Free GARP FRM Part I Valuation and Risk Models Practice Questions (2026)

Sample Questions

Question 1 Easy

Which of the following statements about Expected Shortfall (ES) is correct?

Solution

B is correct. Expected Shortfall is defined as the average loss in the tail beyond the VaR cutoff:

\text{ES}_\alpha = E[L \mid L > \text{VaR}_\alpha]

. It is sometimes called Conditional VaR or Average VaR. Because it averages over all tail outcomes, ES is a coherent (subadditive) risk measure, whereas VaR is not coherent in general.

Question 2 Medium

A bond's current yield is 4.8% and its yield to maturity is 5.2%. This bond is most likely trading:

Solution

A is correct.

Current yield = Annual coupon / Market price. YTM > Current yield implies the bond is priced below par (at a discount). When a bond trades at a discount, the capital gain from pulling to par at maturity adds to the coupon return, making YTM exceed current yield.

Question 3 Hard

A risk team has computed a 1-day 99% parametric VaR of $100,000 for a trading book. Assuming returns are i.i.d. and normally distributed, what is the corresponding 10-day 95% VaR?

Solution

B is correct. Two adjustments are required. First, scale the horizon using the square-root-of-time rule: multiply by

\sqrt{10} = 3.1623

. Second, change the quantile from 99%

(z = 2.326)

to 95%

(z = 1.645)

: multiply by

1.645/2.326 = 0.7073

. Combining, 10-day 95% VaR

= 100{,}000 \times 3.1623 \times 0.7073 \approx 223{,}600

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