A candidate stared at his screen, a sinking feeling in his gut. The question asked for the continuously compounded return of a stock that paid a quarterly dividend. He knew the e^(rt) formula by heart. He calculated the price return, applied the formula, and confidently selected option B. He was wrong. He forgot to account for the dividend yield, a classic Quantitative Methods trap that turns a simple calculation into a point-loser for the unprepared.
These free CFA Level I Quantitative Methods practice questions are designed for the 2026 exam blueprint. They include a mix of conceptual and calculation-based problems covering topics like TVM, probability, and hypothesis testing, complete with detailed explanations that show you how to avoid common traps.
Key facts
- Official Body
- CFA Institute
- Topic Weighting
- 8-12% of the Level I exam
- Number of Questions
- Approximately 14-22 questions
- Key Skills
- Time Value of Money (TVM), probability, statistics, hypothesis testing
- Exam Format
- Computer-based multiple-choice questions
- Study Hours
- 40-50 hours (out of 300+ total for Level I)
About These Free Quantitative Methods Questions
These questions are not just a random sample. They are specifically designed by CFA charterholders to mirror the style and difficulty of the real Level I exam, aligned with the 2026 curriculum. You will find a mix of straightforward calculation problems and more nuanced conceptual questions that require you to think like an analyst.
Each question comes with a detailed explanation that goes beyond just showing the right answer. We'll break down the underlying concept, show the step-by-step math, and most importantly, expose the common traps and tempting wrong answers the exam writers use to catch you off guard. This is the core of the VoraPrep method: we teach you to see the question from the examiner's perspective.
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Quantitative Methods Practice Questions
Work through these 10 questions, ideally under timed conditions (about 90 seconds per question). Check your answers and review the detailed explanations below. Don't just skim the ones you got right; read the "Exam Trap" section to see if you could have fallen for a distractor.
Question 1: Time Value of Money
An investor deposits $10,000 into an account that pays 6% interest, compounded quarterly. How much will the investor have in the account after 5 years?
Question 2: Probability Concepts
The probability of a recession in the next year is 30%. If there is a recession, the probability that a specific company's earnings will decline is 70%. If there is no recession, the probability that the company's earnings will decline is 20%. What is the total probability that the company's earnings will decline?
Question 3: Statistical Concepts
An analyst is evaluating a portfolio with the following expected annual returns:
| Economic Scenario | Probability | Portfolio Return |
|---|---|---|
| Boom | 0.25 | 18% |
| Normal | 0.50 | 12% |
| Bust | 0.25 | -5% |
What is the standard deviation of the portfolio's expected returns?
Question 4: Hypothesis Testing
A portfolio manager claims that her portfolio's mean monthly return is greater than 1.0%. After running a hypothesis test on the portfolio's historical returns, she calculates a p-value of 0.04. If she uses a 5% significance level (α = 0.05), what is the most appropriate conclusion?
Question 5: Correlation and Regression
An analyst runs a simple linear regression of a stock's returns (Y) against the market's returns (X). The results include an R-squared value of 0.45. Which of the following is the best interpretation of this result?
Question 6: Bayes' Theorem
An analyst uses a model to predict stock upgrades. The model correctly identifies 80% of stocks that are actually upgraded (true positive). It incorrectly identifies 10% of stocks as "upgrades" when they are not (false positive). Historically, 5% of stocks in the analyst's universe are upgraded. If the model flags a stock for an upgrade, what is the probability that it will actually be upgraded?
Question 7: Continuously Compounded Returns
A stock is purchased for $50 and sold one year later for $55. The stock paid a dividend of $1.00 during the year. The continuously compounded annual rate of return is closest to:
Question 8: Sampling and Estimation
An analyst takes a random sample of 50 bonds from a large population and finds the sample mean duration is 7.5 years with a sample standard deviation of 1.5 years. What is the 95% confidence interval for the population mean duration? (Use a z-value of 1.96 for 95% confidence).
Question 9: Technical Analysis
A stock's price has been trading between $40 and $50 for several months. Recently, the price broke above $50 on high trading volume. In technical analysis, the former $50 price level is now most likely considered a:
Question 10: Monte Carlo Simulation
Which of the following is the primary limitation of using Monte Carlo simulation for modeling complex financial problems?
Explanations
Question 1: Time Value of Money
✅ The correct answer is C: $13,489.
This is a straightforward TVM calculation, but one where calculator input errors are common.
- The number of periods (N) is 5 years × 4 quarters/year = 20.
- The interest rate per period (I/Y) is 6% per year ÷ 4 quarters/year = 1.5%.
- The Present Value (PV) is -$10,000 (entered as a negative for cash outflow).
- The payment (PMT) is 0, as no additional deposits are made.
Using a financial calculator (like the TI BA II Plus): N = 20 I/Y = 1.5 PV = -10000 PMT = 0 CPT FV → $13,488.54
Question 2: Probability Concepts
✅ The correct answer is A: 35.0%.
This question requires you to use the total probability rule, a fundamental concept in the QM curriculum.
Formula: P(D) = P(D | R) × P(R) + P(D | NR) × P(NR)
- P(D | R) = 70% (Probability of decline given a recession)
- P(R) = 30% (Probability of recession)
- P(D | NR) = 20% (Probability of decline given no recession)
- P(NR) = 1 - P(R) = 1 - 30% = 70% (Probability of no recession)
P(D) = (0.70 × 0.30) + (0.20 × 0.70) P(D) = 0.21 + 0.14 P(D) = 0.35 or 35.0%
Question 3: Statistical Concepts
✅ The correct answer is B: 8.9%.
To find the standard deviation, you must first calculate the expected return (the mean) and then the variance.
Step 1: Calculate the Expected Return (E(R))
E(R) = Σ [P(i) × R(i)] E(R) = (0.25 × 18%) + (0.50 × 12%) + (0.25 × -5%) E(R) = 4.5% + 6.0% - 1.25% = 9.25%Step 2: Calculate the Variance (σ²)
Variance (σ²) = Σ [P(i) × (R(i) - E(R))²] σ² = 0.25 × (18 - 9.25)² + 0.50 × (12 - 9.25)² + 0.25 × (-5 - 9.25)² σ² = 0.25 × (8.75)² + 0.50 × (2.75)² + 0.25 × (-14.25)² σ² = 0.25 × 76.5625 + 0.50 × 7.5625 + 0.25 × 203.0625 σ² = 19.1406 + 3.7813 + 50.7656 = 73.6875 Note: For variance calculations, it's easier to work with decimals for returns (e.g., 0.18, 0.12) and convert back at the end. The variance here is 0.00736875.Step 3: Calculate the Standard Deviation (σ)
Standard Deviation (σ) = √Variance σ = √73.6875 = 8.87%This is closest to 8.9%.
Question 4: Hypothesis Testing
✅ The correct answer is A: Reject the null hypothesis and conclude the mean monthly return is greater than 1.0%.
This question tests your understanding of the p-value decision rule.
- Null Hypothesis (H₀): Mean return ≤ 1.0% (This is what the manager is trying to disprove).
- Alternative Hypothesis (Hₐ): Mean return > 1.0% (This is the manager's claim).
- p-value = 0.04
- Significance level (α) = 0.05
Since 0.04 < 0.05, we reject the null hypothesis. Rejecting H₀ means we have found statistically significant evidence in favor of the alternative hypothesis, Hₐ. Therefore, we conclude the mean monthly return is greater than 1.0%.
Question 5: Correlation and Regression
✅ The correct answer is C: 45% of the variation in the stock's returns can be explained by the variation in the market's returns.
This is a direct interpretation of the coefficient of determination, or R-squared.
An R² of 0.45 means that 45% of the "movement" or variability in our stock's returns is explained by the "movement" in the market's returns. The other 55% is due to other, unexplained factors (firm-specific news, etc.).
Question 6: Bayes' Theorem
✅ The correct answer is A: 29.6%.
This is a classic Bayes' theorem problem. The easiest way to solve it is often by building a small probability table or tree, rather than plugging directly into the formula.
- Upgraded Stocks: 5% of 1,000 = 50 stocks will actually be upgraded.
- Non-Upgraded Stocks: 95% of 1,000 = 950 stocks will not be upgraded.
Now, let's see what the model predicts for each group:
- True Positives (Model says "Upgrade" and it's correct): 80% of the 50 upgraded stocks = 40 stocks.
- False Negatives (Model says "No Upgrade" but it's wrong): 20% of the 50 upgraded stocks = 10 stocks.
- False Positives (Model says "Upgrade" but it's wrong): 10% of the 950 non-upgraded stocks = 95 stocks.
- True Negatives (Model says "No Upgrade" and it's correct): 90% of the 950 non-upgraded stocks = 855 stocks.
The question asks: If the model flags a stock for an upgrade, what is the probability it will actually be upgraded? This is P(Actual Upgrade | Model says "Upgrade").
- Total stocks the model flagged as "Upgrade" = True Positives + False Positives = 40 + 95 = 135.
- Of those, the number that were actually upgraded = True Positives = 40.
Probability = (Actually Upgraded) / (Total Flagged as "Upgrade") = 40 / 135 = 29.63%
Question 7: Continuously Compounded Returns
✅ The correct answer is A: 11.33%.
This question combines a standard holding period return calculation with the formula for continuous compounding. This was the trap from our opening story.
Step 1: Calculate the Holding Period Return (HPR)
HPR = (Ending Price - Beginning Price + Dividend) / Beginning Price HPR = ($55 - $50 + $1) / $50 HPR = $6 / $50 = 0.12 or 12.0%Step 2: Convert the HPR to a Continuously Compounded Return
The formula is R_cc = ln(1 + HPR), where "ln" is the natural logarithm. R_cc = ln(1 + 0.12) R_cc = ln(1.12) R_cc = 0.1133 or 11.33%Question 8: Sampling and Estimation
✅ The correct answer is A: [7.08, 7.92].
This requires you to apply the formula for a confidence interval for a population mean.
Step 1: Identify the components
- Sample Mean (x̄) = 7.5
- Critical Value (z) for 95% confidence = 1.96
- Sample Standard Deviation (s) = 1.5
- Sample Size (n) = 50
Step 2: Calculate the Standard Error of the Mean
Standard Error = s / √n Standard Error = 1.5 / √50 Standard Error = 1.5 / 7.071 = 0.212Step 3: Calculate the Confidence Interval
Interval = 7.5 ± (1.96 × 0.212) Interval = 7.5 ± 0.4155- Lower Bound = 7.5 - 0.4155 = 7.0845
- Upper Bound = 7.5 + 0.4155 = 7.9155
The interval is [7.08, 7.92].
Question 9: Technical Analysis
✅ The correct answer is C: Change in polarity point.
This is a terminology question from technical analysis.
- Resistance: A price level where selling pressure has historically been strong enough to prevent the price from rising further. In this case, $50 was the resistance.
- Support: A price level where buying pressure has historically been strong enough to prevent the price from falling further.
Since the price broke above the former resistance of $50, that $50 level is now expected to act as a floor, or support, for any future pullbacks. This phenomenon is called the change in polarity. Answer B is also correct in a sense, but C is the more precise technical term for the principle at play.
Question 10: Monte Carlo Simulation
✅ The correct answer is C: The output is only as good as the assumptions and inputs provided.
This tests your conceptual understanding of the limitations of a powerful quantitative tool.
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How Did You Score?
Count up your correct answers. Your score here is a small sample, but it can be a valuable diagnostic tool.
If you scored 8 or higher: You have a strong grasp of the core Quantitative Methods concepts. Your focus should be on speed, accuracy, and identifying the subtle tricks in question wording. Are you consistently avoiding the traps? Use a platform like VoraPrep's adaptive question bank to target the most complex problems and solidify your mastery. If you scored 5-7: You have a decent foundation but some clear knowledge gaps. Look at the questions you missed. Was it a specific topic area like Bayes' theorem or hypothesis testing? Or was it a type of error, like a calculator mistake or misinterpreting the question? Your next step is to go back to those specific readings in the curriculum. Don't just re-read; actively work through the end-of-chapter problems. If you scored 4 or lower: This is a red flag. Quantitative Methods is a building block for other topics, and weakness here will cause problems in Equity, Fixed Income, and Portfolio Management. You need to go back to basics. Don't just jump into more practice questions. Use a structured study program with complete textbook-grade lessons to rebuild your understanding from the ground up, focusing on TVM and probability first.No matter your score, the key is to turn this diagnostic into an action plan. Don't just move on. Fix the weak spots now.
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