Quant interview questions

90 questions · page 2 of 3 · Clear filters

• What is the leverage effect in equity returns?Time series · Applied
• Using EWMA with λ = 0.94, yesterday’s volatility estimate was 1% and today’s return is 2%.Time series · Applied
• You have ten years of daily data, start with a two-year training window, expand…Time series · Applied
• 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
• 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
• Can three assets be pairwise correlated at −0.5?Linear algebra · Applied · Free solution
• Geometrically, what does ordinary least squares compute?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
• 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
• 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
• For standard Brownian motion, what is 𝔼[W₃W₇]?Stochastic calculus · Foundation
• What is d(Wₜ²)?Stochastic calculus · Applied · Free solution
• A Brownian motion with drift 0.5 per unit time starts at zero.Stochastic calculus · Applied
• What is 𝔼[e^(0.4W₂)], to four decimal places?Stochastic calculus · Applied
• A spread follows an Ornstein and Uhlenbeck process with reversion speed θ = 0.5 per year.Stochastic calculus · Applied
• A stock has expected return 10%, the risk-free rate is 3% and volatility is 25%.Stochastic calculus · Applied
• What is ∫₀ᵗWₛ dWₛ?Stochastic calculus · Advanced · Free solution
• Which of these is a martingale?Stochastic calculus · Advanced
• What is Var(∫₀²s dWₛ), to three decimal places?Stochastic calculus · Advanced
• A Brownian motion is conditioned to return to zero at time 4.Stochastic calculus · Advanced
• For a standard Brownian motion, what is Pr(max _(t ≤ 4)Wₜ ≥ 2), to four decimal places?Stochastic calculus · Advanced
• What can you say about ∫₀ᵗf(s) dWₛ for a deterministic, square-integrable f?Stochastic calculus · Advanced
• A stock at $100 follows a driftless geometric Brownian motion with 30% volatility.Stochastic calculus · Advanced
• Why price a bond option under the forward measure rather than the risk-neutral one?Stochastic calculus · Expert
• A node holds 40 positive and 60 negative examples. What is its Gini impurity?Machine learning · Foundation
• Why do gradient-boosted trees usually beat deep networks on daily…Machine learning · Applied
• In a ten-dimensional unit cube, what fraction of the volume lies within 0.1 of some face?Machine learning · Applied
• A support vector machine has |w|= 4. What is the width of its margin?Machine learning · Applied