10 Citadel Quantitative Researcher (New Grad) Interview Questions (2026)

Outline

Fermi estimation. US population ≈ 330M. Average haircut frequency ≈ once every 6 weeks (42 days). So ~330M / 42 ≈ 8M per day. Adjust for: kids cut less often, men more often. Show the chain of estimates. Citadel wants to see structured decomposition, not memorized numbers.

Outline

STAR. Pick a research project, hackathon, or course where you wrangled raw data. Walk through: how you assessed data quality, what cleaning you did, how you avoided look-ahead bias, what the signal turned out to be, how you validated it (out-of-sample, cross-validation). Citadel is testing whether you have actual hands-on experience or just clean coursework.

Outline

Specific reasons: multi-strategy platform means diverse problems; data infrastructure is best-in-class; compensation tied to research output not AUM; tight feedback loop between research and deployment. Avoid 'high pay' as the lead. Reference any specific Citadel research you have seen (public papers, conference talks).

Outline

Maintain running sum and running sum-of-squares. Mean = sum/n. Variance = sum_of_squares/n - mean^2. Welford's online algorithm is more numerically stable — discuss the tradeoff (variance can be slightly negative under naive method for nearly-constant streams). Code it up cleanly. Discuss windowing if asked (deque of (value, value^2) for fixed-window).

Outline

Recurrence on state of consecutive successes. Let E_i be expected trials from state i (have seen i in a row). E_k = 0. E_i = 1 + p·E_{i+1} + (1-p)·E_0. Solve recursively: for k=2, p=0.5, get E_0 = 6. General formula: E_0 = (1 - p^k) / (p^k · (1-p)). Derive cleanly; interviewer may ask for the closed form.

Outline

One-sample t-test: t = (sample_mean - 0) / (sample_std / sqrt(n)). Compare to t-distribution with n-1 degrees of freedom. Mention assumptions: returns are i.i.d., approximately normal (true for daily aggregates by CLT). Discuss problems: autocorrelation in real return series invalidates i.i.d. — Newey-West correction or block bootstrap. Show awareness of finance-specific gotchas.

Outline

Var(X + Y) = Var(X) + Var(Y) + 2·Cov(X,Y) = Var(X) + Var(Y) + 2·ρ·σ_X·σ_Y. State and explain in words: when correlation is positive, the sum has higher variance than independent case. Be ready for the follow-up: variance of a portfolio of n assets — leads to the covariance matrix formulation.

Outline

Hypothesis testing. Under H0 (fair), expect 50 heads with std = sqrt(100·0.5·0.5) = 5. Observed 60 = 2 std above mean. Z-score = 2, two-sided p-value ≈ 0.046. So at α=0.05 reject fair; at α=0.01 do not reject. State the test, the assumptions, and the conclusion. Discuss Bayesian alternative: posterior over p with Beta prior.

Outline

Geometric approach. Sample space is the unit square. X+Y>1 is the triangle above the line y = 1-x. Area = 1/2. So probability = 1/2. State that uniform distributions in 2D let you do these problems geometrically — much faster than integration. Be ready for follow-ups (max(X,Y) > 0.5, X*Y > 0.5).

Outline

Total expected error = bias^2 + variance + irreducible noise. Bias is how far your model's average prediction is from truth (underfitting). Variance is how much predictions wiggle around their average across training sets (overfitting). Tradeoff: simpler models have higher bias, lower variance. Show you can apply this to model selection — regularization shifts the tradeoff.