10 Two Sigma Quantitative Researcher (New Grad) Interview Questions (2026)

Outline

STAR. Describe the problem, the two candidates, the criteria (predictive accuracy, interpretability, training cost, robustness to distribution shift), the experiment design (cross-validation, holdout set), and the decision. Two Sigma values researchers who can articulate trade-offs — 'I picked the one with better accuracy' is a weak answer.

Outline

Reference specific aspects: research culture, the Insight platform, multi-asset breadth, the publishing/conference involvement. Avoid generic praise. Show you have read at least one of their public-facing research blog posts. Tie to your personal research goals — interviewers want to see fit, not flattery.

Outline

Single pass. Track min_seen_so_far. For each price, compute price - min_seen and update max_profit. O(n) time, O(1) space. Edge cases: empty array, monotonically decreasing prices (return 0 or negative-best — clarify with interviewer). This is LC 121, common warmup at quant firms.

Outline

Two-sample t-test with pooled variance. Pooled std = sqrt(((n1-1)s1^2 + (n2-1)s2^2) / (n1+n2-2)). t = (mean1 - mean2) / (pooled_std · sqrt(1/n1 + 1/n2)). DOF = n1+n2-2. State assumptions explicitly. Mention Welch's t-test as the more robust alternative when variances may differ.

Outline

Severe overfitting. Diagnose: too many features relative to samples, or features are collinear, or model captured noise. Fixes: regularization (Ridge/Lasso), feature selection, cross-validation, more data, simpler model. Discuss why R-squared on test can drop so far — overfit models memorize training noise that does not generalize.

Outline

MLE estimate: p_hat = 7/10 = 0.7. Standard error: sqrt(p(1-p)/n) = sqrt(0.7·0.3/10) ≈ 0.145. 95% CI ≈ 0.7 ± 1.96·0.145 ≈ [0.41, 0.99]. Mention Bayesian alternative with Beta prior. Discuss why small n gives wide intervals — illustrates the data-hunger of quant research.

Outline

L1 adds sum of absolute weights to loss; L2 adds sum of squared weights. L1 produces sparse models (drives weights to zero exactly) — useful for feature selection. L2 shrinks weights smoothly toward zero, never quite zero. Geometric intuition: L1 constraint is a diamond, L2 is a circle; optimum often hits corners of the diamond. Elastic net combines both.

Outline

Let X1, X2, X3 be order statistics with X1 ≤ X2 ≤ X3. We want P(X3 > 2·X1). Condition on X1 = x; then X2, X3 are uniform on [x, 1] given X1 = x. P(X3 > 2x | X1 = x) involves the joint distribution of remaining order stats. The density of X1 is 3(1-x)^2. Compute by integration. Final answer ≈ 0.75. Walk through cleanly — interviewer is testing whether you can set up the integral, not finish it perfectly.

Outline

A valid covariance matrix is symmetric and positive semi-definite. Check: matrix equals its transpose; all eigenvalues ≥ 0. Equivalently, Cholesky decomposition succeeds. In practice, numerical estimates of cov matrices from real data sometimes fail PSD due to noise — fix with shrinkage (Ledoit-Wolf) or nearest-PSD projection.

Outline

Multicollinearity. The (X^T X) matrix becomes near-singular, so coefficient estimates become unstable — small data changes flip signs and magnitudes wildly. Variance of coefficient estimates inflates. Detect: VIF (variance inflation factor), condition number. Fix: drop one of the correlated features, PCA, or use Ridge regression which is robust to collinearity.