Quant interview questions
1,322 questions in the style trading and research firms ask, from probability and brainteasers to options, statistics and coding. Every question is open to read; the 50 in the free sample show their worked solutions here.
1,322 questions · page 22 of 34
- 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
- An equicorrelated matrix, part 1 of 4Linear algebra · Foundation
- Projecting onto a factor, part 1 of 3Linear algebra · Foundation
- Minimising a quadratic, part 1 of 4Linear algebra · Foundation
- Keeping the big singular values, part 1 of 3Linear algebra · Foundation
- Two correlated assets, part 1 of 3Linear 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
- An equicorrelated matrix, part 2 of 4Linear algebra · Applied
- Projecting onto a factor, part 2 of 3Linear algebra · Applied
- Minimising a quadratic, part 2 of 4Linear algebra · Applied
- Keeping the big singular values, part 2 of 3Linear algebra · Applied
- Two correlated assets, part 2 of 3Linear 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