CRA Financial Risk Modeling & Quantitative Analysis 3 — Questions and Answers
Question 1: A bank's internal model back-test produces 12 exceptions over 250 trading days at 99% VaR. Under Basel traffic light rules, which zone does this fall into?
- Red zone (capital multiplier increase required) (Correct answer)
- Green zone (model accepted)
- Yellow zone (monitoring required)
- Orange zone (model rejected pending review)
Correct answer: Red zone (capital multiplier increase required)
Basel traffic light rules place 10 or more exceptions in the red zone, triggering mandatory increases to the capital multiplier for market risk.
Question 2: Which risk measure satisfies all four axioms of coherence (translation invariance, subadditivity, positive homogeneity, and monotonicity)?
- Expected Shortfall (Correct answer)
- Value at Risk
- Semi-variance
- Maximum drawdown
Correct answer: Expected Shortfall
Expected Shortfall is a coherent risk measure; VaR famously violates subadditivity, meaning diversification can appear to increase risk when measured by VaR.
Question 3: In credit risk modeling, what does the asset correlation parameter ρ control in the Vasicek single-factor model?
- The sensitivity of an obligor's asset returns to the common systematic factor (Correct answer)
- The recovery rate given default
- The probability of default in isolation
- The maturity adjustment for long-term exposures
Correct answer: The sensitivity of an obligor's asset returns to the common systematic factor
In the Vasicek model, ρ determines how much of an obligor's asset value movements are driven by the shared market factor versus idiosyncratic shocks.
Question 4: A risk analyst computes a 1-day 99% parametric VaR of $2M. After applying a liquidity-adjusted horizon of 10 days, what is the adjusted VaR assuming i.i.d. returns?
- $6.32M (Correct answer)
- $20M
- $2M
- $63.2M
Correct answer: $6.32M
Scaling by √10 gives $2M × √10 ≈ $2M × 3.162 = $6.32M under the square-root-of-time assumption.
Question 5: What is the primary limitation of Historical Simulation for computing VaR?
- It relies entirely on past data and cannot account for unprecedented market conditions (Correct answer)
- It assumes returns are normally distributed
- It cannot handle portfolios with options
- It requires specifying a parametric distribution for each risk factor
Correct answer: It relies entirely on past data and cannot account for unprecedented market conditions
Historical Simulation uses actual past returns as scenarios, so it cannot capture tail risks from events that have not occurred in the historical window.
Question 6: Which test is commonly used to assess whether a time series of financial returns exhibits autoregressive conditional heteroskedasticity (ARCH effects)?
- Engle's ARCH-LM test (Correct answer)
- Jarque-Bera test
- Augmented Dickey-Fuller test
- Ljung-Box Q test
Correct answer: Engle's ARCH-LM test
Engle's Lagrange Multiplier test regresses squared residuals on lagged squared residuals to detect clustering of variance, the hallmark of ARCH effects.
Question 7: In extreme value theory (EVT), the Peaks Over Threshold (POT) method models tail losses using which distribution?
- Generalized Pareto Distribution (GPD) (Correct answer)
- Generalized Extreme Value Distribution (GEV)
- Log-normal distribution
- Student's t-distribution
Correct answer: Generalized Pareto Distribution (GPD)
The POT method fits a Generalized Pareto Distribution to exceedances above a chosen high threshold, providing a theoretically justified model for the tail.
CRA Financial Risk Modeling & Quantitative Analysis 3
A bank's internal model back-test produces 12 exceptions over 250 trading days at 99% VaR.
Under Basel traffic light rules, which zone does this fall into?