Practice · Quant prep · Citadel
Citadel quant research interview
Citadel's quantitative research interviews start with code, not puzzles. The firm says so on its own careers pages, and it is the most common surprise for candidates who prepared only probability.
The process, from Citadel's own pages
- First round. A 45 to 60 minute video interview using CoderPad, covering programming, research ability, data structures and algorithms, and problem solving. Python and C++ are the core languages, but any language is welcome. Source
- Second round. Onsite: usually three to five 60-minute interviews, each mixing technical and behavioural questions. Source
- Final review. Hiring managers across teams decide where you fit; if several teams want you, you choose with your recruiter. Source
- Two firms at once. Interviewing for quantitative research means talking to Citadel and Citadel Securities together. The whole process usually takes four to five weeks. Source
- What the role asks for. Strong probability and statistics (machine learning, time series, pattern recognition, NLP), turning models into code in Python, R or C++, and independent research. Source
What candidates report
Many candidates report an online test before the first interview, with a couple of coding problems and multiple-choice questions on probability and statistics. Later rounds are described as probability puzzles, regression and estimation questions, and coding.
What Citadel is testing
The interview page's advice is unusually direct: spend time on the problem before writing code, ask clarifying questions, share your thought process, discuss trade-offs, and take hints when you get stuck. A silent candidate who writes correct code scores worse than one who explains a slightly slower solution.
The statistics questions tend to test whether you understand what a method does rather than whether you remember its formula: what happens to a regression when the data is duplicated, what one correlation says about another, why an estimator is biased. The problems below are of that kind.
Six practice problems
Written by us to match the types Citadel is publicly reported to ask. None is a copy of a Citadel question.
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Corr(x, y) = 0.6, the standard deviation of x is 1 and of y is 2. You regress y on x, then x on y. What is the product of the two slopes?
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0.36
The slope of y on x is ρ·σy/σx = 1.2, and of x on y is ρ·σx/σy = 0.3. Their product is ρ² = 0.36, whatever the scales. The two regression lines coincide only when |ρ| = 1.
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You duplicate every row of a dataset and rerun ordinary least squares. What happens to the coefficient estimates and to their standard errors?
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Estimates unchanged; standard errors shrink by a factor of about 0.71
The normal equations are unchanged when every row appears twice, so the estimates are identical. The standard errors are computed as if you had 2n independent observations, so they shrink by 1/√2 ≈ 0.71 (almost exactly, once the degrees-of-freedom correction is included). The data contain no new information: the smaller errors are false precision.
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X and Y are independent standard normal variables. What is P(X > Y + 1)?
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About 0.240
X − Y is normal with mean 0 and variance 2, so P(X − Y > 1) = P(Z > 1/√2) = 1 − Φ(0.707) ≈ 0.240. Turning a comparison of two variables into one variable's tail is the reusable step.
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Corr(A, B) = 0.9 and Corr(B, C) = 0.9. What is the smallest possible value of Corr(A, C)?
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0.62
Think of correlations as cosines of angles between vectors. A and B are at arccos 0.9 ≈ 25.8°, as are B and C, so A and C are at most 51.7° apart: Corr(A, C) ≥ cos(2 arccos 0.9) = 2(0.81) − 1 = 0.62. At exactly 0.62 the correlation matrix is singular; below it, the matrix stops being a valid correlation matrix.
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You estimate a variance by dividing the sum of squared deviations from the sample mean by n instead of n − 1. With n = 10, what fraction of the true variance does this estimator give on average?
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0.9
Deviations are measured from the sample mean, which is fitted to the same data, so they are slightly too small: their expected sum of squares is (n − 1)σ². Dividing by n gives (n − 1)/n = 0.9 of σ² on average. Dividing by n − 1 removes the bias.
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A price series arrives one number at a time. Describe how to report the mean of the last 50 prices after each new price, in constant time per update.
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Keep a running sum and a queue of the last 50 values
Add each new price to the sum and push it onto a queue; once the queue holds 51 values, pop the oldest and subtract it. The mean is sum/50. Each update is O(1) time and the memory is O(50). In an interview, mention the floating-point drift from repeated addition and subtraction, and that recomputing the sum occasionally fixes it.
Practise under time
How to prepare for Citadel
Prepare for the first round as a coding interview: data structures, algorithms and clean Python or C++ written while talking. Then cover probability, regression and estimation at the level of explaining why, not just computing. Have a two-minute account ready of a project you did, with a result and a decision you made in it; the first round asks about it.
Preparing for Citadel or Citadel Securities? The assessment hour covers both halves, the coding and the statistics, and tells you which is further from ready. The assessment hour.