Here are three original FRM Part I-style questions, with the correct answer and a detailed explanation. Try to answer before reading the solution: each one should take 2 to 3 minutes with a financial calculator.
Question 1: parametric VaR (Valuation and Risk Models)
A portfolio is worth EUR 10 million. Its daily returns are normally distributed with a mean of zero and a standard deviation of 1.5%. What is the 1-day VaR at a 99% confidence level?
- A. EUR 246,750
- B. EUR 348,900
- C. EUR 1,103,300
- D. EUR 150,000
Correct answer: B. For a normal distribution, the 99% quantile is 2.326. VaR = 2.326 × 1.5% × EUR 10,000,000 ≈ EUR 348,900. Answer A uses the 95% quantile (1.645), answer C is a 10-day VaR (× √10) and answer D leaves out the quantile.
Question 2: forward price (Financial Markets and Products)
A non-dividend-paying stock trades at EUR 100. The risk-free rate is 4% a year with continuous compounding. What is the forward price of a 6-month contract?
- A. EUR 98.02
- B. EUR 102.00
- C. EUR 102.02
- D. EUR 104.08
Correct answer: C. With no dividends, F = S × e^(r × T) = 100 × e^(0.04 × 0.5) = 100 × e^0.02 ≈ EUR 102.02. Answer B applies simple interest instead of continuous compounding, answer D uses a one-year maturity and answer A discounts instead of compounding.
Question 3: expected credit loss (Valuation and Risk Models)
A bank lends EUR 5 million to a company. The one-year probability of default is 2% and the recovery rate in default is 40%. What is the one-year expected loss?
- A. EUR 60,000
- B. EUR 40,000
- C. EUR 100,000
- D. EUR 3,000,000
Correct answer: A. Expected loss = probability of default × loss given default × exposure = 2% × (1 − 40%) × EUR 5,000,000 = EUR 60,000. Answer B uses the recovery rate instead of the loss given default, answer C ignores recovery and answer D ignores the probability of default.