Quant interview preparation

Prop market making and quantitative research, weighted the way the interviews actually are: probability and expected value, statistics and machine learning, market making logic, programming and options. Every question is either traced to a named firm from a public candidate report, or tagged at desk level when we could not trace it, and every probability answer shows the reasoning path rather than just the number.

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Question bank

100 questions, mapped to the firms that asked them

Questions
100
Traced to a firm
53
Firms
15
Updated
September 2026
Asked at
All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4D.E. Shaw3Jane Street3AQR Capital Management2DRW2Millennium Management2Schonfeld2Squarepoint Capital2Susquehanna International Group2Belvedere Trading1Optiver1
Topic
All topicsProbability10Coins, cards and games6Expected value8Statistics11Market making15Estimation and mental maths4Stochastic processes4Regression5Machine learning6Time series6Programming10Options and derivatives8Fit and motivation7
Level
AnyCoreIntermediateHard
Type
AnyBrainteaserTechnicalCaseMarket viewFit
Showing 1–2 of 2 · filtered from 100Clear filters
  1. 016You win a hundred dollars if you roll a ten with two dice. How much would you risk to play?Market makingIntermediatetechnicalAkuna CapitalTrading · Chicago · 2025

    Say this

    Fair value is eight dollars and a third. Three of the 36 outcomes make ten, so probability is 1/12 and the expected payoff is 100 over 12. I would pay up to about seven to leave edge, and if I am being asked to make a two-way price I would quote around 7 at 9.

    Then walk it

    1. Count the outcomes: 6-4, 4-6, 5-5. Three ways out of 36, so 1/12, about 8.33 percent.
    2. Expected payoff 100 times 1/12 equals 8.33. That is fair value, and fair value is where you break even, not where you trade.
    3. So I need edge. I would bid 7 and offer 9 if I have to two-way it, which is about a dollar and a half of edge either side, roughly fifteen percent of fair value. That width reflects the fact that I cannot hedge a one-off die roll.
    4. Size matters as much as price. This bet has a standard deviation of about 28 dollars against a mean of 8.33, which is a terrible ratio. I would do it small even at a good price, and I would want to repeat it many times rather than do it once large.
    5. If the game is repeatable and I can do it a thousand times, I pay closer to 8. The edge I demand is compensation for variance I cannot diversify, and repetition diversifies it.

    Where candidates lose it

    Answering with the fair value of 8.33 as if that were your bid. A trader never pays fair value, and saying eight and a third is what I would risk tells the interviewer you do not understand where the money comes from. Quote a price below fair value, name your width, and say your size.

    Expect next

    • Now make me a two-way market on it and I will trade you.
    • What if I could roll a hundred times?
    • What is the standard deviation of your P&L on one play?

    Reported by candidates at Akuna Capital (Trading, Chicago, 2025). Source: Wall Street Oasis.

  2. 062You have made me a market. If the true answer falls inside your market, how much would you risk to win a hundred dollars?Market makingHardtechnicalAkuna CapitalTrading · Chicago · 2025

    Say this

    That depends entirely on how wide I quoted and how confident I am, and those two are linked. If I quoted a tight market I should not be very confident the answer is inside it, so I would risk little. If I quoted wide, I should be confident, and I would risk more. The honest answer is to price my own probability and then bet a fraction of Kelly.

    Then walk it

    1. The question is a consistency check. A tight market is a strong claim, and the interviewer is testing whether my stated width matches my stated confidence. If I said 300 at 310 on the number of Starbucks in New York and then say I am 90 percent sure the truth is inside, one of those is a lie.
    2. So I quantify. Suppose I think there is a 60 percent chance the answer is inside my market. Then risking x to win 100 has expected value 0.6 times 100 minus 0.4 times x, which is positive for x below 150. So fair value is 150 and I would bet meaningfully below that.
    3. Kelly gives the size: bet a fraction of capital equal to edge over odds. At 60 percent on an even-money-ish bet the full Kelly fraction is around 20 percent of capital, and I would take a quarter to a half of that, because my 60 percent is itself an estimate and overbetting Kelly is far more punishing than underbetting.
    4. I would also name the asymmetry in the setup. The interviewer chooses whether to take the bet, so they only take it when they think my price is wrong. That is adverse selection, and it means I should shade my number down from the naive fair value.
    5. So a concrete answer: with a 60 percent belief and an adversary who selects, I would risk around 50 to 70 dollars to win 100, and I would say out loud that I am shading below the 150 fair value because you get to choose whether to trade.

    Where candidates lose it

    Giving a bravado number like I'd risk a thousand, or refusing to name a figure. Both fail. Also failing to notice that your quoted width already implied a confidence level, so an answer inconsistent with your own market gets picked apart immediately. Name your probability, compute fair value, then shade for adverse selection.

    Expect next

    • So tighten your market and answer again.
    • What if I let you choose which side of the bet to take?
    • Explain why you shaded below fair value.

    Reported by candidates at Akuna Capital (Trading, Chicago, 2025). Source: Wall Street Oasis.

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.