A candidate sees a question asking for the 95% Value-at-Risk (VaR) of a $10 million portfolio. He recognizes the inputs and quickly applies the parametric formula he memorized: portfolio value × Z-score × standard deviation. He picks his answer and moves on, feeling efficient. He later finds out he failed the exam by a narrow margin. The question had provided a set of historical returns, and the examiner was testing his judgment to apply the historical simulation method, not the parametric one. This is the most dangerous trap in the VRM section: mistaking calculation speed for correct model selection.
This article provides free practice questions for the FRM Part I Valuation and Risk Models (VRM) section, updated for the 2026 exam. Each question includes a detailed explanation of the correct answer and why the distractors are wrong, covering critical topics like Value-at-Risk (VaR), options pricing, and fixed-income valuation.
Key facts
- Official Body
- Global Association of Risk Professionals (GARP)
- Exam Cost (Part I)
- $400 one-time enrollment fee plus a $600 (early) to $800 (standard) registration fee.
- Exam Sections
- 4 domains (Foundations, Quants, FMP, VRM)
- VRM Section Weighting
- 30% of the Part I exam (30 questions)
- Passing Score
- Not a fixed percentage; determined by the FRM Committee after each exam.
- Format
- 100 multiple-choice questions (computer-based)
GARP reports the May 2023 pass rate for the FRM Part I exam was 47% (GARP), though this figure fluctuates with each testing window.
Valuation and Risk Models Practice Questions
These questions are designed to replicate the style and difficulty you'll face on the actual FRM Part I exam. They are not simple definition checks. They are scenarios crafted to test your ability to apply concepts from the VRM curriculum. Ready to test your knowledge? Try VoraPrep's adaptive FRM practice question bank with a free trial.
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Work through these questions one by one. Read the full explanation even if you get the answer right. Understanding the distractors is just as important as understanding the correct solution.
Question 1: Bond Pricing Calculation
A risk manager is evaluating a 5-year, $1,000 face value bond with a 6% annual coupon. The bond's yield-to-maturity (YTM) is currently 8%. If the YTM is expected to increase by 100 basis points, which of the following is the best estimate of the bond's new price?
This is a foundational bond pricing question. You must calculate the present value of the bond's future cash flows (coupons and principal) using the new, higher discount rate.
Step 1: Define the Bond's Parameters
- N (Number of periods) = 5
- FV (Face Value) = $1,000
- PMT (Annual Coupon Payment) = 6% × $1,000 = $60
- New YTM (I/Y) = 8% + 100 basis points = 8% + 1% = 9%
Step 2: Calculate the Present Value (Price)
You need to discount each cash flow back to the present using the 9% yield. Using a financial calculator is fastest: N=5, I/Y=9, PMT=60, FV=1000. Compute PV, which gives -890.15.The manual calculation is: Price = [60 ÷ (1.09)¹] + [60 ÷ (1.09)²] + [60 ÷ (1.09)³] + [60 ÷ (1.09)⁴] + [(60 + 1000) ÷ (1.09)⁵] Price = 55.05 + 50.50 + 46.33 + 42.51 + 689.76 = $890.15
Analysis of Distractors
- A. $922.78: This is the bond's price at the original 8% YTM. It's a classic trap for candidates who miss the "increase by 100 basis points" detail.
- C. $960.07: This result comes from incorrectly decreasing the yield to 7%. It tests if you understand the inverse relationship between yields and bond prices.
- D. $1,081.11: This is the price of a bond with a 6% YTM and an 8% coupon, reversing the key numbers. It's a distractor designed to catch calculation errors.
Question 2: Option Gamma Characteristics
Which of the following statements about option Gamma is correct?
Gamma measures the rate of change of an option's delta. It is a second-order Greek that captures the convexity of an option's value. Think of it as the "acceleration" of the option's price relative to the underlying's price movement.
Gamma is at its maximum for at-the-money (ATM) options. This is because the delta of an ATM option is the most sensitive to changes in the underlying's price; a small move can swing the delta significantly. This effect is magnified as the option gets closer to expiration, as there is less time for the stock price to revert.
Analysis of Distractors
- A. Gamma is highest for deep in-the-money or deep out-of-the-money options: This is incorrect. For deep ITM or OTM options, gamma is near zero. A deep ITM call's delta is already near 1.0 and a deep OTM call's delta is near 0. They cannot change much, so their gamma is low.
- B. Gamma represents the sensitivity of an option's price to changes in volatility: This is the definition of Vega, not Gamma. Examiners frequently test your ability to distinguish between the Greeks.
- D. A long option position always has negative gamma: This is the opposite of the truth. A long position in any option (call or put) has positive gamma. It is the option seller (short position) who has negative gamma and is exposed to accelerating losses.
Question 3: Parametric VaR Calculation
A portfolio manager holds a $50 million portfolio with a daily standard deviation of 1.5%. Assuming portfolio returns are normally distributed and have a mean of zero, what is the 10-day 99% Value-at-Risk (VaR)? (The one-tailed Z-score for 99% confidence is 2.33)
This question tests your ability to calculate parametric VaR and scale it over time. The key is remembering to scale volatility using the square root of time.
Step 1: Identify the Inputs
- Portfolio Value (P) = $50,000,000
- Daily Volatility (σ_daily) = 1.5% or 0.015
- Confidence Level = 99%, which corresponds to a Z-score (α) of 2.33
- Time Horizon (T) = 10 days
Step 2: Calculate the 1-Day VaR
First, find the 1-day 99% VaR. 1-day VaR = P × α × σ_daily 1-day VaR = $50,000,000 × 2.33 × 0.015 = $1,747,500Step 3: Scale the VaR to the 10-Day Horizon
To scale VaR under the IID (independent and identically distributed) assumption, you multiply the 1-day VaR by the square root of the time horizon (T). 10-day VaR = 1-day VaR × √10 10-day VaR = $1,747,500 × 3.16227... = $5,525,970Analysis of Distractors
- A. $1,747,500: This is the 1-day VaR. This is the most common trap for candidates who forget to scale for the time horizon.
- C. $2,330,000: This is a nonsensical calculation, likely from omitting the volatility term.
- D. $17,475,000: This is the result if you incorrectly scale VaR linearly (multiplying by 10) instead of by the square root of 10. This is a critical conceptual error.
Question 4: Parametric VaR Limitations
Which of the following is a primary limitation of the parametric (variance-covariance) method for calculating Value-at-Risk?
The parametric method, also known as the variance-covariance method, is built on a critical assumption: that the returns of the assets in the portfolio follow a normal distribution.
This assumption is its greatest strength (speed) and its greatest weakness. Real-world financial returns often exhibit "fat tails" (leptokurtosis) and skewness. This means extreme negative events happen more frequently than a normal distribution would predict. The parametric method systematically underestimates the risk of these tail events.
Analysis of Distractors
- A. It is computationally intensive and slow to calculate: This is false. The parametric method is the fastest VaR calculation method. Monte Carlo simulation is the method known for being computationally intensive.
- B. It struggles to model non-linear payoffs from derivatives: While the basic delta-normal method does struggle with options, this is a symptom of the underlying normality assumption. The core, fundamental limitation is the assumption of normally distributed returns, which gives rise to the problems with non-linear payoffs. C is the more fundamental answer.
- D. It requires a long history of market data to be accurate: This describes the historical simulation method, which relies directly on a past window of actual returns. The parametric method only needs current volatility and correlation estimates.
Question 5: Black-Scholes-Merton Model Factors
A European call option on a non-dividend-paying stock has a strike price of $50. The current stock price is $52, the risk-free rate is 3%, and the option expires in 6 months. According to the Black-Scholes-Merton model, which of the following events would cause the value of this call option to decrease?
This question tests your understanding of the factors that influence an option's price, as described by the Black-Scholes-Merton (BSM) model. You don't need to calculate the price, just understand the relationships (the option Greeks).
A call option gives the holder the right to buy the stock at the strike price in the future. The present value of that future payment is discounted using the risk-free rate. If the risk-free rate decreases, the present value of the strike price you have to pay becomes higher. A higher effective cost to exercise the option makes the call option itself less valuable. This relationship is captured by the Greek Rho.
Analysis of Distractors
- A. An increase in the stock's volatility: Higher volatility increases the value of both calls and puts (positive Vega). More volatility means a higher chance of the stock price ending deep in-the-money.
- B. An increase in the time to expiration: More time gives the stock more opportunity to move favorably. This increases the value of a standard European or American call option.
- D. An increase in the current stock price: As the stock price rises, the call option moves further in-the-money, which directly increases its value (positive Delta).
| Factor Increase | Call Price Effect | Relevant Greek |
|---|---|---|
| Stock Price | Increase | Delta |
| Strike Price | Decrease | (none) |
| Volatility | Increase | Vega |
| Time to Expiration | Increase | Theta (negative) |
| Risk-Free Rate | Increase | Rho |
Question 6: Expected Shortfall (ES) vs. VaR
A risk analyst calculates the worst 10 daily losses for a portfolio over the last 200 days. The losses, ordered from worst to least-worst, are: -$15M, -$12M, -$11M, -$9M, -$8.5M, -$8M, -$7M, -$6.5M, -$6M, -$5.8M. What is the 97.5% Expected Shortfall (ES) for this portfolio based on this historical data?
This question tests a critical concept: the difference between VaR and Expected Shortfall (ES).
Step 1: Determine the Number of Observations in the Tail
The confidence level is 97.5%, so the tail size (alpha) is 1 − 97.5% = 2.5%. Number of tail observations = 2.5% × 200 days = 5 observations.Step 2: Identify the Losses in the Tail
The tail consists of the 5 worst losses from the provided data: -$15M, -$12M, -$11M, -$9M, -$8.5MStep 3: Calculate the Expected Shortfall (ES)
ES is the simple average of the losses in the tail. ES = (-$15M − $12M − $11M − $9M − $8.5M) ÷ 5 ES = (-$55.5M) ÷ 5 = -$11.1MAnalysis of Distractors
- A. -$8.5M: This is the 97.5% Value-at-Risk (VaR), not the Expected Shortfall. It's the minimum loss within the tail, but ES requires averaging all losses in the tail. This is the most common trap on the exam.
- B. -$11.0M: A close distractor designed to catch a minor calculation error.
- D. -$15.0M: This is the single worst loss, which would be the 99.5% VaR and ES (since 0.5% of 200 is 1 observation).
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How Did You Score?
Count your correct answers. This short quiz is a useful indicator of your current grasp of Valuation and Risk Models concepts.
- 5-6 out of 6: Excellent. You have a strong command of the core concepts. Your focus should be on practicing more complex, multi-step problems to build speed and accuracy. Explore the VoraPrep FRM question bank to find challenging questions that combine multiple topics.
- 3-4 out of 6: Solid foundation, but with some gaps. You likely understand the main ideas but may be tripping on specific details, like the difference between VaR and ES or the assumptions behind a model. Review the explanations for the questions you missed. Use VoraPrep's adaptive learning engine to target these weak areas.
- 0-2 out of 6: This indicates a need for a fundamental review. VRM is a challenging topic. A low score means you should go back to the beginning of the VRM material. Focus on understanding why the formulas work before you try to memorize them.
Regardless of your score, the next step is consistent, targeted practice. Merely reading about risk models is not enough to pass. You must solve problems.
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If you found these questions helpful, they are just a small sample of what's available in the full VoraPrep FRM Part I course. Legacy prep courses often rely on 100+ hours of passive video lectures and static question banks, costing upwards of $1,500. This is an inefficient way to study for a quantitative exam like the FRM.
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- Spaced-Repetition Flashcards: An FSRS algorithm to help you memorize key formulas and definitions efficiently.
- Personalized Daily Study Plan: An automated planner that tells you exactly what to study each day.
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