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

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STAR. Pick a real episode of self-directed learning — a research project, hackathon, or course where you ramped on a new technique. Walk through the learning process, the application, and the outcome. DRW values intellectual curiosity and quick ramp.

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Start with a wide spread — maybe 45 bid, 55 ask. Reasoning: customer might know something you don't (adverse selection). After they trade, update your prior based on which side they took. If they buy at 55, raise both bid and ask. Discuss how you balance spread width vs trade frequency. DRW wants to see your thinking, not a memorized formula.

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Specific reasons: trading firm rather than asset management (compensation tied to your P&L not AUM); diversified across asset classes including crypto, fixed income, commodities; long-tenured firm with low turnover; collegial culture compared to some competitors. Reference any DRW-specific content you have read. Avoid the 'high pay' lead.

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Maintain a deque of the last k values and a running sum. On each new value: append, update sum. If deque exceeds k, pop the oldest and subtract from sum. Average = sum / current_size. O(1) per update. Mention edge cases: warmup before k values arrive.

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Two heaps: max-heap for lower half, min-heap for upper half. Maintain invariant |sizes differ by ≤ 1|. Insert: add to one heap, rebalance by moving top across if needed. Median: if even, average tops; if odd, return top of larger. Walk through with a small sequence of inserts. Code it up cleanly.

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P(all three distinct AND in increasing order) = P(distinct) · P(in order | distinct). Number of strictly increasing 3-tuples from {1..6} is C(6,3) = 20. Total outcomes 6^3 = 216. So probability = 20/216 = 5/54. Alternative: directly count cases where r1<r2<r3. Walk through the combinatorial logic explicitly.

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By symmetry, each position is equally likely for the white ball. So P(last) = 1/100. State the symmetry argument upfront — direct enumeration takes forever. Generalize: in a uniformly random permutation, every position is equally likely for any specific element.

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Difference of squares trick: 17·23 = (20-3)(20+3) = 400 - 9 = 391. State the trick briefly, give the answer. DRW expects sub-5-second responses on these. Practice (a-b)(a+b) for a,b near round numbers.

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Strategy: guess higher if more high cards remain, lower if more low cards. Expected accuracy depends on the deck composition at each step. The exact expected value is around 30 correct guesses out of 51 — computed by dynamic programming over deck states. State the strategy clearly; the exact number is less important than showing the optimization framework.

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Coupon collector formula. E = n · H_n where H_n is the n-th harmonic number. For n=6: E = 6 · (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6) = 6 · 2.45 = 14.7. Derive: after collecting k distinct, probability of next being new is (n-k)/n, expected wait is n/(n-k). Sum over k = 0..n-1. State the derivation upfront.