Free GARP FRM Part II Risk and Investment Management Practice Questions

Practice 66 free Risk and Investment Management questions for GARP FRM Part II.

66 Questions
24 Easy
27 Medium
15 Hard
2026 Syllabus

Sample Questions

Question 1 Easy
Which of the following statements BEST describes the central insight of factor theory in investment management?
Solution
A is correct. Factor theory holds that an asset's expected return is determined by its exposures (betas) to a set of systematic risk factors (e.g., market, size, value, momentum, term, credit) and the prices of risk associated with each factor. Idiosyncratic risk is diversifiable and therefore earns no premium in equilibrium.
Question 2 Medium
A portfolio has 100 daily P&L observations. The five worst daily P&L values (in $ millions) are: -10, -8, -7, -6, and -5. What is the 1-day 95% Expected Shortfall (ES)?
Solution
C is correct. Expected Shortfall at 95% confidence is the conditional average loss in the worst 5% tail. With 100 observations, the 5% tail contains the five worst losses: 10, 8, 7, 6, 5 ($M). ES=(10+8+7+6+5)/5=36/5=7.2\text{ES} = (10 + 8 + 7 + 6 + 5)/5 = 36/5 = 7.2. The 1-day 95% ES is $7.2M.
Question 3 Hard
A portfolio's daily P&L is normally distributed with zero mean. The one-day 95% parametric VaR is $1 million. Using z0.95=1.645z_{0.95} = 1.645, z0.99=2.326z_{0.99} = 2.326, and assuming square-root-of-time scaling, the 10-day 99% expected shortfall is closest to:
Solution
A is correct. First back out the dollar standard deviation from the given 95% VaR: σV=$1,000,000/1.645=$607,903\sigma V = \$1{,}000{,}000 / 1.645 = \$607{,}903. Next, the daily 99% expected shortfall multiplier under normality is ϕ(z0.99)/(1−0.99)=0.02665/0.01≈2.665\phi(z_{0.99})/(1-0.99) = 0.02665/0.01 \approx 2.665, where ϕ\phi is the standard normal density. Then daily 99% ES =2.665×$607,903≈$1,620,000= 2.665 \times \$607{,}903 \approx \$1{,}620{,}000. Scaling to a 10-day horizon by 10≈3.162\sqrt{10} \approx 3.162 gives $1,620,000×3.162≈$5.12\$1{,}620{,}000 \times 3.162 \approx \$5.12 million.
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