Citadel and Two Sigma Research OA Guide

How it works

The sitting has two sections totaling 40 minutes. The first, Probability & stochastic processes, runs 22 minutes for 14 items drawn from a pool covering Poisson process arrival counts, order statistics (the expected maximum of several uniform draws), geometric waiting times, the variance of a difference of independent variables, and the defining property of a Markov chain's stationary distribution.

The second, Inference & research integrity, runs 18 minutes for 12 items: how many false positives to expect from testing many worthless strategies at a fixed significance level, spotting look-ahead bias in a backtest rule, spotting survivorship bias in how a universe is constructed, how many more Monte Carlo paths are needed to halve a standard error, and how to read a high t-statistic alongside a near-zero R-squared.

Both sections are pure multiple choice with four options each, and both have allowBack set to false - once you answer an item, the next one loads and there is no return pass within that section.

How scoring works

Both sections carry a penalty of 0 - no negative marking, so every item should get an answer even under time pressure, per the sitting's own stated rules.

No generator in either section sets a marks value, so all 26 items are worth one raw mark each; the per-section result reports how many of the 14 (or 12) were answered correctly, wrongly, or skipped.

allowBack is false on both sections, so an item is locked the moment it is answered - there is no later pass to revisit anything in either the probability section or the inference section.

Probability & stochastic processes

For any Poisson-process item, remember the count over an interval of length t is Poisson(lambda t) - mean and variance are both exactly lambda t, not the per-unit rate lambda alone and not its square root. This single fact, applied correctly, answers a large share of this section's items instantly.

For order statistics, the expected maximum of n independent Uniform(0,1) draws is n/(n+1), which climbs toward 1 as n grows - a quick sanity check against a distractor that puts the answer at 1/2 or below.

For a geometric waiting-time item (flips until the first head), the mean is 1/p - larger for a less likely event, which rules out distractors that decrease as p shrinks.

For a variance-of-a-difference item, remember variances add regardless of the sign in the expression: Var(X - Y) = Var(X) + Var(Y) under independence, not their difference.

22 minutes for 14 items is under 1.6 minutes each, so these are meant to be fast recalls of a named result. If you find yourself re-deriving a formula mid-sitting, memorize it before the next one.

Inference & research integrity

For multiple-comparisons items, the expected number of false positives from testing k worthless strategies at the 5% level is k times 0.05, a mechanical calculation.

Keep look-ahead bias and survivorship bias distinct: look-ahead is using information not yet available at the decision point (trading on a close using that same close), while survivorship is building a universe only from things that are still around today, silently dropping the delisted and the bankrupt.

For the Monte Carlo standard-error item, remember standard error scales as 1 over the square root of n - halving it requires four times as many paths, not two.

When a question pairs a large t-statistic with a tiny R-squared, the correct reading is that the relationship is reliably non-zero but explains almost none of the variance - both statements are true at once, and neither invalidates the other.

This section rewards recognizing the pattern; there is little to compute, which is why it gets less time per item than the probability section. Use that as a pacing cue.

Pacing across the whole sitting

40 minutes total across 26 items averages to roughly 1.5 minutes each, but the two sections are separately timed, so time saved in probability cannot be spent in inference and vice versa - pace each section on its own clock.

The probability section rewards instant recall of a small set of named formulas; if any of them is shaky, fix it before the sitting; there is no slack built in to re-derive results live.

The inference section is pattern recognition. If an item's answer is not clear within 20-30 seconds, the underlying concept needs a review, and more time on that single question will not help.

A worked example

1. State the model: the count of arrivals from a Poisson process over an interval of length t is itself Poisson-distributed with parameter lambda t.

   $$N_t \sim \text{Poisson}(\lambda t)$$

2. Plug in the given rate and interval length.

   $$\lambda = 4 \text{ per minute}, \qquad t = 3 \text{ minutes} \quad\Rightarrow\quad \lambda t = 12$$

3. Use the defining property of the Poisson distribution: its mean and its variance are both equal to the parameter itself.

   $$E[N_t] = \lambda t = 12, \qquad \operatorname{Var}(N_t) = \lambda t = 12$$

4. So the expected number of arrivals in 3 minutes is 12 and the variance is also 12 - not the per-minute rate of 4 left unscaled, and not the square root of 12.

Common mistakes

• Leaving a Poisson mean or variance at the per-minute rate lambda instead of scaling by the interval length t.

• Confusing the expected maximum of n uniform draws, n/(n+1), with the mean of a single draw, 1/2.

• On the multiple-comparisons item, treating a strategy that clears a 5% significance test as proven real. Testing k worthless strategies produces k times 0.05 false positives in expectation.

• Mixing up look-ahead bias (using information unavailable at decision time) with survivorship bias (sampling only what is still around today) - they are tested as distinct items.

• Inferring that a near-zero R-squared means a reported t-statistic must be wrong. Significance and explanatory power are separate questions and both can be true at once.

Why interviews test this

The probability section maps directly onto the day-to-day toolkit of a quant researcher - Poisson processes for event modeling, order statistics, Markov chains for regime detection - and firms test it as a floor requirement: these results need to be automatic, because a research role built on top of shaky foundational recall will be slow and error-prone on every subsequent project.

The inference section exists because the mistakes it tests stay invisible until a strategy is live and losing money. A researcher who does not check for look-ahead bias, survivorship bias and multiple-comparisons inflation will produce backtests that look excellent and are not. A hiring desk would rather find that out in a screen than after capital is at stake.

Play Quant Research Screen on Outcry

Quant Research Screen is free to play on Outcry, in the Mock Screens section, and every run is timed and scored. Read the guide once, then play Quant Research Screen and check your score against the strategy above. The guide book has a written guide for every other game, and the practice hub and mock assessments put the same skills under a real screen's clock.