Blog · Quant interviews
The market-making interview game, played out
"Make me a market" is less a probability question than a conversation about risk. The fair value is usually easy. What the interviewer watches is how wide you quote, what you do when they trade, and whether you ask who you are trading with.
The game runs the same way at most market makers. The interviewer names something uncertain, such as the sum of some dice, the number of windows in a building or tomorrow's temperature, and asks for a bid and an offer: the price at which you will buy and the price at which you will sell. They may buy from you, sell to you or do nothing. Then they change something and you quote again. Below is one round played out with numbers, then the part of the game most candidates miss.
The opening quote
Three dice are rolled behind a screen. "Make me a market on the total."
The fair value is 3 × 3.5 = 10.5. The standard deviation of the total is √(3 × 35/12) ≈ 2.96. A quote of 10 at 11, half a point either side, is tight; 8 at 13 is wide. Neither is wrong in itself. What matters is that you can say why. Here nobody knows more about the dice than you do, so there is no reason to be wide, and a tight quote such as 10 at 11 is the right start. Quoting 5 at 16 to be safe is the most common opening mistake: it is a market nobody would trade on, and the interviewer will simply ask you to tighten it.
Say how many you are quoting for, too. "10 at 11, five up" means you will buy or sell five at those prices. If you leave the size out, the interviewer will ask.
Being traded with
"I buy five at 11." You are now short five at 11, against a fair value of 10.5, so you expect to make half a point on each. Say so: tracking your position and its expected profit aloud is part of the test.
"One of the dice is a 5." The fair value is now 5 + 2 × 3.5 = 12. Your short is losing a point each in expectation. Move the quote to the new value, then lean it towards reducing your position. Centred, it would be 11.5 at 12.5. You are short and would like to buy back, so raise the bid: 12 at 12.5 invites sellers and still sells above fair value if someone buys. Leaning the quote is exactly the instinct the game is for.
What the interviewer is looking for at this stage is quick, calm updating. You will lose on some trades. A candidate who refuses to move the quote, or who widens it to 6 at 18 after one bad trade, is telling the interviewer how they would trade a real loss.
The question to ask: who is trading with me?
In the dice game nobody sees the dice, so a trade tells you nothing. Real counterparties are not like that, and the better interviewers change the rules to see whether you notice. Suppose instead:
A card is drawn from ten, numbered 1 to 10. Half the time the other side has seen it and trades only when it profits them; otherwise they buy or sell at random.
The fair value before any trade is 5.5. Against a purely random trader, 5 at 6 would earn half a point a trade. Now work out what being lifted at 6 means. If the trader has seen the card, they buy only when it is 7 or more. If not, they buy half the time, whatever the card. Given that they bought, the expected card is
(½ × (7 + 8 + 9 + 10)/10 + ½ × ½ × 5.5) ÷ (½ × 4/10 + ½ × ½) = 3.075 ÷ 0.45 ≈ 6.83
So a sale at 6 loses 0.83 on average. Every offer from 6 up to 6.83 loses; only above 41/6 ≈ 6.83 does a lift stop costing you money, and by symmetry the bid has to sit below 4.17. The market has to be about 2.7 wide, where against uninformed traders 1 was enough. That widening is adverse selection, and it is the reason spreads exist. An interviewer who hears you ask "does the other side know anything I don't?" before you quote has heard the most important thing a market maker says.
Markets on things you cannot calculate
Some prompts have no exact fair value: the number of piano tuners in London, the height of the building you are in. These are estimation questions with a quote at the end. Build the estimate from parts you can defend, say which part you trust least, and set the width from that. A quote such as 150 at 400 for an estimate you might be wrong about by a factor of two is reasonable; the width is roughly proportional to the level, because the uncertainty is in ratios rather than in units.
Then expect to be traded against. If the interviewer buys at 400, ask yourself whether they know the answer. Usually they do. Moving your estimate up after their trade is not weakness, it is the adverse selection lesson applied.
What is being marked
| What you do | What it shows |
|---|---|
| State the fair value and its uncertainty before quoting | You price before you trade |
| Quote a width you can justify, with a size | You will actually make a market |
| Keep track of your position and profit aloud | You know your risk at every moment |
| Move quickly to the new value after information | You do not anchor on a losing position |
| Lean the quote to reduce a position | You manage inventory, not just value |
| Ask whether the other side is informed, and widen if so | You understand why spreads exist |
Forty-two practice questions on expected value and quoting, each with a worked answer, are in the market-making question bank. The firms that use the game most are covered in our Optiver, IMC and DRW guides.
Questions people ask
How wide should my first market be?
As wide as your uncertainty about the value and about the other side justifies, and no wider. When nobody has better information, as with dice behind a screen, a tight market around the fair value is right. When the counterparty may know more, widen, and say that this is why. Interviewers mark the reasoning, not the exact numbers.
Is the aim to make money in the game?
Not exactly. Interviewers often trade against you with information you do not have, so you will lose some trades whatever you do. What they want to see is that you know your position, update your price when you learn something, and do not panic or freeze after a loss.
What if the interviewer keeps buying from me?
Take it as information. Repeated buying suggests they think the value is higher, so raise your quote, and lean it to cover the short you are building. Keeping the same offer while someone keeps lifting it is the error the question is designed to catch.
Do I need to know options theory for this?
Not for the game itself, which is about expected value, uncertainty and information. Some firms follow it with questions on options, such as the value of a call on a die roll, but those are separate rounds.
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The Quant Careers Report
Market-making games appear in the trading rounds at most of the firms the report covers. It sets out how 13 firms interview, the pay they state and when to apply.