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. 015Two games have exactly the same expected value. Which one would you choose to play?Expected valueIntermediatetechnicalAkuna CapitalSales and Trading · Chicago · 2025Belvedere TradingProp Trading · Chicago · 2022

   Say this

   If the expected values tie, I choose on variance, on how many times I get to play, and on whether any outcome can wipe me out. As a one-off with a fixed stake I take the lower-variance game. Repeated many times with the ability to size, I might prefer the higher-variance one.

   Then walk it

   1. First, ask the question the interviewer wants you to ask: how many times do I get to play, and can I choose my size? Those two facts change the answer completely.
   2. One shot, fixed size: take low variance. Same mean, less dispersion, strictly better under any concave utility, and a trader's utility is concave because a bad first day costs them their limits.
   3. Repeated, and I can size: variance becomes something I can dial. Kelly says bet a fraction proportional to edge over variance, so the high-variance game just gets a smaller position. Per unit of risk they may be identical.
   4. Then the killer criterion, which is ruin. If one game has any probability of a loss larger than my capital, its long-run growth rate is minus infinity regardless of its expected value. Expected value is a bad objective when the bet is not repeatable.
   5. One more real consideration: correlation with everything else I have on. A game with the same mean and variance but zero correlation to my book is worth more than one that doubles my existing exposure. On a desk that is usually the deciding factor.

   Where candidates lose it

   Saying I am indifferent because the expected values are equal. That answers the arithmetic and fails the question, which is about risk preference. Also do not just say I prefer lower variance and stop, because the interesting answer depends on repetition, sizing and ruin. Ask the clarifying question first.

   Expect next

   • What if you could play one of them a thousand times?
   • How would you size each one?
   • Explain the Kelly criterion and why traders bet less than Kelly.

   Reported by candidates at Akuna Capital (Sales and Trading, Chicago, 2025); Belvedere Trading (Prop Trading, Chicago, 2022). Source: Wall Street Oasis.

2. 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.

3. 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.

4. 077Given an array and a window of size k, return the maximum in each window as it slides.ProgrammingIntermediatetechnicalAkuna CapitalQuant Development · Chicago · 2025

   Say this

   Monotonic deque, O(n) total. Keep a deque of indices whose values are strictly decreasing. Before pushing a new index, pop from the back everything smaller than the new value, and pop from the front anything that has fallen out of the window. The front is always the maximum.

   Then walk it

   1. Why the deque is monotonic: if a new element is larger than something behind it, that older smaller element can never be the maximum of any future window, because the new one is both larger and more recent. So it is safe to discard permanently.
   2. Each index is pushed once and popped once, so the total work is O(n) even though a single step can pop many elements. That amortised argument is the thing to say out loud, because it is what distinguishes this from the naive O(n k).
   3. Store indices, not values, so you can test whether the front has expired by comparing front index against i minus k plus 1.
   4. Alternatives and why they are worse: a max heap gives O(n log k) and needs lazy deletion of expired entries. A balanced BST or a multiset gives O(n log k) too. Both are fine and both are beaten by the deque.
   5. Where this actually matters on a trading system, which is worth mentioning: rolling extremes over a tick window, running high and low for a breakout signal, and rolling maximum drawdown. The same structure with the comparison reversed gives you the rolling minimum, and the O(1) amortised cost per tick is what makes it usable in a hot path.

   Where candidates lose it

   Reaching for a heap and stopping there. The heap answer is acceptable but it is not the answer to this question, and the interviewer is specifically looking for the monotonic deque and the amortised O(n) argument. Also remember to expire the front by index, which is the bug that shows up most often in live coding.

   Expect next

   • Prove the amortised complexity.
   • Now give me the rolling median instead.
   • How would you handle a window defined by time rather than by count?

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

5. 097Describe a technical challenge you solved, so that a non-expert understands it but an expert still learns something.Fit and motivationHardsuperdayAkuna CapitalTrading · Chicago · 2026

   Say this

   Structure it in three layers. One sentence on the problem in plain language that anyone would care about, then the mechanism in an analogy with no jargon, then one specific technical detail that a specialist would find non-obvious. The last layer is what the question is really asking for.

   Then walk it

   1. Layer one, the stakes in plain words: our pipeline took six hours and we needed it in twenty minutes, or the model was accurate in testing and wrong in production and nobody knew why.
   2. Layer two, the mechanism by analogy. Pick an analogy that is load-bearing rather than decorative. For a cache: it is like keeping the twenty files you use on your desk instead of walking to the archive each time, and the hard part is deciding what to throw off the desk.
   3. Layer three, the detail for the expert. One precise, surprising thing. The bottleneck was not compute, it was that we were re-parsing timestamps sixty million times, and interning them cut the runtime by eighty percent. Or: the bug was that the validation split was random rather than chronological, so the model was reading the future.
   4. Say what you rejected and why. That is where an expert learns something, because it shows the decision space and not just the destination.
   5. And control the length. Ninety seconds, then stop and let them ask. The hardest part of this question is not the content, it is the discipline to stop talking, and a candidate who tests understanding by pausing rather than narrating for five minutes has already demonstrated the skill being measured.

   Where candidates lose it

   Picking either the audience-friendly version or the expert version and doing only one. The question explicitly demands both layers. Also do not choose your most complicated project, choose the one where you can name one genuinely surprising detail, because the surprise is what makes an expert lean in.

   Expect next

   • What was the alternative you rejected, and why?
   • How did you know your fix actually worked?
   • Explain it again, but in thirty seconds.

   Reported by candidates at Akuna Capital (Trading, Chicago, 2026). 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.