Free GARP FRM Part II Market Risk Practice Questions

Practice 92 free Market Risk questions for GARP FRM Part II.

92 Questions
32 Easy
39 Medium
21 Hard
2026 Syllabus

Sample Questions

Question 1 Easy
Which of the four axioms of coherent risk measures is generally NOT satisfied by Value-at-Risk (VaR)?
Solution
D is correct. VaR satisfies monotonicity, translation invariance, and positive homogeneity for any distribution, but it generally fails subadditivity outside restricted cases such as elliptical (e.g., multivariate normal) loss distributions. Concretely, one can construct two positions whose combined VaR exceeds the sum of standalone VaRs, contradicting the diversification benefit that coherence requires. This subadditivity failure is the central motivation for switching to Expected Shortfall, which is coherent.
Question 2 Medium
Using the same 100 daily P&L observations as before, with the five worst losses equal to -$10M, -$8M, -$7M, -$6M, and -$5M (and the 6th-worst loss equal to -$4M), what is the 1-day 95% expected shortfall (ES)?
Solution
C is correct. ES at the 95% level is the average loss conditional on exceeding the 95% VaR. With 100 observations, the worst 5%5\% corresponds to the 5 worst losses. Therefore ES0.95=15(10+8+7+6+5)=365=$7.2M\text{ES}_{0.95} = \frac{1}{5}(10 + 8 + 7 + 6 + 5) = \frac{36}{5} = \$7.2\text{M}.
Question 3 Hard
A risk manager fits a Generalized Pareto Distribution (GPD) to losses exceeding a threshold u=5u = 5 million. The estimated parameters are shape ΞΎ=0.25\xi = 0.25 and scale Ξ²=2.0\beta = 2.0 million. Of n=1,000n = 1{,}000 total observations, Nu=50N_u = 50 exceed the threshold. Using the GPD-based formula, the 99.5% one-day VaR is closest to:
Solution
C is correct. The GPD-based VaR formula is VaRΞ±=u+Ξ²ΞΎ[(nNu(1βˆ’Ξ±))βˆ’ΞΎβˆ’1].\text{VaR}_\alpha = u + \frac{\beta}{\xi}\left[\left(\frac{n}{N_u}(1-\alpha)\right)^{-\xi} - 1\right]. With u=5u = 5, Ξ²=2.0\beta = 2.0, ΞΎ=0.25\xi = 0.25, n/Nu=1000/50=20n/N_u = 1000/50 = 20, and 1βˆ’Ξ±=0.0051 - \alpha = 0.005: the inner term is 20Γ—0.005=0.1020 \times 0.005 = 0.10. Then 0.10βˆ’0.25=100.25β‰ˆ1.77830.10^{-0.25} = 10^{0.25} \approx 1.7783. So VaR99.5%=5+2.00.25(1.7783βˆ’1)=5+8Γ—0.7783=5+6.23β‰ˆ11.23\text{VaR}_{99.5\%} = 5 + \frac{2.0}{0.25}(1.7783 - 1) = 5 + 8 \times 0.7783 = 5 + 6.23 \approx 11.23 million, closest to 11.6 million.
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