CRA Monte Carlo Simulation & VaR 2

Question 1

Which variance reduction technique in Monte Carlo simulation uses pairs of random numbers that are negatively correlated to reduce estimation error?

Accepted Answer

Antithetic variates

Answer

Antithetic variates generates pairs of random numbers (u, 1-u) that are negatively correlated, averaging their outcomes to reduce variance in the estimate.

Question 2

A 10-day 99% VaR of $5 million means there is a 1% probability that losses will exceed $5 million over:

Accepted Answer

A 10-trading-day period

Answer

The time horizon is explicitly stated in the VaR definition — a 10-day 99% VaR refers to losses over a 10-trading-day holding period.

Question 3

In Monte Carlo VaR, which distribution assumption is most commonly used to model daily equity returns as a starting point?

Accepted Answer

Lognormal distribution

Answer

Equity prices are typically modeled as lognormal, meaning daily log-returns follow a normal distribution, which is the standard starting point in Monte Carlo equity VaR models.

Question 4

What is the primary purpose of using a Cholesky decomposition in a multi-asset Monte Carlo simulation?

Accepted Answer

To incorporate correlation structure between assets

Answer

Cholesky decomposition of the correlation matrix is used to generate correlated random variables, ensuring simulated asset returns reflect observed correlations.

Question 5

Expected Shortfall (ES) at the 99% confidence level is best described as:

Accepted Answer

The average loss in the worst 1% of scenarios

Answer

ES (also called CVaR) is the conditional expectation of losses given that the loss exceeds the VaR threshold — i.e., the average of the worst 1% of outcomes.

(CRA) Certified Risk Analyst Practice Test

(CRA) Certified Risk Analyst Practice Test

CRA Monte Carlo Simulation & VaR 2