Market-Making Interview Questions: Worked Drills

A market-making interview exercise asks you to make decisions while someone trades against your prices. You need to explain a fair value, quote a bid and ask, track the resulting position, and revise your decisions as information changes. An attractive-looking spread alone does not establish that your trades are profitable.

The exercises below are original practice scenarios. They build from a fully specified payoff to inventory management and informed trading. Each answer states its assumptions so you can challenge the reasoning, rather than memorize a price.

For employer context, Jane Street's Probability & Markets guide includes making markets alongside probability and expected value. Its trading interview overview emphasizes methodical, collaborative problem solving. Your own interview format may differ; confirm logistics with your recruiter.

1. Define the contract before quoting

Imagine a contract that settles for the result of one fair six-sided die. A result of four pays $4 per contract. Settlement happens after all trades. There are no fees, borrowing charges or position limits for the first exercise, and fractional-dollar prices are allowed. You are risk-neutral and have no private information.

Question: what is its expected payoff, and what does a quote of 3.25 / 3.75 mean?

Show answer and explanation

The expected payoff is (1 + 2 + 3 + 4 + 5 + 6) / 6 = $3.50.

Your bid is $3.25: you buy a contract from someone who sells to you. Your ask is $3.75: you sell a contract to someone who buys from you. The spread is $0.50 and the midpoint is $3.50.

Buying at $3.25 has expected settlement profit of $0.25. Selling at $3.75 also has expected settlement profit of $0.25, provided the counterparty's decision contains no information about the die result. Neither trade guarantees a profit.

Before answering, ask about the contract, trade quantity, timing and allowed prices. Do both sides see the same information? Can the other person decide whether to trade? Does every contract settle on the same die, or on an independent die? These details change the risk and sometimes the fair value.

For the definitions behind the exercise, read market making, bid-ask spreads and expected value.

2. Track cash and inventory through every fill

Use the same contract, starting with zero cash and zero inventory. Keep the quote at 3.25 / 3.75 for this drill. The counterparty buys two contracts, then sells you three, then buys one. Positive inventory means you own contracts. Positive cash means money received.

Question: after each trade, what are your inventory and cash? If the die settles at four, what is your total profit?

Show answer and explanation

Counterparty action	Your trade	Inventory change	Cash change	Total inventory	Total cash
Buys two	Sell two at 3.75	−2	+7.50	−2	+7.50
Sells three	Buy three at 3.25	+3	−9.75	+1	−2.25
Buys one	Sell one at 3.75	−1	+3.75	0	+1.50

You finish flat with $1.50 cash. Settlement adds zero because inventory is zero. Your profit is $1.50 whether the die settles at one, four or six.

For this simple contract, total settlement profit is cash + inventory × settlement value. After the second trade alone, settlement at four would give −2.25 + 1 × 4 = $1.75. At that point you still have payoff risk.

Say each update aloud: “They bought two, so I sold two. I am short two and have received seven dollars fifty.” This prevents the common error of recording the customer's purchase as your own purchase. Keep price and quantity separate; one fill can contain several contracts.

3. Explain risk when expected profit looks good

Reset your position. An uninformed counterparty sells you four contracts at $3.25. All four settle on the same die.

Question: compute profit if the die shows one, three or six. What is expected profit?

Show answer and explanation

Your inventory is +4 and cash is −$13. Profit is 4 × settlement − 13.

Settlement	Total profit
1	−$9
3	−$1
6	+$11

Expected profit is 4 × 3.50 − 13 = $1. Four favorable expected-value trades can still produce a large loss relative to their expectation.

The shared settlement matters. Buying four contracts increases exposure to one outcome; it does not diversify across four independent dice. If each contract settled independently, expected profit would remain $1, but the distribution of total profit would change.

A useful follow-up is to impose a two-contract position limit. You should then explain why you cannot accept all four at the original quantity. Ask whether partial fills are permitted. An interview exercise may reward a defensible refusal or a smaller quote rather than unlimited trading.

4. Separate an inventory adjustment from a value update

You are long four contracts. The die remains fair and no new information has arrived. Now add an exposure-management objective: you would like to reduce the position, even if that means accepting less expected profit per sale.

Question: explain a possible quote adjustment without claiming that the die's expected payoff changed.

Show answer and explanation

One illustrative adjustment is moving the quote from 3.25 / 3.75 to 3.10 / 3.60, with a smaller quantity available at the bid. The lower ask makes buying from you more attractive; the lower bid makes selling to you less attractive. Both effects can help reduce a long position.

The $3.50 expected payoff is unchanged. Your quoted midpoint is now $3.35 because inventory affects the prices at which you are willing to trade. The exact adjustment is a policy choice, not a uniquely correct number.

Whether this works depends on customer behavior and the rules of the game. Someone can decline to trade, and a more attractive ask sacrifices some expected margin. If your position limit is binding, price changes alone may be insufficient; reduce size or stop buying.

Explain the direction before selecting numbers. If you are short, the motivation reverses: you may want to encourage sellers and discourage additional buyers. Widening both sides symmetrically around the same midpoint does not specifically target one inventory direction.

Book a quant consultation if you want to discuss how to structure practice around your trading background and target roles. Bring a completed ledger and the decisions you found hardest to explain.

5. Reprice when information changes the payoff

Reset inventory to zero. Before you quote, a reliable announcement reveals that the die result is even, but not which even number occurred. Each of two, four and six remains equally likely.

Question: what is the new fair value? Is the original ask of $3.75 still favorable for you?

Show answer and explanation

The conditional expected payoff is (2 + 4 + 6) / 3 = $4. Selling at $3.75 now has expected profit of 3.75 − 4 = −$0.25 per contract. Your old quote is stale.

An illustrative symmetric quote would be 3.75 / 4.25 if you retain the original half-spread. This is a fresh value estimate, unlike the inventory adjustment in the previous exercise.

Do not move the quote merely because someone traded. State what information the trade or announcement provides. Updating requires a model of what the other side knows and why they act. A customer needing cash and a customer who knows settlement are different counterparties.

6. Test adverse selection with a fully specified customer

Return to the unrevealed fair die. Quote 3.25 / 3.75. Now assume the counterparty sees the actual result before trading. They can trade exactly one contract. They buy when the result exceeds your ask and sell when it is below your bid.

Question: calculate your expected profit per interaction. Why does a positive spread fail to protect you?

Show answer and explanation

They sell to you on results one, two and three. Your respective profits are −2.25, −1.25 and −0.25. They buy from you on four, five and six, producing profits of −0.25, −1.25 and −2.25 for you.

The six outcomes are equally likely. Expected profit is (−2.25 − 1.25 − 0.25 − 0.25 − 1.25 − 2.25) / 6 = −$1.25.

Conditional on a customer buying, the average settlement is five, so selling at $3.75 loses $1.25 on average. Conditional on a customer selling, average settlement is two, so buying at $3.25 also loses $1.25 on average.

The unconditional $3.50 expectation was correct before considering customer behavior. It is insufficient for evaluating a fill selected by an informed person. You need expected payoff conditional on the trade. Review conditional probability if that distinction feels unfamiliar.

In this particular game, a bid of one and ask of six would prevent strictly profitable informed trades, assuming the customer declines trades with zero advantage. That eliminates trading rather than creates a useful business. Realistic exercises can introduce uninformed demand, noisy information, competition or costs; state those changes before drawing conclusions.

How to review your practice

Replay a short sequence with a partner who changes only one assumption at a time. First check bookkeeping, then add a position limit, then introduce a public signal, then change the counterparty's information. Avoid changing all four together before you can explain the simpler cases.

Afterward, answer five questions: Did I define settlement? Did I record my side of each trade? Did I distinguish expected profit from possible loss? Did I explain why a fill changed my estimate? Did I separate inventory management from a genuine information update?

If the arithmetic caused hesitation, practice the calculations in mental math for quant trading. Use the quant interview study plan to alternate written solutions with spoken exercises. The goal is a chain of decisions you can defend when the assumptions change.