Statistics Risk Assessment & Management 2

Question 1

Which statistical measure is most commonly used to quantify the spread of potential losses in a risk distribution?

Accepted Answer

Standard deviation

Answer

Standard deviation measures the dispersion of outcomes around the expected value, making it the primary metric for quantifying risk spread.

Question 2

Value at Risk (VaR) at a 95% confidence level means that losses will exceed the VaR estimate in approximately what percentage of cases?

Accepted Answer

5%

Answer

A 95% VaR means losses exceed the threshold in 5% of scenarios — the remaining 5% tail of the distribution.

Question 3

In risk management, Expected Shortfall (ES) improves on VaR because it:

Accepted Answer

Averages losses beyond the VaR threshold

Answer

Expected Shortfall (also called CVaR) computes the mean of all losses exceeding the VaR cutoff, capturing tail severity that VaR ignores.

Question 4

A risk analyst models losses with an exponential distribution. If the mean loss is $200,000, what is the probability that a single loss exceeds $400,000?

Accepted Answer

e⁻² ≈ 13.5%

Answer

For an exponential distribution, P(X > 2μ) = e^(−2) ≈ 0.135, because the rate λ = 1/μ and P(X > t) = e^(−λt).

Question 5

Which technique randomly samples from probability distributions to simulate thousands of possible risk outcomes?

Accepted Answer

Monte Carlo simulation

Answer

Monte Carlo simulation generates large numbers of random scenarios by sampling input distributions, producing an empirical loss distribution.

Statistics Practice Test

Statistics Practice Test

Statistics Risk Assessment & Management 2