Practice · Quant prep · Two Sigma
Two Sigma interview questions
Two Sigma hires researchers the way a statistics department would: it wants to see how you handle data you have not seen before and how honestly you judge your own result. The puzzles that dominate trading-firm interviews matter less here.
The process, from Two Sigma's own pages
- Format. Interviews are held over video, all of a day's interviews on the same link; the firm may end a day early if it decides the fit is not there, and says it will keep you informed. Source
- Content. A combination of technical and behavioural interviews, with separate preparation guides for software engineering and for quantitative research and data science. Source
- Who can apply. Quantitative research interns should be studying a technical or quantitative subject with about one year left in their programme, at any level from bachelor's to doctorate. Source
- No finance needed. Finance is described as nice to have; more than half of the firm's employees come from outside finance. Source
- When to apply. Applications open the summer or autumn before the programme, the firm recruits on campus in the autumn, and it receives tens of thousands of applications, so early is better. Source
What candidates report
Candidates describe an online assessment first, often coding with a statistical element, then technical interviews on data analysis, coding and statistics, and for PhD candidates a discussion of their research. The details vary by team and year.
What Two Sigma states it pays
Base pay as written in Two Sigma’s own job adverts for the 2027 cycle, before any bonus. The weekly figures are for the ten-week internship.
| Role | Where | Stated base pay | |
|---|---|---|---|
| Quantitative Researcher – Intern 2027 (BS) | New York | $4,900 a week; 10 weeks | Advert |
| Quantitative Researcher – Intern 2027 (MS) | New York | $5,000 a week | Advert |
| Quantitative Researcher – Intern 2027 (PhD) | New York | $5,500 a week | Advert |
PDF · Edition 2 · £79
The Quant Careers Report
Two Sigma’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 Two Sigma is testing
The statistics questions are rarely about formulas. They test whether you know what a number means: why a correlation of 0.5 does not make one variable half of another, what a regression slope tells you in each direction, how much a result from a few hundred observations can be trusted. Expect follow-ups that change one assumption and ask what moves.
The coding is practical: reading a dataset, computing something correctly and efficiently, and noticing when the data is lying to you. Being right about edge cases, missing values and leakage counts for more than speed.
Six practice problems
Written by us to match the types Two Sigma is publicly reported to ask. None is a copy of any question Two Sigma has used.
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X and Y are independent standard normal variables. What is the correlation between X and X + Y?
Show the answer
1/√2 ≈ 0.707
Cov(X, X + Y) = Var(X) = 1, and Var(X + Y) = 2. So the correlation is 1/(1 × √2) = 1/√2. Adding an independent variable of the same size halves the shared variance, which is a quick way to reason about noisy versions of a signal.
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Regressing y on x gives a slope of 2, and the correlation between them is 0.5. What slope do you get regressing x on y?
Show the answer
0.125
The slope of y on x is ρσᵧ/σₓ and the slope of x on y is ρσₓ/σᵧ, so their product is ρ² = 0.25. The second slope is 0.25/2 = 0.125, not 1/2. Regression is not symmetric, and the gap between the two lines is exactly how much of the variance is unexplained.
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A coin is tossed 100 times and shows 60 heads. How many standard errors is that from what a fair coin would give, and is it significant at the 5% level?
Show the answer
2 standard errors; borderline: the exact two-sided p-value is about 0.057
A fair coin gives 50 heads with standard deviation √(100 × 0.25) = 5, so 60 is 2 standard errors away. The normal approximation puts the two-sided p-value near 0.046, but the exact binomial value is 0.057. At this sample size the answer depends on which you use, which is the point an interviewer wants you to notice.
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Four numbers are drawn from a uniform distribution on [0, θ], and the largest is 10. What is the unbiased estimate of θ based on the maximum?
Show the answer
12.5
The maximum of n uniforms on [0, θ] has expected value nθ/(n + 1), so it underestimates θ. Scaling by (n + 1)/n removes the bias: (5/4) × 10 = 12.5. The same reasoning is the classic answer to estimating how many tanks were produced from captured serial numbers.
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A strategy has a daily Sharpe ratio of 0.1. Assuming independent days, roughly what is its annual Sharpe ratio over 252 trading days?
Show the answer
About 1.59
Mean return scales with the number of days and volatility with its square root, so the Sharpe ratio scales with √252 ≈ 15.9. Annual Sharpe ≈ 0.1 × 15.9 = 1.59. The assumption of independent days is the weak point: autocorrelated returns make this overstate or understate the true figure.
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What is the smallest number of comparisons that always suffices to find both the maximum and the minimum of 100 numbers?
Show the answer
148
Compare the numbers in 50 pairs; the larger of each pair is a candidate for the maximum and the smaller for the minimum. That is 50 comparisons, then 49 to find the maximum of 50 candidates and 49 for the minimum: 148 in total, against 198 for two separate passes. For n even the count is 3n/2 − 2.
Practise under time
Written probability test: Fifteen probability and statistics questions, easy to hard, 30 minutes.
How to prepare for Two Sigma
Revise the statistics you would use on real data rather than on exam questions: regression in both directions, confidence intervals, multiple testing, and what changes when observations are not independent. Write small analyses in Python until loading, cleaning and summarising data is quick, and prepare to explain one project in depth, including what did not work.
Preparing for a Two Sigma research process? The strategy hour tells you where your statistics and coding stand against what the firm screens for. What the hour covers, £250.