Quant interview preparation

Questions

100

Traced to a firm

53

Firms

15

Updated

September 2026

Asked at

All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4DED.E. Shaw3Jane Street3ACAQR Capital Management2DRW2Millennium Management2Schonfeld2SCSquarepoint 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

1. 061What is a market maker actually paid for, and how do you decide how wide to quote?Market makingCoretechnicalProp trading firmsQuant trading

   Say this

   You are paid to provide immediacy, and the bid-ask spread is the fee. Width is set by the risks you are taking on: how uncertain you are about fair value, how much adverse selection you expect, how long you will be stuck with the position, and how volatile it is while you hold it.

   Then walk it

   1. The business model in one line: buy at the bid, sell at the offer, turn over the inventory many times a day, and capture a fraction of the spread on each round trip. You are not forecasting direction, you are being compensated for warehousing risk.
   2. The four inputs to width. One, uncertainty about the true value, which is wide in an illiquid name and tight in a liquid one. Two, expected adverse selection, which is the probability the person trading with you knows something. Three, expected holding period until you can offload or hedge. Four, volatility over that holding period.
   3. A rough decomposition: half-spread should cover expected adverse selection cost plus inventory risk plus your fixed costs, plus a margin. In a liquid future the first term dominates and you quote one tick. In a wide illiquid option you might quote ten percent of the premium.
   4. Then the competitive constraint. You do not quote your theoretical width, you quote the tightest width you can justify given who else is on the book, because the trade goes to the best price. So in practice width is min of what I need and what the competition forces.
   5. The number worth knowing: on a liquid listed equity the effective spread is often under a basis point and market makers still make money, because they do enormous volume and their adverse selection is managed in milliseconds. On an illiquid corporate bond a dealer might need 50 basis points for the same economics, because they will hold it for days.

   Where candidates lose it

   Describing market making as making money on the spread with nothing about adverse selection or inventory. The spread is gross revenue, not profit. A candidate who cannot name the two costs that eat it has not understood the business, and this is the single most common weakness in trading interviews.

   Expect next

   • What is your biggest cost as a market maker?
   • Why would you ever quote a market wider than the competition?
   • When would you not want to quote at all?
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.

3. 063Make me a market on something you cannot possibly know, and be ready for me to trade either side.Market makingCorephone / first roundProp trading firmsQuant trading

   Say this

   I would estimate fair value out loud, set a width that reflects how uncertain I am, quote it, and then stand by it. And I would say my size, because a market without a size is not a market.

   Then walk it

   1. Do the estimate first and say it: here is my central estimate and here is why. Then convert uncertainty into width. If my estimate is 300 but I could easily be wrong by fifty percent, my market should be something like 250 at 350, not 298 at 302.
   2. Then quote a size. Ten dollars a unit, or one lot. Naming your size unprompted is a strong signal, because it shows you understand a quote is a commitment.
   3. The interviewer will then trade you and immediately ask if you are happy, or they will tell you the answer is far outside your market. Both are tests of composure. The correct reaction is to update and re-quote, not to argue.
   4. When they trade one side, that is information. If you get lifted instantly on your offer, the market is probably above your offer, so shift both bid and offer up and consider widening. Skewing rather than freezing is what separates a trader from a calculator.
   5. The one thing you must not do is quote too tight to look confident. A tight market you cannot defend gets arbitraged in one question, and the interviewer will do it on purpose. Wide but honest beats tight and wrong, and you can always tighten once you have explained your uncertainty.

   Where candidates lose it

   Quoting a market so tight that any trade immediately loses you money, usually because the candidate thinks a narrow spread looks impressive. It looks the opposite. Also never quote a market without a size, and never argue when you get picked off. Update and re-quote.

   Expect next

   • I buy at your offer. Are you happy?
   • Now tighten your market by half.
   • The answer is actually double your offer. What went wrong in your estimate?
4. 064You are long five hundred lots and the market keeps offering below you. What do you do with your quotes?Market makingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   Skew. Lower both my bid and my offer so I am more likely to sell than to buy, because I want to reduce inventory, and widen if the flow suggests the market is informed. Skewing quotes is how a market maker manages inventory without crossing the spread.

   Then walk it

   1. The mechanism: a market maker's reservation price moves against their inventory. Long inventory means I value the next unit less, so my fair value shifts down and my quotes should shift with it. That is the core result of the Avellaneda-Stoikov style inventory models.
   2. Skewing is cheaper than hedging aggressively. If I dump 500 lots at market I pay the spread plus impact immediately. If I skew, I get paid the spread to unwind, just more slowly.
   3. But I need to distinguish two situations. If the offers are noise traders, I keep skewing and unwind profitably. If the offers are informed flow ahead of news, skewing just means I keep buying into a falling market, which is how market makers blow up.
   4. The tell is whether the market comes back. If I sell some and the price recovers, I was providing liquidity. If every trade is followed by the market moving further against me, I am being run over and I should widen, reduce size, or cross the spread and get flat.
   5. So the decision rule I would say out loud: skew first, size down second, and cross the spread third if my position is still growing against me. And I would have a hard limit set in advance, because the one thing you cannot do is decide your maximum loss while you are losing.

   Where candidates lose it

   Answering hold and wait for it to come back, which is the losing trader's answer. Also answering just hedge without noting that hedging costs the spread. The interviewer wants to see the skew mechanism named, and wants to hear you distinguish noise flow from informed flow.

   Expect next

   • How do you tell whether the flow is informed?
   • At what point do you cross the spread and get flat?
   • How would you set your position limit in advance?
5. 065What is adverse selection and why is it a market maker's real cost?Market makingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   Adverse selection is the fact that whoever trades with you chose to, and sometimes they chose because they know something you do not. Your quote gets hit disproportionately when it is wrong, so on average the trades you get are worse than the trades you wanted.

   Then walk it

   1. The mechanism: you post a two-sided quote at your fair value. Uninformed flow hits both sides roughly equally and you earn the spread. Informed flow only takes the side that is mispriced, so those trades lose you money immediately.
   2. The measurement is simple and it is what every market making desk tracks: mark your fills against the mid price a few seconds or minutes later. If your buys are systematically below where the market goes, you are being adversely selected. The industry term is markout.
   3. This is why the spread must be wide enough that the profit from uninformed flow covers the loss to informed flow. Glosten and Milgrom's model makes the spread purely a function of the probability of informed trading, with zero inventory risk at all.
   4. It explains observable behaviour. Spreads widen before earnings and economic releases, when the probability of informed flow spikes. Market makers pay for retail order flow precisely because retail flow is less informed, so it is worth more.
   5. And the extreme version is why quotes get pulled. If adverse selection becomes severe enough that no spread compensates, the correct response is not to widen but to stop quoting. That is what a flash crash looks like from the inside, and saying that shows you understand the business rather than just the term.

   Where candidates lose it

   Confusing adverse selection with inventory risk. Inventory risk is the price moving while you hold a position you did not want. Adverse selection is getting the position in the first place precisely when it is wrong. Interviewers ask candidates to distinguish them, so have both definitions crisp and know that markout is how you measure it.

   Expect next

   • How is that different from inventory risk?
   • How would you measure it on your own fills?
   • Why is retail order flow worth paying for?
6. 066Explain the Kelly criterion, and why do real traders bet less than it says?Market makingHardtechnicalQuant tradingProp trading firms

   Say this

   Kelly maximises the expected growth rate of your capital by betting a fraction equal to your edge divided by the odds. For an even-money bet at probability p, that fraction is 2p minus 1. Real traders bet a fraction of it because Kelly assumes you know your edge exactly, and overbetting is far more damaging than underbetting.

   Then walk it

   1. The derivation in one line: maximise the expected log of wealth, because log wealth is additive across repeated bets and its expectation governs the long-run growth rate. For a bet paying b to 1 with win probability p, the optimal fraction is (pb minus (1-p)) over b.
   2. Numbers: a 55 percent even-money bet gives f equal to 0.1, so ten percent of capital. A 60 percent bet gives 20 percent. That is a lot more than most people's intuition, which is the first surprise of Kelly.
   3. For continuous returns the analogue is mean over variance, which is why a Sharpe ratio maps directly to a leverage level. Full Kelly leverage equals the Sharpe divided by the volatility.
   4. The asymmetry is the key insight. Growth rate as a function of bet size is a concave parabola, so betting half Kelly gives you three quarters of the growth with half the volatility. Betting double Kelly gives you zero growth. Overestimating your edge by a factor of two therefore destroys the entire benefit.
   5. And full Kelly's drawdowns are intolerable in practice: the probability of at some point halving your capital under full Kelly is fifty percent. Nobody running other people's money survives that, and no risk manager permits it. So a quarter to a half Kelly is standard, and the honest reason is parameter uncertainty plus career risk, not mathematics.

   Where candidates lose it

   Reciting the formula without the asymmetry. The gradeable insight is that the growth curve is flat near the optimum and falls off a cliff past it, which is why uncertainty in your edge estimate pushes you to bet less. Also mention the fifty percent chance of a fifty percent drawdown, because it makes the practical argument concrete.

   Expect next

   • What is the probability of a fifty percent drawdown under full Kelly?
   • How does Kelly relate to mean-variance optimisation?
   • How would you size when your edge estimate itself has a standard error?
7. 067What is the difference between a market order and a limit order, and who pays the spread?Market makingCorephone / first roundProp trading firmsQuant trading

   Say this

   A market order takes whatever price is available and pays the spread for certainty of execution. A limit order posts a price and waits, earning the spread if it fills, but with no guarantee it fills at all. You are choosing between price risk and execution risk.

   Then walk it

   1. The taker of liquidity pays. Buy with a market order and you pay the offer, which is above mid, so you start down by half the spread. The passive side on the other end of that trade collects it.
   2. On most exchanges the fee structure reinforces this: makers get a rebate, takers pay a fee. So the maker's economics are spread capture plus rebate minus adverse selection.
   3. The cost of a limit order is not zero, it is optionality you are giving away. A resting bid is a free put you have written to the market: it fills when the price is falling and does not fill when the price rises. That is adverse selection expressed as execution risk.
   4. So the choice is horizon-dependent. If I need to be done now because I have information or a hedge to put on, I pay the spread. If I am providing liquidity or my signal has a multi-day horizon, I post and wait.
   5. Worth adding the practical middle ground, since this is what execution desks actually do: split the order, post passively and cross only when the queue is not filling or when the signal decays. Implementation shortfall against the arrival price is how you measure whether you got that balance right.

   Where candidates lose it

   Getting the definitions right but not answering who pays the spread. The taker pays. The second miss is treating a limit order as free, when the real cost is the option you have written to anyone with better information. Say that and you are ahead of most candidates.

   Expect next

   • What is the hidden cost of a resting limit order?
   • How would you decide between posting and crossing?
   • What is implementation shortfall?
8. 068Why do market makers widen their quotes before a scheduled event like an earnings release or a central bank decision?Market makingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   Because both of their costs spike at once. Expected volatility over the holding period jumps, and the probability that whoever trades with them is better informed jumps too. Wider spreads are the price of continuing to quote into that.

   Then walk it

   1. Inventory risk: any position you hold through the release is exposed to a gap, not a diffusion. You cannot hedge or unwind through the print, so the relevant horizon volatility is much larger.
   2. Adverse selection: more participants have a view, some have better information or faster access to the number, and the flow immediately before a release is disproportionately informed.
   3. You can see it in the options market directly. Implied volatility on the expiry that spans the event is elevated, and it collapses the moment the number is out. That is the volatility crush, and it is a pure statement about event risk being priced.
   4. The usual sequence is widen, then reduce size, then in the final seconds many makers pull quotes entirely, which is why the book gets thin right before a Fed statement and depth collapses.
   5. The interesting trade is on the other side of it. If you think the market is overpaying for the event, you sell that volatility, but the position has a short gamma profile through a gap, so you size it for the tail and not for the expected move. Saying that shows you understand why a wide quote is a risk decision and not just a fee increase.

   Where candidates lose it

   Answering only because volatility is higher. Half the answer is adverse selection, and the interviewer is listening for both. Also be ready to connect it to the options market, since the implied vol term structure around an event is the same phenomenon priced explicitly.

   Expect next

   • What happens to implied volatility right after the print?
   • Would you rather be long or short gamma into the event?
   • Why does the order book get thin rather than just wide?
9. 069You quote a tight market and get lifted on your offer immediately. Are you happy?Market makingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   No, not immediately. An instant fill is usually bad news: it means my offer was the cheapest thing available, which suggests my fair value was too low. I would shift my market up, not celebrate the spread I just earned.

   Then walk it

   1. The right frame is that a fill is information. If the market wanted my offer that fast, my offer was probably below consensus fair value.
   2. The fill I actually want is slow and two-sided: I buy on the bid, sell on the offer, and end the day roughly flat having collected the spread many times. Getting filled on one side only is a warning.
   3. So the immediate action is to move both quotes in the direction of the flow and reconsider the width. The mid moves up, and I may widen because I am now less sure where fair value is.
   4. How to measure whether it was actually bad: markout. Look at the mid a minute later. If the market is above where I sold, I was adversely selected regardless of the spread I booked. Booking the spread and losing on the markout is the classic way a market maker loses money while showing positive spread capture.
   5. The one case where I am genuinely happy is if I know the flow is uninformed, for instance a retail-sized order or a predictable end-of-day hedger. Then an instant fill is exactly the business. So the honest answer is: it depends who traded with me, and I would want to know that before I formed a view.

   Where candidates lose it

   Saying yes, I made the spread. That is the answer of somebody who thinks the spread is profit rather than gross revenue. Instant one-sided fills are the signature of adverse selection, and the interviewer is checking whether your instinct is to update or to congratulate yourself.

   Expect next

   • How would you check whether you were picked off?
   • What do you do with your quotes now?
   • When would an instant fill be good news?
10. 070Something goes badly wrong on your book during the session. How do you react?Market makingIntermediatetechnicalOld Mission CapitalProp Trading · Chicago · 2025

    Say this

    Reduce risk first, diagnose second, and tell someone immediately. In that order. The instinct to understand the problem before acting on it is the wrong instinct when the position is still live and the loss is still growing.

    Then walk it

    1. Step one, stop the bleeding. Pull quotes, flatten or hedge the exposure I did not intend to have, and cap any automated system that might still be adding to it. Getting smaller is almost never the wrong move under uncertainty.
    2. Step two, escalate. Tell the senior trader on the desk and the risk desk straight away, before I know the cause. Every trading floor's disaster stories are about someone who tried to fix it quietly first.
    3. Step three, establish the facts. What is my actual position, what is the realised and unrealised loss, is the pricing wrong or is the position wrong, and is anything still running that I have not stopped.
    4. Step four, only then diagnose and fix. A bad parameter, a stale feed, a hedge that did not go through, a fat finger, a genuine adverse move.
    5. And afterwards, write it up. A one-page post-mortem with a concrete control change is what stops the same failure twice. What a desk actually wants to hear from a junior candidate is that you act to reduce risk without needing permission, and escalate without needing to look competent first. Composure plus disclosure, in that order.

    Where candidates lose it

    Answering that you would investigate the cause first. On a live book that is exactly backwards, and a prop trading interviewer is listening for the reduce-then-escalate-then-diagnose sequence. Also do not claim you would stay completely calm. Say you would act on a checklist precisely because you would not be calm.

    Expect next

    • Who do you tell, and how quickly?
    • Tell me about a time you made a real mistake and what you did.
    • What would you put in the post-mortem?

    Reported by candidates at Old Mission Capital (Prop 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.