Financial Risk Modeling & Quantitative Analysis Flashcards

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

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.

In a GARCH(1,1) model, what do the parameters α and β represent?

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.

A risk analyst uses Principal Component Analysis (PCA) on a yield curve. What is the primary purpose?

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.

What is the key assumption of the square-root-of-time rule when scaling daily VaR to a longer horizon?

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.

Which copula is most appropriate for modeling asymmetric tail dependence where extreme losses co-occur more often than extreme gains?

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.

A Monte Carlo simulation generates 10,000 scenarios for a portfolio. At 99% confidence, the VaR corresponds to which loss rank?

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).

What does the Cornish-Fisher expansion adjust for when estimating VaR?

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.