Quant interview questions

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• Two stocks have a return correlation of 0.9. Does that make them a good pairs trade?Time series · Advanced
• What does the Wold decomposition guarantee about a covariance-stationary process?Time series · Advanced
• In what sense is the Kalman filter optimal?Time series · Advanced
• Under a normal distribution, roughly how many trading days pass between moves…Time series · Advanced
• You have five price series and suspect more than one cointegrating relationship.Time series · Advanced
• In the Engle–Granger test you regress one price on another and run a unit-root…Time series · Advanced
• A hidden level follows a random walk with innovation variance 1 and is observed…Time series · Expert
• A 3 × 3 matrix has eigenvalues 3, −1 and 2. What is its determinant?Linear algebra · Foundation
• A 5 × 8 matrix has rank 3. What is the dimension of its null space?Linear algebra · Foundation
• Square matrices A and B have det A = 2 and det B = −3.Linear algebra · Foundation
• What is the top-left entry of the inverse of [[4, 7], [2, 6]]?Linear algebra · Foundation
• For invertible square matrices A and B, which identity is correct?Linear algebra · Foundation
• What is the rank of [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?Linear algebra · Foundation
• What is the cosine of the angle between (1,2,2) and (2,1,2), to three decimals?Linear algebra · Foundation
• What is the largest eigenvalue of [[2, 1], [1, 2]]?Linear algebra · Foundation
• You build X₂ = 0.6 Z₁+c Z₂ from independent standard normals so that X₂ is…Linear algebra · Foundation
• A covariance matrix has eigenvalues 6, 2, 1 and 1.Linear algebra · Foundation
• Can three assets be pairwise correlated at −0.5?Linear algebra · Applied · Free solution
• You run PCA on yield-curve changes across maturities. What is the first component?Linear algebra · Applied
• Geometrically, what does ordinary least squares compute?Linear algebra · Applied
• How do you simulate a vector of correlated normal variables with covariance Σ?Linear algebra · Applied
• A 10 × 10 correlation matrix has a largest eigenvalue of 6.Linear algebra · Applied
• What is the rank of uvᵀ for non-zero vectors u and v in ℝⁿ?Linear algebra · Applied
• When does Ax = b have at least one solution?Linear algebra · Applied
• A matrix has largest singular value 100 and smallest 0.5. What is its condition number?Linear algebra · Applied
• With A = [[2, 1], [1, 3]] and x = (1,2)ᵀ, what is the first component of ∇ₓ(xᵀAx)?Linear algebra · Applied
• A matrix has eigenvalues 1, 2 and 3. What is the trace of A²?Linear algebra · Applied
• A is a 3 × 5 matrix of rank 3. How many solutions does Ax = b have for a given b?Linear algebra · Applied
• Project y = (1,2,3) onto the span of (1,1,1). What is the squared length of the residual?Linear algebra · Applied
• P is the orthogonal projection onto a 3-dimensional subspace of ℝ¹⁰.Linear algebra · Applied
• A two-state Markov chain has transition matrix [[0.9, 0.1], [0.5, 0.5]] (rows sum to one).Linear algebra · Applied
• A symmetric matrix has eigenvalues 2 and 4. What is the trace of its inverse?Linear algebra · Applied
• For A = [[2, 1], [1, 2]] and x = (1,2)ᵀ, what is the Rayleigh quotient xᵀAx/xᵀx?Linear algebra · Applied
• What is the bottom-right entry of the lower-triangular Cholesky factor L of…Linear algebra · Applied
• A portfolio holds 50% in each of two assets with volatilities 20% and 10% and…Linear algebra · Applied
• Setting the gradient of lVerty−XβrVert²+λlVertβrVert² to zero gives which solution?Linear algebra · Applied
• What is the most negative pairwise correlation that five assets can all share?Linear algebra · Advanced · Free solution
• You estimate a 500 × 500 sample covariance matrix from 250 days of demeaned returns.Linear algebra · Advanced
• A symmetric matrix has eigenvalues 10, 6 and 2.Linear algebra · Advanced
• A matrix has singular values 5, 4, 2 and 1.Linear algebra · Advanced