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. 014Here is a game. What is the expected value of winning under three different strategies, and which one would you choose?Expected valueHardsuperdayJane StreetTrading · London · 2025OptiverGeneralist · Chicago · 2025

   Say this

   Set up the state and the decision rule before you compute anything, price each strategy with a clean conditional expectation, then choose on expected value first and on variance and ruin risk second. Say the comparison out loud as you go so the interviewer can follow your bookkeeping.

   Then walk it

   1. Step one, define the state precisely: what you know when you decide, and what the payoff function is. Most errors in these problems are specification errors, not arithmetic.
   2. Step two, price each strategy by conditioning on the first move. E of payoff equals the sum over first outcomes of probability times conditional value. If the game is repeated or recursive, write V in terms of V and solve the fixed point.
   3. Step three, do the arithmetic in fractions, not decimals. Fractions let the interviewer audit you and they do not accumulate error.
   4. Step four, choose. If one strategy dominates on expected value, say so and stop. If they are close, break the tie on the second moment: I would take the lower-variance strategy at the same expected value, and I would pay a small amount of expected value to avoid a path that can lose more than my stake.
   5. Then state the assumption you are relying on, unprompted: whether you may stop adaptively, whether the game is repeated, and whether the payoff is linear in money. Those three change the answer more than the arithmetic does.

   Where candidates lose it

   Diving into arithmetic before defining the state, and then losing track of which branch you are on. The other failure is picking the highest expected value without a word about variance. A trading floor cares about the distribution of outcomes, so say which strategy you would actually run with real money and why.

   Expect next

   • Now suppose you can play the game a hundred times. Does your choice change?
   • What if the payoff were doubled but the probability halved?
   • What is the variance of your preferred strategy?

   Reported by candidates at Jane Street (Trading, London, 2025); Optiver (Generalist, Chicago, 2025). Source: Wall Street Oasis.

2. 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.

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.