Free FRM practice questions

1. 01

   Risk foundations

   Question 1. A stock has a beta of 1.5 with the market portfolio. The risk-free rate is 6.0% per year and the expected market return is 10.0% per year. According to the CAPM, the stock's expected return is ___.

   Answer to question 1

   AA. 0.0%BB. 10.0%CC. 12.0%DD. 15.0%

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2. 02

   Quantitative analysis

   Question 2. Under the null hypothesis that the first m autocorrelations of a stationary raw time series are jointly equal to zero, which asymptotic distribution is followed by the Ljung-Box Q statistic?

   Answer to question 2

   AA. Student's t-distribution with m - 1 degrees of freedomBB. Standard normal distributionCC. F-distribution with m numerator and T - m denominator degrees of freedomDD. Chi-square distribution with m degrees of freedom

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3. 03

   Financial markets and products

   Question 3. A commercial bank that holds a portfolio of floating-rate loans earning benchmark SOFR plus a contractual credit spread can synthetically transform this portfolio into a fixed-rate asset by:

   Answer to question 3

   AA. paying a fixed swap rate against floating SOFR, which yields a combined interest stream of the fixed swap rate minus the original credit spread.BB. restructuring the underlying loan agreements to convert floating borrower obligations directly into fixed-rate benchmark payments.CC. entering an interest rate swap to receive fixed and pay SOFR, generating an effective net yield equal to the swap fixed rate plus the credit spread.DD. exchanging floating receipts for fixed swap inflows, which replaces the default risk of the loan portfolio with the credit exposure of the swap counterparty.

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4. 04

   Valuation and risk models

   Question 4. To protect a fixed-income portfolio against substantial parallel interest rate shocks using a duration and convexity hedging strategy rather than a duration-only hedge, a risk manager must:

   Answer to question 4

   AA. solve a system of two linear equations using two distinct hedging instruments to simultaneously drive net dollar duration and net dollar convexity to zero.BB. use a single hedging instrument under the assumption that yield changes follow a thin-tailed normal distribution where curvature effects are negligible.CC. match the exact timing and nominal value of every underlying cash flow across all payment dates to eliminate parallel slope exposure.DD. adjust key rate durations across individual curve tenors to specifically isolate and neutralize non-parallel yield curve reshaping.

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5. 05

   Quantitative analysis

   Question 5. Which of the following best characterizes how a risk manager applies Principal Component Analysis (PCA) to compress high-dimensional yield curve data while retaining maximum explanatory power?

   Answer to question 5

   AA. It isolates a select subset of original benchmark tenors and removes all other maturities to eliminate redundant risk factors.BB. It extracts factors that are fully statistically independent across all market regimes, eliminating non-linear tail co-movements during market stress.CC. It generates orthogonal linear combinations of all original tenors ordered by descending eigenvalue, producing linearly uncorrelated factors that capture maximal system-wide variance.DD. It performs non-linear transformations on individual maturities to guarantee that an identical proportion of variance is preserved for every single yield curve tenor.

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Questions from the MiloPrep question bank. Independently authored practice, not official exam items. This short set is for learning and does not predict an exam score.