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. 021If n(n+1)/2 is the sum of the integers from one to n, what is the formula for the sum of the squares, and can you derive it?Estimation and mental mathsCoretechnicalSquarepoint CapitalTrading · London · 2025

    Say this

    n(n+1)(2n+1)/6. The fastest derivation is telescoping: expand (k+1) cubed minus k cubed as 3k squared plus 3k plus 1, sum both sides from 1 to n, and solve for the sum of squares.

    Then walk it

    1. Left side telescopes to (n+1) cubed minus 1.
    2. Right side is 3S2 plus 3S1 plus n, where S2 is what you want and S1 is the known n(n+1)/2.
    3. So 3S2 equals (n+1) cubed minus 1 minus 3n(n+1)/2 minus n. Grind it out and you get S2 equals n(n+1)(2n+1)/6.
    4. Check at n equal to 3: 1 plus 4 plus 9 equals 14, and 3 times 4 times 7 over 6 equals 14. Always test a small case out loud, it costs three seconds and catches sign errors.
    5. The reason a desk asks this: it is the derivation that matters, not the formula. The same telescoping trick gives the sum of cubes, which is n squared (n+1) squared over 4, and it is the discrete analogue of integration by parts. And the practical use is immediate, because the variance of a uniform die and the variance of a linear time trend in a regression both fall straight out of this sum.

    Where candidates lose it

    Reciting the formula with no derivation. The interviewer already knows the formula, so the answer is worth nothing on its own. Show the telescoping and verify on n equals 3. Fumbling the algebra after setting it up correctly is forgivable; having no method is not.

    Expect next

    • Now the sum of cubes.
    • Use it to get the variance of a fair n-sided die.
    • What is the sum of 1 over k squared as n goes to infinity?

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

  2. 036The sample variance with the n minus one correction is unbiased. Is its square root an unbiased estimator of the standard deviation?StatisticsHardtechnicalSquarepoint CapitalQuantitative Research · London · 2026

    Say this

    No. The square root is concave, so by Jensen's inequality the expected square root is strictly less than the square root of the expected value. The sample standard deviation is biased downwards, always, for any distribution with positive variance.

    Then walk it

    1. Jensen: for a strictly concave g, E of g(X) is less than g of E of X unless X is degenerate. With g the square root and X the unbiased sample variance, E of s is less than sigma.
    2. Size the bias for normal data. E of s equals c4(n) times sigma, where c4 is a known constant involving gamma functions. At n equal to 2, c4 is about 0.798, so you understate sigma by 20 percent. At n equal to 10 it is 0.9727, a 2.7 percent understatement. At n equal to 30 it is 0.9914.
    3. So the bias is order 1/(4n) and it vanishes as n grows. It is a real problem for short samples and irrelevant for long ones.
    4. Unbiasedness is also not preserved under any nonlinear transform, which is the general lesson. The unbiased estimator of sigma squared does not give you an unbiased estimator of sigma, or of 1/sigma, or of log sigma.
    5. Where this bites on a desk: annualised volatility estimated from a few weeks of data, and any Sharpe ratio, since the Sharpe divides by s. Understating s inflates the Sharpe, so short-sample Sharpes are biased upwards. That is worth saying because it connects a textbook Jensen question to a live problem in strategy evaluation.

    Where candidates lose it

    Saying yes because the variance estimator is unbiased. Unbiasedness does not survive a nonlinear function. Name Jensen explicitly, give the direction of the bias, and quantify it with c4 for at least one small n. The follow-up about Sharpe ratios is where the real conversation is, so get there yourself.

    Expect next

    • How would you correct it?
    • What does that imply for a Sharpe ratio estimated on a short sample?
    • Is the sample correlation coefficient unbiased?

    Reported by candidates at Squarepoint Capital (Quantitative Research, London, 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.