← Morgan Stanley Interview Insights
Start by framing the framework's purpose and scope, then walk through the modeling pipeline from marginal distributions to dependence and simulation, and finish with scenario generation, validation, and communication of limitations. Emphasize practical trade-offs and how you'd ensure robustness and transparency.
Pro tip: Show you understand that no single model captures all risks—demonstrate how you'd combine statistical rigor with expert judgment and stress scenarios to cover tail risks, and always communicate assumptions and limitations clearly to stakeholders.
Clarify the portfolio, risk measures (e.g., VaR, ES), confidence levels, and horizons. Identify key constraints like data availability and regulatory requirements.
Fit marginal distributions to WTI and Brent returns (e.g., using EVT for tails) and calibrate a t-copula to capture tail dependence. Validate the copula fit with goodness-of-fit tests.
Generate correlated scenarios via the t-copula and inverse marginal CDFs. Aggregate P&L over multi-day horizons, accounting for autocorrelation and overlapping returns.
Incorporate historical, hypothetical, conditional, and reverse stress scenarios to complement the statistical model and capture plausible extreme events.
Backtest the model, perform sensitivity analysis, and document limitations. Communicate results and caveats clearly to stakeholders, emphasizing model risk.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Felt like a warmup but I still second-guessed myself on the last part.
Start by stating the general formula for the variance of a sum: Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y). Then explain that when X and Y are independent, Cov(X,Y)=0, so the variance simplifies to the sum of variances. When they are dependent, Cov(X,Y) = ρσ_Xσ_Y, so Var(X+Y) = σ_X^2 + σ_Y^2 + 2ρσ_Xσ_Y. Finally, address normality: the sum of two jointly normal variables is always normal, but if they are only marginally normal and not jointly normal, the sum may not be normal.
Pro tip: Emphasize that independence implies zero correlation but zero correlation does not imply independence (except in the joint normal case). Also, mention that in finance, joint normality is often assumed, but it's crucial to verify, as dependence structures can break normality of sums.
Write Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y). This applies regardless of distribution.
When X and Y are independent, Cov(X,Y)=0, so Var(X+Y) = Var(X) + Var(Y).
When dependent, Cov(X,Y) = ρσ_Xσ_Y, so Var(X+Y) = σ_X^2 + σ_Y^2 + 2ρσ_Xσ_Y.
If X and Y are jointly normally distributed, then any linear combination, including X+Y, is normally distributed. If they are only marginally normal but not jointly normal, X+Y may not be normal.
Relate to data science and finance: understanding dependence and joint normality is key for risk modeling and portfolio variance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I've seen this a hundred times so I just answered it.
State clearly that you should switch, then explain the probabilities using a simple enumeration or conditional probability argument. Emphasize that the host's action is not random—it reveals information that changes the probability distribution.
Pro tip: Mention that the host's behavior is crucial: if the host revealed a door at random and it happened to be a goat, the probabilities would be 50-50. This shows you understand the assumptions and can avoid a common pitfall.
Confirm the setup: three doors, one car, two goats; you pick one; the host, who knows where the car is, always opens a different door with a goat. This ensures everyone is on the same page.
Clearly say that you should switch, because switching wins with probability 2/3 while staying wins with probability 1/3.
Use a simple argument: initially, the probability your chosen door has the car is 1/3, and the probability the car is behind one of the other two doors is 2/3. When the host reveals a goat, that 2/3 probability collapses onto the remaining unopened door, so switching wins with probability 2/3.
If needed, enumerate all possible outcomes (e.g., car behind door 1, 2, or 3) to show that switching wins in 2 out of 3 cases. Alternatively, mention that a Monte Carlo simulation would confirm the 2/3 probability.
Clarify that the host's action is not random and depends on knowledge of the car's location. If the host opened a door randomly and it happened to be a goat, the probabilities would be different (1/2 each).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Divide the 8 balls into three groups: 3, 3, and 2. Weigh the two groups of 3 against each other; if they balance, the heavier ball is in the remaining 2, and one more weighing finds it. If they don't balance, take the heavier group of 3, weigh one against another, and the heavier or the unweighed ball is the answer.
Pro tip: Emphasize that the optimal strategy uses the balance scale's three possible outcomes (left heavy, right heavy, balanced) to maximize information gain, which is why dividing into three groups is key. This demonstrates algorithmic thinking beyond brute force.
Recognize that you have exactly two weighings and need a deterministic method. The balance scale gives three outcomes per weighing, so you can distinguish up to 3^2 = 9 possibilities, which is enough for 8 balls.
Split the 8 balls into groups of 3, 3, and 2. This leverages the three outcomes of the first weighing to narrow down the heavier ball to a smaller set.
Place 3 balls on each side of the balance. If they balance, the heavier ball is in the remaining 2; if not, it's in the heavier group of 3.
If the first weighing balanced, weigh the remaining 2 balls against each other to find the heavier one. If it didn't balance, take the heavier group of 3 and weigh one ball against another; if they balance, the unweighed ball is heavier, otherwise the heavier side reveals the ball.
Walk through each possible outcome to show the method always works within two weighings. This demonstrates thoroughness and confidence in the solution.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.