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.
113 questions · page 2 of 3 · Clear filters
- 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
- You run PCA on yield-curve changes across maturities. What is the first component?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 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
- 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
- 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
- You estimate a correlation matrix for 100 assets from 400 days of independent…Linear algebra · Advanced
- A spread follows an Ornstein and Uhlenbeck process with reversion speed θ = 0.5 per year.Stochastic calculus · Applied
- You cluster assets by return correlation with k-means and the result looks arbitrary.Machine learning · Applied
- A regularised linear model beats your tuned gradient-boosting ensemble out of sample.Machine learning · Advanced
- Two features are nearly identical, and a random forest reports low importance for both.Machine learning · Advanced
- You cluster a universe of assets from their correlation matrix.Machine learning · Advanced
- Each tree’s prediction has variance 1 and any two trees’ predictions correlate at 0.3.Machine learning · Advanced
- You winsorise a standardised cross-section at ±3.Alpha and signal research · Foundation
- A stock has a beta of 1.2, the risk-free rate is 3% and the equity risk premium is 5%.Alpha and signal research · Foundation
- A sample variance is 0.05, the shrinkage target is 0.04 and the shrinkage intensity is 0.3.Alpha and signal research · Foundation
- An investor with mean–variance risk aversion γ = 3 chooses the weight w =…Alpha and signal research · Foundation
- A signal has an information coefficient of 0.05 and you make 400 independent bets a year.Alpha and signal research · Applied · Free solution
- Your information coefficient is fixed and you want to double your information ratio.Alpha and signal research · Applied · Free solution
- A colleague reports a daily information coefficient of 0.35 on a liquid equity universe.Alpha and signal research · Applied
- You hold four uncorrelated assets in equal weight, each with 20% volatility.Alpha and signal research · Applied
- Under the square-root law of market impact, quadrupling your order size…Alpha and signal research · Applied
- A signal has an information coefficient of 0.05 at a one-day lag and a decay…Alpha and signal research · Applied
- Two uncorrelated assets have volatilities of 10% and 20%.Alpha and signal research · Applied
- You decide to buy at $100.00, fill 10,000 shares at an average of $100.15, and…Alpha and signal research · Applied
- You backtest a signal on today’s members of an index, using ten years of their history.Alpha and signal research · Applied
- Two standardised signals have information coefficients 0.04 and 0.03 and are…Alpha and signal research · Applied
- A signal’s daily IC averages 0.02 with a standard deviation of 0.10 across 250 days.Alpha and signal research · Applied
- A signal has IC 0.05 and breadth of 400 independent bets a year, but portfolio…Alpha and signal research · Applied
- Grinold’s rule sets expected residual return to IC × σ × z.Alpha and signal research · Applied
- A fund returned 12% with a risk-free rate of 2%.Alpha and signal research · Applied
- When have momentum strategies historically suffered their worst drawdowns?Alpha and signal research · Applied
- A portfolio holds 50% each in two uncorrelated assets with volatilities 20% and 10%.Alpha and signal research · Applied
- What does the Black–Litterman model do?Alpha and signal research · Applied
- Two uncorrelated strategies have Sharpe ratios 1.0 and 0.5.Alpha and signal research · Applied
- A portfolio trades 20% of its value each day (one-way) and pays a half-spread…Alpha and signal research · Applied