Financial Risk Management Advanced — Questions and Answers

Question 1: Under the Basel III framework, what is the minimum Common Equity Tier 1 (CET1) capital ratio required for banks?

4.5% (Correct answer)
6.0%
8.0%
10.5%

Correct answer: 4.5%

Basel III sets the minimum CET1 ratio at 4.5% of risk-weighted assets, with an additional 2.5% capital conservation buffer on top.

Question 2: Which risk measure captures the expected loss in the tail of the distribution beyond the VaR threshold?

Expected Shortfall (CVaR) (Correct answer)
Conditional VaR only at 95%
Stress VaR
Incremental Risk Charge

Correct answer: Expected Shortfall (CVaR)

Expected Shortfall (also called CVaR or ES) is the average of losses that exceed the VaR threshold, capturing tail risk more fully than VaR alone.

Question 3: A $100M bond portfolio has a modified duration of 6 and yields rise by 50 bps. What is the approximate price change?

-$3,000,000 (Correct answer)
+$3,000,000
-$6,000,000
-$300,000

Correct answer: -$3,000,000

Price change ≈ -Modified Duration × ΔYield × Portfolio Value = -6 × 0.005 × $100M = -$3M.

Question 4: In the context of credit risk, what does the Loss Given Default (LGD) represent?

The fraction of exposure lost when a borrower defaults (Correct answer)
The probability that a borrower will default
The total outstanding exposure at the time of default
The expected recovery rate minus collateral value

Correct answer: The fraction of exposure lost when a borrower defaults

LGD is the proportion of the exposure at default that is not recovered after the borrower defaults, typically expressed as 1 minus the recovery rate.

Question 5: Which stress testing approach involves applying a consistent set of severe but plausible macroeconomic scenarios to a portfolio?

Scenario analysis (Correct answer)
Sensitivity analysis
Historical simulation
Monte Carlo simulation

Correct answer: Scenario analysis

Scenario analysis stress tests a portfolio using coherent macroeconomic narratives (e.g., recession, rate spike) rather than changing one variable at a time.

Question 6: What is the primary purpose of a Credit Valuation Adjustment (CVA)?

To adjust the fair value of derivatives for counterparty default risk (Correct answer)
To calculate regulatory capital for market risk
To measure operational risk losses from system failures
To assess interest rate risk in the banking book

Correct answer: To adjust the fair value of derivatives for counterparty default risk

CVA is the market value of counterparty credit risk embedded in OTC derivatives, representing the expected loss due to counterparty default.

Question 7: A bank uses the Internal Ratings-Based (IRB) approach for credit risk. Which parameter does the bank itself estimate under the Foundation IRB (F-IRB) approach?

Probability of Default (PD) only (Correct answer)
PD, LGD, and EAD
LGD and EAD only
Only the Maturity (M) parameter

Correct answer: Probability of Default (PD) only

Under F-IRB, banks estimate PD internally but use supervisory estimates for LGD, EAD, and maturity; under Advanced IRB, banks estimate all parameters.

Question 8: Which of the following best describes the 'wrong-way risk' in counterparty credit risk?

Exposure increases precisely when counterparty creditworthiness deteriorates (Correct answer)
Exposure decreases when market volatility rises
Collateral value increases when counterparty defaults
Netting agreements reduce exposure when correlation is high

Correct answer: Exposure increases precisely when counterparty creditworthiness deteriorates

Wrong-way risk arises when the exposure to a counterparty is positively correlated with the counterparty's probability of default, amplifying potential losses.

Question 9: In a variance-covariance VaR model, increasing the holding period from 1 day to 10 days scales VaR by which factor (assuming i.i.d. returns)?

√10 ≈ 3.162 (Correct answer)
10
√252 ≈ 15.87
2

Correct answer: √10 ≈ 3.162

Under the square-root-of-time rule for i.i.d. returns, VaR scales by the square root of the holding period, so 1-day VaR × √10 gives the 10-day VaR.

Question 10: Which liquidity risk metric measures the time it would take to liquidate a portfolio under stressed market conditions?

Liquidity-Adjusted VaR (LVaR) (Correct answer)
Net Stable Funding Ratio (NSFR)
Liquidity Coverage Ratio (LCR)
Current Ratio

Correct answer: Liquidity-Adjusted VaR (LVaR)

LVaR incorporates bid-ask spreads and market depth to estimate losses from unwinding positions over a realistic liquidation horizon under stress.

Question 11: A credit default swap (CDS) with a notional of $10M and a 200 bps spread requires annual premium payments of:

$200,000 (Correct answer)
$2,000,000
$20,000
$1,000,000

Correct answer: $200,000

Annual premium = Notional × CDS spread = $10,000,000 × 0.0200 = $200,000.

Question 12: Under FRTB (Fundamental Review of the Trading Book), which risk measure replaces VaR as the primary internal model metric?

Expected Shortfall at 97.5% (Correct answer)
VaR at 99.9%
Stressed VaR at 99%
Incremental Default Risk at 99.9%

Correct answer: Expected Shortfall at 97.5%

FRTB mandates Expected Shortfall at 97.5% confidence (calibrated to a stressed period) in place of the previous 99% VaR, better capturing tail risk.

Question 13: A portfolio manager wants to hedge the vega risk of a long options position. The most direct approach is to:

Buy or sell options with offsetting vega exposure (Correct answer)
Short the underlying asset
Enter an interest rate swap
Buy Treasury bonds

Correct answer: Buy or sell options with offsetting vega exposure

Vega risk (sensitivity to implied volatility changes) can only be hedged with instruments that also have vega, primarily other options.

Question 14: The Herfindahl-Hirschman Index (HHI) is used in credit risk to measure:

Concentration risk within a loan portfolio (Correct answer)
Market risk in equity portfolios
Operational risk event frequency
Liquidity risk in funding markets

Correct answer: Concentration risk within a loan portfolio

HHI sums the squared exposure shares of each borrower or sector, providing a measure of portfolio concentration; a high HHI signals elevated concentration risk.

Question 15: What does the Incremental Risk Charge (IRC) in Basel 2.5 capture that standard VaR does not?

Default and migration risk for credit-sensitive positions in the trading book (Correct answer)
Operational losses from internal process failures
Systemic risk across the entire financial system
Interest rate risk in the banking book

Correct answer: Default and migration risk for credit-sensitive positions in the trading book

IRC was introduced to capture the default and credit migration risk for unsecuritized credit products in the trading book over a one-year horizon at 99.9% confidence.

Question 16: In extreme value theory (EVT), the Generalized Pareto Distribution (GPD) is used to model:

The distribution of losses that exceed a high threshold (Correct answer)
Normal day-to-day portfolio returns
Recovery rates on defaulted bonds
Interest rate term structure dynamics

Correct answer: The distribution of losses that exceed a high threshold

EVT uses GPD to fit the tails of loss distributions, specifically modeling observations that exceed a high threshold to better estimate extreme quantiles like VaR and ES.

Question 17: A firm's operational risk capital under the Basel III Standardized Approach (SA) is primarily driven by:

Business Indicator (BI) scaled by an Internal Loss Multiplier (Correct answer)
VaR calculated from operational loss history
A fixed percentage of gross income
Regulatory-assigned risk weights by event type

Correct answer: Business Indicator (BI) scaled by an Internal Loss Multiplier

The Basel III SA uses the Business Indicator (a proxy for revenue) multiplied by marginal coefficients and an Internal Loss Multiplier based on the firm's historical losses.

Question 18: Which of the following is a key assumption of the Merton structural model of credit risk?

A firm defaults when asset value falls below the face value of debt at maturity (Correct answer)
Default can only occur on coupon payment dates
Recovery rates are fixed at 40% regardless of asset value
Default intensity follows a Poisson process

Correct answer: A firm defaults when asset value falls below the face value of debt at maturity

In the Merton model, equity is a call option on firm assets; default occurs if asset value falls below debt face value at the debt's maturity date.

Question 19: Gamma risk in options trading refers to:

The rate of change of delta with respect to the underlying price (Correct answer)
Sensitivity of option price to changes in implied volatility
Sensitivity of option price to the passage of time
The rate of change of vega with respect to implied volatility

Correct answer: The rate of change of delta with respect to the underlying price

Gamma measures how much delta changes for a unit move in the underlying, indicating the curvature of the option's price-underlying relationship.

Question 20: Under the Liquidity Coverage Ratio (LCR) rule, what minimum percentage of net cash outflows over 30 days must a bank hold in High-Quality Liquid Assets (HQLA)?

100% (Correct answer)
75%
60%
125%

Correct answer: 100%

The LCR requires banks to maintain HQLA at least equal to 100% of projected net cash outflows over a 30-day stress period, ensuring short-term resilience.

Question 21: A risk manager observes that a portfolio's historical VaR backtesting shows 12 exceptions over 250 trading days at the 99% confidence level. According to Basel's traffic light framework, this result falls in which zone?

Red zone — model likely flawed (Correct answer)
Green zone — acceptable performance
Yellow zone — increased scrutiny required
Amber zone — regulatory review pending

Correct answer: Red zone — model likely flawed

The red zone begins at 10 or more exceptions over 250 days; 12 exceptions signals that the model likely underestimates risk and requires immediate review.

Financial Risk Management Advanced

Under the Basel III framework, what is the minimum Common Equity Tier 1 (CET1) capital ratio required for banks?

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