Quant interview questions

378 questions · page 5 of 10 · Clear filters

• 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
• You run PCA on raw features measured in wildly different units, and one feature…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
• Two uncorrelated assets have variances 0.04 and 0.01 and expected excess returns 8% and 3%.Linear algebra · Advanced
• A correlation matrix estimated from patchy data has a small negative eigenvalue.Linear algebra · Advanced
• Assets A and B correlate at 0.9, and B and C at 0.9.Linear algebra · Advanced
• You estimate a correlation matrix for 100 assets from 400 days of independent…Linear algebra · Advanced
• Two assets have volatilities 20% and 10% and correlation 0.5.Linear algebra · Advanced
• In maximising a Gaussian likelihood over a symmetric covariance matrix Σ, what…Linear algebra · Advanced
• For standard Brownian motion, what is 𝔼[W₃W₇]?Stochastic calculus · Foundation
• For standard Brownian motion, what is Var(W₁+W₂)?Stochastic calculus · Foundation
• What is the correlation between W₁ and W₄ for standard Brownian motion?Stochastic calculus · Foundation
• What is d(Wₜ²)?Stochastic calculus · Applied · Free solution
• For standard Brownian motion, what is 𝔼[W₄⁴] – the fourth moment at time 4?Stochastic calculus · Applied