Free GARP FRM Part I Foundations of Risk Management Practice Questions

Practice 200 free Foundations of Risk Management questions for GARP FRM Part I.

200 Questions
63 Easy
91 Medium
46 Hard
2026 Syllabus

Sample Questions

Question 1 Easy
Which of the following losses is the clearest example of operational risk?
Solution
D is correct. Operational risk is the risk of loss arising from inadequate or failed internal processes, people, and systems, or from external events. A payments-system outage that produces duplicated, unrecoverable wires is a process-and-systems failure, which falls squarely within operational risk.
Question 2 Medium
A bank's loan portfolio has a probability of default (PD) of 2%, a loss given default (LGD) of 40%, and an exposure at default (EAD) of $50 million. What is the expected loss (EL) on the portfolio?
Solution
A is correct. Expected loss is computed as EL=PD×LGD×EADEL = PD \times LGD \times EAD. Substituting: EL=0.02×0.40×$50,000,000=$400,000EL = 0.02 \times 0.40 \times \$50{,}000{,}000 = \$400{,}000. This is the mean loss the bank expects from this portfolio over the horizon and is the amount typically covered through pricing and loan loss provisions.
Question 3 Hard
A diversified bank holds three independent business lines with the following standalone unexpected losses (ULs): Line 1 = $80 million, Line 2 = $60 million, Line 3 = $40 million. Assume pairwise correlations of 0.5 between every pair of lines. What is the bank's portfolio UL, and what is the diversification benefit relative to the simple sum of standalone ULs?
Solution
D is correct. Portfolio UL with pairwise correlations is computed as ULP=∑iULi2+2∑i<jρij ULi ULj.UL_P = \sqrt{\sum_i UL_i^2 + 2\sum_{i<j}\rho_{ij}\,UL_i\,UL_j}. Squared terms: 802+602+402=6400+3600+1600=11,60080^2 + 60^2 + 40^2 = 6400 + 3600 + 1600 = 11{,}600. Cross terms with ρ=0.5\rho = 0.5: 2×0.5×(80⋅60+80⋅40+60⋅40)=1×(4800+3200+2400)=10,4002 \times 0.5 \times (80\cdot60 + 80\cdot40 + 60\cdot40) = 1 \times (4800 + 3200 + 2400) = 10{,}400. Sum = 22,00022{,}000; ULP=22,000≈$148.3UL_P = \sqrt{22{,}000} \approx \$148.3 million. The simple sum of standalone ULs is $80+$60+$40=$180\$80 + \$60 + \$40 = \$180 million, so the diversification benefit is $180−$148.3≈$31.7\$180 - \$148.3 \approx \$31.7 million.
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