FRM P1 Part I: mock exams and practice questions

Sample question 1 · Foundations of Risk Management

Which statement best describes how a bank should treat expected and unexpected credit losses?

1. A Expected losses should be covered by loan pricing and provisions, while capital is held as a buffer against unexpected losses.
2. B Capital should be sized to cover expected losses, while unexpected losses are absorbed by loan pricing and provisions.
3. C Diversifying across many borrowers removes unexpected losses, so capital is needed only for expected losses.
4. D Both expected and unexpected losses should be covered entirely by loan pricing, so no capital buffer is required.

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Answer: A. Expected loss (EL) is the mean of the loss distribution (PD x LGD x EAD). Because it is anticipated, it is treated as a cost: it is built into the interest rate or fee and covered by provisions.

Unexpected loss (UL) is the amount by which losses may exceed EL at a chosen confidence level. Banks hold (economic or regulatory) capital to absorb UL so that they remain solvent in bad years. Diversification lowers UL but cannot remove the systematic part driven by correlated defaults.

Sample question 2 · Valuation and Risk Models

Halvorsen Capital holds an equity portfolio worth $40 million. Daily returns are assumed to be normally distributed with a mean of zero and a standard deviation of 1.1%, and returns are independent from day to day. What is the 10-day 99% value at risk (VaR) of the portfolio?

1. A $1,023,593
2. B $2,288,653
3. C $3,236,885
4. D $10,235,931

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Answer: C. With a zero mean, VaR = V x sigma x z.

- 1-day 99% VaR = 40,000,000 x 0.011 x 2.32635 = $1,023,593
- Under independence, volatility scales with the square root of time: 10-day VaR = $1,023,593 x sqrt(10) = $1,023,593 x 3.1623 = $3,236,885.