CRA Financial Risk Modeling & Quantitative Analysis 2 — Questions and Answers
Question 1: Which statistical measure captures the average loss in the tail of a loss distribution beyond the VaR threshold?
- Expected Shortfall (CVaR) (Correct answer)
- Standard deviation
- Semi-variance
- Tracking error
Correct answer: Expected Shortfall (CVaR)
Expected Shortfall (also called CVaR or Conditional VaR) measures the average loss given that losses exceed the VaR level, capturing tail risk better than VaR alone.
Question 2: In a GARCH(1,1) model, what do the parameters α and β represent?
- α = ARCH effect (reaction to shocks), β = GARCH effect (persistence of volatility) (Correct answer)
- α = mean reversion speed, β = long-run variance
- α = drift term, β = autocorrelation coefficient
- α = skewness adjustment, β = kurtosis adjustment
Correct answer: α = ARCH effect (reaction to shocks), β = GARCH effect (persistence of volatility)
In GARCH(1,1), α captures how much current volatility reacts to the latest squared return shock, while β measures how much past conditional variance persists.
Question 3: A risk analyst uses Principal Component Analysis (PCA) on a yield curve. What is the primary purpose?
- Reduce the dimensionality of correlated interest rate factors (Correct answer)
- Eliminate all basis risk from the portfolio
- Calculate the exact duration of each bond
- Forecast future default probabilities
Correct answer: Reduce the dimensionality of correlated interest rate factors
PCA decomposes correlated yield curve movements into uncorrelated principal components, typically capturing level, slope, and curvature shifts with far fewer factors.
Question 4: What is the key assumption of the square-root-of-time rule when scaling daily VaR to a longer horizon?
- Returns are i.i.d. (independently and identically distributed) (Correct answer)
- Volatility follows a deterministic path
- Correlations increase proportionally with time
- The portfolio has no options or nonlinear exposures
Correct answer: Returns are i.i.d. (independently and identically distributed)
The square-root-of-time rule assumes i.i.d. returns so that variance scales linearly with time, allowing daily VaR to be multiplied by √T for a T-day horizon.
Question 5: Which copula is most appropriate for modeling asymmetric tail dependence where extreme losses co-occur more often than extreme gains?
- Clayton copula (Correct answer)
- Gaussian copula
- Frank copula
- Independence copula
Correct answer: Clayton copula
The Clayton copula exhibits strong lower tail dependence, making it suitable for modeling scenarios where joint extreme losses are more likely than joint extreme gains.
Question 6: A Monte Carlo simulation generates 10,000 scenarios for a portfolio. At 99% confidence, the VaR corresponds to which loss rank?
- The 100th largest loss (Correct answer)
- The 10th largest loss
- The 1,000th largest loss
- The 9,900th largest loss
Correct answer: The 100th largest loss
At 99% confidence with 10,000 scenarios, VaR is the loss at the 1% tail, which is the 100th largest loss (10,000 × 0.01 = 100).
Question 7: What does the Cornish-Fisher expansion adjust for when estimating VaR?
- Non-normality in the return distribution (skewness and excess kurtosis) (Correct answer)
- Time-varying correlations between assets
- Liquidity-adjusted holding periods
- Model parameter estimation error
Correct answer: Non-normality in the return distribution (skewness and excess kurtosis)
The Cornish-Fisher expansion modifies the standard normal quantile to account for skewness and excess kurtosis in actual return distributions, improving VaR accuracy.
CRA Financial Risk Modeling & Quantitative Analysis 2
Which statistical measure captures the average loss in the tail of a loss distribution beyond the VaR threshold?