NEWEST FINANCIAL RISK MANAGER
(FRM) EXAM | ULTIMATE EXAM WITH
CORRECT ANSWERS AND RATIONALES
FOR CERTIFICATION SUCCESS
1. A portfolio has a 1-day 99% Value at Risk (VaR) of
$15 million. This means that:
A) There is a 1% chance that the portfolio will lose
more than $15 million in one day
B) There is a 99% chance that the portfolio will lose
more than $15 million
C) The expected loss is $15 million
D) The maximum possible loss is $15 million
E) The portfolio will never lose more than $15 million
Correct answer: A
Rationale: VaR is a threshold such that losses
exceeding that threshold occur with a specified
probability (1% in this case).
2. A portfolio has an expected return of 10% and a
standard deviation of 18%. The risk-free rate is 3%.
The Sharpe ratio is:
,A) 0.39
B) 0.50
C) 0.56
D) 0.67
E) 0.78
Correct answer: A
Rationale: (0.10 - 0.03) / 0.18 = 0..18 = 0.3889.
3. A stock has a beta of 1.3. The expected market
return is 9%, and the risk-free rate is 4%. Using
CAPM, the expected return is:
A) 9.5%
B) 10.0%
C) 10.5%
D) 11.0%
E) 11.5%
Correct answer: C
Rationale: 4% + 1.3 × (9% - 4%) = 4% + 6.5% = 10.5%.
,4. A bond has a modified duration of 6 years and a
convexity of 40. If interest rates increase by 50 basis
points, the approximate percentage change in the
bond price is:
A) -3.0%
B) -2.95%
C) -3.05%
D) -2.5%
E) -3.5%
Correct answer: B
Rationale: ΔP/P ≈ -D × Δy + 0.5 × C × (Δy)² = -6 × 0.005 +
0.5 × 40 × 0.000025 = -0.03 + 0.0005 = -0.0295 = -
2.95%.
5. A bank has a loan portfolio with total exposure of
$200 million. The probability of default (PD) is 3%, and
the loss given default (LGD) is 50%. The expected
loss is:
A) $1 million
B) $2 million
C) $3 million
D) $4 million
, E) $5 million
Correct answer: C
Rationale: EL = EAD × PD × LGD = $200M × 0.03 ×
0.50 = $200M × 0.015 = $3M.
6. Under the Basel II standardized approach for
credit risk, the risk weight for a sovereign (AAA to
AA-) is generally:
A) 0%
B) 20%
C) 50%
D) 100%
E) 150%
Correct answer: A
Rationale: High-rated sovereigns have a 0% risk
weight.
7. The "probability of default" (PD) in credit risk
models is:
A) The likelihood that a borrower will default within a
given time horizon
(FRM) EXAM | ULTIMATE EXAM WITH
CORRECT ANSWERS AND RATIONALES
FOR CERTIFICATION SUCCESS
1. A portfolio has a 1-day 99% Value at Risk (VaR) of
$15 million. This means that:
A) There is a 1% chance that the portfolio will lose
more than $15 million in one day
B) There is a 99% chance that the portfolio will lose
more than $15 million
C) The expected loss is $15 million
D) The maximum possible loss is $15 million
E) The portfolio will never lose more than $15 million
Correct answer: A
Rationale: VaR is a threshold such that losses
exceeding that threshold occur with a specified
probability (1% in this case).
2. A portfolio has an expected return of 10% and a
standard deviation of 18%. The risk-free rate is 3%.
The Sharpe ratio is:
,A) 0.39
B) 0.50
C) 0.56
D) 0.67
E) 0.78
Correct answer: A
Rationale: (0.10 - 0.03) / 0.18 = 0..18 = 0.3889.
3. A stock has a beta of 1.3. The expected market
return is 9%, and the risk-free rate is 4%. Using
CAPM, the expected return is:
A) 9.5%
B) 10.0%
C) 10.5%
D) 11.0%
E) 11.5%
Correct answer: C
Rationale: 4% + 1.3 × (9% - 4%) = 4% + 6.5% = 10.5%.
,4. A bond has a modified duration of 6 years and a
convexity of 40. If interest rates increase by 50 basis
points, the approximate percentage change in the
bond price is:
A) -3.0%
B) -2.95%
C) -3.05%
D) -2.5%
E) -3.5%
Correct answer: B
Rationale: ΔP/P ≈ -D × Δy + 0.5 × C × (Δy)² = -6 × 0.005 +
0.5 × 40 × 0.000025 = -0.03 + 0.0005 = -0.0295 = -
2.95%.
5. A bank has a loan portfolio with total exposure of
$200 million. The probability of default (PD) is 3%, and
the loss given default (LGD) is 50%. The expected
loss is:
A) $1 million
B) $2 million
C) $3 million
D) $4 million
, E) $5 million
Correct answer: C
Rationale: EL = EAD × PD × LGD = $200M × 0.03 ×
0.50 = $200M × 0.015 = $3M.
6. Under the Basel II standardized approach for
credit risk, the risk weight for a sovereign (AAA to
AA-) is generally:
A) 0%
B) 20%
C) 50%
D) 100%
E) 150%
Correct answer: A
Rationale: High-rated sovereigns have a 0% risk
weight.
7. The "probability of default" (PD) in credit risk
models is:
A) The likelihood that a borrower will default within a
given time horizon
