26 questions reported in Two Sigma interviews, organised by the group that asks them. Every question carries a model answer and graded feedback on your own attempt.
Questions
Easy · Medium
Hard
Model builds
Built in the spreadsheet grid
Multiple testing, out-of-sample discipline, capacity and decay. 18 questions
A first-round check that a research candidate can separate a strategy outcome from the market outcome it rode along with.
A paper portfolio returns 8% in a month while its benchmark returns 5%. What is the portfolio's active return? Is that enough to call the signal good?
Asked to see whether you can explain a counterintuitive result clearly under pressure.
Three doors: one hides a car, two hide goats. You pick door 1. The host. Who knows what's behind each door. Opens door 3 revealing a goat, then offers you the chance to switch to door 2. Should you…
A practical junior-researcher question testing whether you can calculate and interpret a simple rank-based signal diagnostic.
A signal ranks four stocks from strongest to weakest as A, B, C, D. Their next-month realised-return ranks from best to worst are A, C, B, D. Using Spearman rank correlation, calculate the information…
A common first-round check that you can make differently scaled signals comparable before combining them.
A stock's 12-month earnings-revision score is 18. Across the investable universe, the score has a mean of 10 and standard deviation of 4. What is its z-score, and why might a quant researcher use it…
Researchers are expected to explain a simple factor test before writing a complex model around it.
You believe companies with the strongest earnings revisions will outperform. Explain how you would test that idea using decile portfolios. What result would make you interested, and what result would…
A foundational research-process question for candidates who may use machine learning on financial data.
What are training, validation and test sets in quantitative research? Why should a time-series financial dataset be split chronologically rather than randomly shuffled?
A research-team scenario used to test whether a junior candidate can communicate a disciplined go or no-go decision under a deadline.
At 4pm, a senior researcher asks you to add a new vendor's "customer demand score" to tomorrow's signal run. The vendor says the history reaches 2018, but its documentation does not state when each…
Quant research interviews probe statistical judgement over formula recall.
A researcher backtests 200 signals and finds one with a t-statistic of 2.5 predicting next-day returns. Should you trade it? Explain what's wrong and what you'd require instead.
An offer-level research case: interviewers want a decision and a validation plan, not another feature idea.
You inherit a monthly equity signal with a 1.1 gross Sharpe ratio from 2005–2024. It rebalances the full universe, has 180% annual turnover, loses half its Sharpe after estimated costs, and most of…
Quant research interviews hand you output and ask what it means.
You regress a stock's returns on the market and get beta 1.2 (standard error 0.15), alpha 0.3% monthly (standard error 0.4%), and R² of 0.45. What do you conclude?
A Bayesian question testing whether you anchor on the prior or the evidence.
A test for a condition affecting 1 in 1,000 people is 99% accurate. 99% true positive rate and 99% true negative rate. Someone tests positive. What is the probability they have the condition?
Tests whether you can approximate rather than recall.
In a room of 23 people, what is the probability at least two share a birthday? Explain your reasoning and why the answer surprises people.
A classic Bayesian warm-up at quant trading firms.
You have two coins. One is fair; the other lands heads 75% of the time. You pick one at random and flip it 3 times, getting heads every time. What is the probability you picked the biased coin?
A research review question after a promising factor weakens in its most recent out-of-sample period.
A cross-sectional equity signal had a strong information coefficient for eight years, but its last 18 months are near zero. How would you decide whether this is noise, a regime change, or a research…
Systematic trading interviews use this to test whether you can reason about strategy economics.
A strategy makes 250 trades a year, wins 55% of the time, and wins and losses are the same size (1 unit). Estimate the annual Sharpe ratio. What does this tell you about how much edge a systematic…
A recurring structure in quant interviews. Set up the recursion, don't simulate.
You start at position 0. Each step you move +1 with probability 0.5 and −1 with probability 0.5. What is the expected number of steps to first reach +3? Then: what changes if the walk is bounded below…
Standard for quantitative research and risk roles.
What are the assumptions behind OLS regression? Which are most frequently violated in financial data, and what do you do about it?
A judgement-heavy research review testing whether you can reject a persuasive model output for the right technical reason.
A machine-learning equity model has a strong backtest and a positive out-of-sample result. But when you rerun it across adjacent training windows, its top feature alternates between a valuation ratio,…
Expected value under pressure, adverse selection and inventory risk. 5 questions
An early research screen that tests statistical hygiene before a candidate proposes a signal.
You find that a stock rose on 70% of the days when a popular sports team won. Can you trade this result? What checks would you run before treating it as evidence?
A research discussion at a systematic or market-making firm tests whether your backtest resembles tradeable reality.
You propose a pairs trade that buys the underperformer and shorts the outperformer when two historically correlated stocks diverge. How would you test whether the strategy is real before trading…
A systematic-trading interview tests whether a candidate follows a risk process when a live position conflicts with a backtest.
Your mean-reversion strategy is long a stock after a three-standard-deviation selloff. The position is down another 4% intraday, while the model still says buy. What do you check before deciding…
A portfolio-construction question after several apparently independent signals lose money together.
Four market-neutral strategies have low correlations in their monthly backtests. During a volatile week, all lose money and gross exposure breaches an internal limit. How would you diagnose the common…
Trading firms use this to test whether you understand compounding and ruin.
You have an edge: a bet that pays 2:1 and wins 40% of the time. What fraction of your capital should you bet, and why not more?
Stochastic calculus, VaR and expected shortfall, and model limitations. 3 questions
Quant-risk candidates are expected to translate a correlation assumption into a portfolio-risk estimate without confusing volatility with return.
A portfolio is 50% in Asset A with 20% annual volatility and 50% in Asset B with 10% annual volatility. Their correlation is 0.25. Calculate the portfolio's annual volatility and explain what drives…
Foundational maths underpinning every valuation method.
Derive the formula for a growing perpetuity. Then value: (a) $100/year forever at a 10% discount rate, (b) the same cash flow growing at 3%, and (c) $100/year for 10 years at 10%.
Quant research and derivatives interviews test conceptual understanding over derivation.
Why do we model stock prices as geometric Brownian motion rather than arithmetic Brownian motion? What does Itô's lemma tell us, and why is the drift of log returns lower than the drift of prices?
Write your answer, get it graded on technical accuracy, completeness and communication, and see exactly which mechanic you missed.
Company tags reflect where a question type is commonly reported in interviews. They are not sourced from, endorsed by, or affiliated with Two Sigma.