Advanced Financial Risk Manager (FRM)
Multiple Choice Questions (MCQs) with
Answers and Explanations for FRM
Certification and Graduate-Level Risk
Management Exams
1. A trading portfolio has a daily Value at Risk (VaR) of $4 million at the 99% confidence
level. Which interpretation is most accurate?
A. The portfolio will lose exactly $4 million once every 100 trading days.
B. The expected daily loss is $4 million.
C. There is a 1% probability that the portfolio will lose more than $4 million over one
trading day.
D. The maximum possible daily loss is limited to $4 million.
Explanation: VaR estimates a loss threshold for a specified confidence level and time horizon. A
99% one-day VaR of $4 million implies there is a 1% chance that losses will exceed $4 million
in one trading day.
2. Which limitation of Value at Risk (VaR) is most directly addressed by Expected Shortfall
(Conditional VaR)?
A. VaR ignores historical data.
B. VaR does not measure the magnitude of losses beyond the confidence threshold.
C. VaR overestimates diversification benefits.
D. VaR assumes zero market volatility.
Explanation: Expected Shortfall estimates the average loss conditional on losses exceeding the
VaR threshold, providing information about tail risk that VaR alone does not capture.
3. A bank uses a one-factor credit risk model. Which variable primarily drives the
correlation between defaults?
A. Recovery rates
, B. Loan maturity
C. A common systematic risk factor affecting all borrowers
D. Individual borrower credit scores only
Explanation: One-factor credit risk models assume that default correlation arises primarily from
exposure to a shared systematic economic factor.
4. Which Greek measures the sensitivity of an option's value to changes in the volatility of
the underlying asset?
A. Delta
B. Gamma
C. Vega
D. Theta
Explanation: Vega measures the change in an option's value resulting from a one-percentage-
point change in implied volatility.
5. A financial institution funds long-term fixed-rate loans with short-term variable-rate
deposits. Which risk is most significant?
A. Currency risk
B. Interest rate risk due to maturity mismatch
C. Commodity price risk
D. Operational risk
Explanation: Funding long-term fixed-rate assets with short-term liabilities exposes the
institution to refinancing risk and adverse interest rate movements.
6. Which risk measure satisfies the subadditivity property required of a coherent risk
measure?
A. Historical VaR
B. Parametric VaR
C. Expected Shortfall
Multiple Choice Questions (MCQs) with
Answers and Explanations for FRM
Certification and Graduate-Level Risk
Management Exams
1. A trading portfolio has a daily Value at Risk (VaR) of $4 million at the 99% confidence
level. Which interpretation is most accurate?
A. The portfolio will lose exactly $4 million once every 100 trading days.
B. The expected daily loss is $4 million.
C. There is a 1% probability that the portfolio will lose more than $4 million over one
trading day.
D. The maximum possible daily loss is limited to $4 million.
Explanation: VaR estimates a loss threshold for a specified confidence level and time horizon. A
99% one-day VaR of $4 million implies there is a 1% chance that losses will exceed $4 million
in one trading day.
2. Which limitation of Value at Risk (VaR) is most directly addressed by Expected Shortfall
(Conditional VaR)?
A. VaR ignores historical data.
B. VaR does not measure the magnitude of losses beyond the confidence threshold.
C. VaR overestimates diversification benefits.
D. VaR assumes zero market volatility.
Explanation: Expected Shortfall estimates the average loss conditional on losses exceeding the
VaR threshold, providing information about tail risk that VaR alone does not capture.
3. A bank uses a one-factor credit risk model. Which variable primarily drives the
correlation between defaults?
A. Recovery rates
, B. Loan maturity
C. A common systematic risk factor affecting all borrowers
D. Individual borrower credit scores only
Explanation: One-factor credit risk models assume that default correlation arises primarily from
exposure to a shared systematic economic factor.
4. Which Greek measures the sensitivity of an option's value to changes in the volatility of
the underlying asset?
A. Delta
B. Gamma
C. Vega
D. Theta
Explanation: Vega measures the change in an option's value resulting from a one-percentage-
point change in implied volatility.
5. A financial institution funds long-term fixed-rate loans with short-term variable-rate
deposits. Which risk is most significant?
A. Currency risk
B. Interest rate risk due to maturity mismatch
C. Commodity price risk
D. Operational risk
Explanation: Funding long-term fixed-rate assets with short-term liabilities exposes the
institution to refinancing risk and adverse interest rate movements.
6. Which risk measure satisfies the subadditivity property required of a coherent risk
measure?
A. Historical VaR
B. Parametric VaR
C. Expected Shortfall
