FRM Advanced Topics 3 — Questions and Answers
Question 1: When hedging a bond portfolio, immunization that matches both duration and convexity provides protection against:
- Only small parallel yield shifts
- Larger parallel shifts more accurately than duration alone (Correct answer)
- Non-parallel twists in the curve
- Credit spread widening
Correct answer: Larger parallel shifts more accurately than duration alone
Adding convexity matching improves the approximation of price changes for larger parallel rate moves beyond first-order duration.
Question 2: A key limitation of historical simulation VaR compared to parametric VaR is that historical simulation:
- Assumes normally distributed returns
- Cannot capture fat tails
- Relies entirely on the observed sample period and may miss unobserved events (Correct answer)
- Requires a variance-covariance matrix
Correct answer: Relies entirely on the observed sample period and may miss unobserved events
Historical simulation is bounded by the scenarios in the lookback window, so events not in the sample are not represented.
Question 3: In a total return swap, the total return payer effectively:
- Retains the credit and market risk of the reference asset
- Transfers the credit and market risk of the reference asset to the receiver (Correct answer)
- Buys protection on its own debt
- Earns the reference asset's price appreciation
Correct answer: Transfers the credit and market risk of the reference asset to the receiver
The total return payer passes all economic performance of the asset to the receiver, shedding both market and credit risk.
Question 4: Wrong-way risk in counterparty credit exposure refers to the situation where:
- Exposure decreases as counterparty credit quality worsens
- Exposure increases as counterparty credit quality worsens (Correct answer)
- Collateral fully offsets exposure
- Exposure is uncorrelated with default probability
Correct answer: Exposure increases as counterparty credit quality worsens
Wrong-way risk arises when the exposure to a counterparty rises at the same time its probability of default increases.
Question 5: Which Greek measures the rate of change of an option's delta with respect to the underlying price?
- Vega
- Theta
- Gamma (Correct answer)
- Rho
Correct answer: Gamma
Gamma is the second derivative of option value with respect to the underlying, i.e., the sensitivity of delta.
Question 6: A risk manager backtesting a 99% one-day VaR over 250 days using the Basel traffic-light approach would fall in the 'red zone' starting at approximately how many exceptions?
- 1 exception
- 4 exceptions
- 5 exceptions
- 10 exceptions (Correct answer)
Correct answer: 10 exceptions
Under the Basel traffic-light test, ten or more exceptions in 250 days places the model in the red zone.
Question 7: The funding valuation adjustment (FVA) in derivatives pricing primarily reflects:
- The cost of counterparty default
- The cost of funding uncollateralized derivative positions (Correct answer)
- The benefit of posting collateral
- Regulatory capital charges
Correct answer: The cost of funding uncollateralized derivative positions
FVA captures the funding cost or benefit associated with hedging and collateralizing uncollateralized derivative trades.
FRM Advanced Topics 3
When hedging a bond portfolio, immunization that matches both duration and convexity provides protection against: