CRA Financial Risk Modeling & Quantitative Analysis 2

Question 1

Which statistical measure captures the average loss in the tail of a loss distribution beyond the VaR threshold?

Accepted Answer

Expected Shortfall (CVaR)

Answer

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?

Accepted Answer

α = ARCH effect (reaction to shocks), β = GARCH effect (persistence of volatility)

Answer

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?

Accepted Answer

Reduce the dimensionality of correlated interest rate factors

Answer

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?

Accepted Answer

Returns are i.i.d. (independently and identically distributed)

Answer

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?

Accepted Answer

Clayton copula

Answer

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.

(CRA) Certified Risk Analyst Practice Test

(CRA) Certified Risk Analyst Practice Test

CRA Financial Risk Modeling & Quantitative Analysis 2