Solve stress testing and probability
Quantitative Interview Questions
This interview assesses a candidate's proficiency in statistics, probability, and quantitative risk modeling through a series of distinct problems.
1. Commodity Stress Testing
You are tasked with managing risk for a portfolio exposed to West Texas Intermediate (WTI) and Brent crude positions. Describe a comprehensive framework to stress test this portfolio. Assume you have access to historical daily returns for both commodity series and your objective is to generate joint downside scenarios over a 10-day horizon.
Explain how you would approach modeling the following components:
- Marginal distributions of individual commodity returns.
- The dependence structure between WTI and Brent crude.
- Tail risk within the portfolio.
If you choose to utilize a t-copula for modeling dependence, elaborate on the specific workflow you would follow and provide a clear justification for why a t-copula might be preferable to a Gaussian copula in this context.
2. Variance of a Sum
Consider two normally distributed random variables, X and Y, with respective means mu_X and mu_Y, standard deviations sigma_X and sigma_Y, and a correlation coefficient rho.
- What is the variance of their sum,
Var(X + Y), whenXandYare independent? - What is
Var(X + Y)whenXandYare dependent? - Under what specific condition is the sum
X + Yitself normally distributed?
3. Monty Hall Problem
Imagine you are on a game show facing three closed doors. Behind one door is a car, and behind the other two are goats. You choose one door. The host, who knows where the car is, then opens one of the other two doors, always revealing a goat. At this point, you are given the option to either stick with your initial choice or switch to the remaining unopened door. What strategy maximizes your chance of winning the car, and what is the probability of winning with that strategy?
4. Eight Balls Puzzle
You have eight visually identical balls. You are told that exactly one of these balls is heavier than the other seven, which all have identical weight. Using a balance scale at most two times, describe a strategy that will always identify the heavier ball.
AI interview prep
Core dilemma
Designing robust quantitative models for financial risk assessment and decision-making under uncertainty, balancing theoretical rigor with practical applicability, computational constraints, and the ability to capture extreme market events.
3 tradeoffs and 2 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Solve stress testing and probability
Quantitative Interview Questions
This interview assesses a candidate's proficiency in statistics, probability, and quantitative risk modeling through a series of distinct problems.
1. Commodity Stress Testing
You are tasked with managing risk for a portfolio exposed to West Texas Intermediate (WTI) and Brent crude positions. Describe a comprehensive framework to stress test this portfolio. Assume you have access to historical daily returns for both commodity series and your objective is to generate joint downside scenarios over a 10-day horizon.
Explain how you would approach modeling the following components:
- Marginal distributions of individual commodity returns.
- The dependence structure between WTI and Brent crude.
- Tail risk within the portfolio.
If you choose to utilize a t-copula for modeling dependence, elaborate on the specific workflow you would follow and provide a clear justification for why a t-copula might be preferable to a Gaussian copula in this context.
2. Variance of a Sum
Consider two normally distributed random variables, X and Y, with respective means mu_X and mu_Y, standard deviations sigma_X and sigma_Y, and a correlation coefficient rho.
- What is the variance of their sum,
Var(X + Y), whenXandYare independent? - What is
Var(X + Y)whenXandYare dependent? - Under what specific condition is the sum
X + Yitself normally distributed?
3. Monty Hall Problem
Imagine you are on a game show facing three closed doors. Behind one door is a car, and behind the other two are goats. You choose one door. The host, who knows where the car is, then opens one of the other two doors, always revealing a goat. At this point, you are given the option to either stick with your initial choice or switch to the remaining unopened door. What strategy maximizes your chance of winning the car, and what is the probability of winning with that strategy?
4. Eight Balls Puzzle
You have eight visually identical balls. You are told that exactly one of these balls is heavier than the other seven, which all have identical weight. Using a balance scale at most two times, describe a strategy that will always identify the heavier ball.