Practice · Quant prep · D. E. Shaw
D. E. Shaw interview process
D. E. Shaw recruits early and decides its intern class early, so most of the preparation has to happen before you apply. The process is long by industry standards and ends with conversations with your references.
The process, from D. E. Shaw's own pages
- The steps. An application review, a phone interview, then virtual interviews, conversations with your references, and finally an offer. Source
- Extra material. Some candidates are asked for a writing or code sample, or to complete a case study; the process varies by role. Source
- Timing. Applications are considered on a rolling basis, the intern class is usually finalised early in the first quarter of the internship year, and the firm recommends applying by the end of the previous calendar year. Source
- The quantitative analyst internship. A research project that typically explores a range of statistical modelling techniques, with a mentor in a quantitative research group; 12 weeks in New York, June to August 2027. Source
- Who it is for. Students usually approaching their final year of full-time study; no finance experience required; an exceptional aptitude for abstract reasoning, problem solving and quantitative thinking. Source
What candidates report
Candidates describe a recruiter or phone screen followed by a day of several back-to-back interviews, with probability, statistics and problem solving for quantitative roles and coding for technical ones, and a request for references near the end.
What D. E. Shaw states it pays
Base pay as written in D. E. Shaw’s own job adverts for the 2027 cycle, before any bonus. The same advert adds a $25,000 sign-on bonus, housing or a $10,000 housing allowance, travel, and stipends for study materials and equipment.
| Role | Where | Stated base pay | |
|---|---|---|---|
| Quantitative Analyst Intern, Summer 2027 | New York | $25,000 a month | Advert |
PDF · Edition 2 · £79
The Quant Careers Report
D. E. Shaw’s process step by step and the pay it states in its adverts, side by side with 12 other trading firms, plus when to apply and five timed practice papers with worked solutions.
What D. E. Shaw is testing
The advert asks for abstract reasoning more than for any particular technique, and the interviews follow suit. Expect problems you have not seen, where the test is whether you can find a clean way in and explain it, often a symmetry or a way to count that avoids brute force.
Because the research project involves statistical modelling, expect questions on conditional probability, tails of distributions and estimation alongside the puzzles. Checking an answer with a quick sanity bound before committing to it is noticed.
Six practice problems
Written by us to match the types D. E. Shaw is publicly reported to ask. None is a copy of any question D. E. Shaw has used.
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A permutation of 1 to 10 is chosen at random. What is the expected number of inversions, pairs i < j whose values are out of order?
Show the answer
22.5
Each of the 45 pairs is out of order with probability 1/2, by symmetry. Linearity of expectation gives 45/2 = 22.5, without ever computing the distribution. Insertion sort makes exactly one swap per inversion, so this is also its average number of swaps.
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What is the probability that a five-card hand from a standard deck contains five different ranks?
Show the answer
2112/4165 ≈ 0.507
Choose 5 distinct ranks, C(13, 5) = 1287 ways, and a suit for each card, 4⁵ = 1024 ways, out of C(52, 5) = 2,598,960 hands. The ratio is about 0.507, so slightly more than half of all hands have no pair at all.
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A stick is broken at a uniformly random point. What is the expected ratio of the shorter piece to the longer?
Show the answer
2 ln 2 − 1 ≈ 0.386
Let the break be at U; by symmetry take U uniform on [0, 1/2], so the ratio is U/(1 − U). Its average is 2∫₀^½ u/(1 − u) du = 2(ln 2 − 1/2) = 2 ln 2 − 1. The expected ratio is not the ratio of expected lengths, 1/4 to 3/4, which would give 1/3.
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A fair coin is tossed six times. What is the probability of exactly three heads?
Show the answer
5/16
C(6, 3) = 20 sequences out of 64, so 20/64 = 5/16 ≈ 0.31. The most likely single outcome still happens less than a third of the time, and for 2n tosses the chance of an exact tie falls like 1/√(πn).
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Z is standard normal. What is P(Z > 2 | Z > 1)?
Show the answer
About 0.143
P(Z > 2)/P(Z > 1) = 0.0228/0.1587 ≈ 0.143. Normal tails fall off faster than exponentially, so being past one standard deviation makes being past two only about one chance in seven; for an exponential distribution the same conditional probability would not depend on how far out you already are.
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How many zeros does 2026! end in?
Show the answer
505
Each trailing zero needs a factor 10, and fives are scarcer than twos. Count them: ⌊2026/5⌋ + ⌊2026/25⌋ + ⌊2026/125⌋ + ⌊2026/625⌋ = 405 + 81 + 16 + 3 = 505.
Practise under time
Hard paper: Ten hard probability and puzzle questions, 45 minutes.
How to prepare for D. E. Shaw
Apply in the autumn: by the firm's own account the intern class is mostly settled early in the year, so a strong application in March competes for very few places. Practise unfamiliar problems where the work is in finding the right way to count, and say each step aloud. Line up two referees who know your quantitative work before you start, since references come at the end.
Applying to D. E. Shaw this cycle? The strategy hour checks your problem solving and your application against what its process looks for, in time for the autumn deadline. What the hour covers, £250.