, ask and transaction prices in a specialist market with heterogeneously informed traders”, Journal of Financial Economics 14(1), 71–100. The checked publisher abstract establishes that asymmetric information can create a spread without positive expected dealer profits.
  • Marco Avellaneda and Sasha Stoikov (2008), “High-frequency trading in a limit order book”, Quantitative Finance 8(3), 217–224, especially §§2.1–2.4. The model separates inventory-sensitive valuation from the likelihood of quote execution under stylised price and arrival assumptions.
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  • market making
  • liquidity
  • bid ask spread
  • inventory risk
  • adverse selection
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