CFA Level I Quantitative Methods practice questions

25 exam-style questions from across Quantitative Methods, which is 11–14% of the Level I exam (roughly 20–25 of the 180 questions). Pick an answer to see whether you were right, why each option is right or wrong, and the lesson to go back to.

Allow about 90 seconds a question, the exam pace. Every question is original and written for the CFA Level I curriculum.

Module 1 Returns of Financial Assets

1Two 3-year bonds have the same issuer quality. One trades actively and yields 5.6%. The other rarely trades and yields 6.1%. The 0.5% difference is best described as a:

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The answer is B.

A. The issuers are equally creditworthy, so default risk is held constant. A higher yield does not automatically mean a riskier borrower. The trap
B. The only difference is how easily each bond can be sold, and that is what a liquidity premium pays for.
C. Both bonds mature in 3 years, so maturity is held constant.

From the lesson Required return: risk-free rate, inflation and risk premia
2An investor buys shares at INR 450, receives a dividend of INR 6 per share at the end of the period and sells at INR 468. The holding period return is closest to:
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The answer is C.

A. Ignores the dividend: 18 ÷ 450. The trap
B. Divides by the ending price: 24 ÷ 468.
C. (468 − 450 + 6) ÷ 450 = 24 ÷ 450 = 5.33%.
On your calculator
1. 468−450+6=÷450= 0.0533
1. 468ENTER450−6+450÷ 0.0533
ENTER enter (on the HP, puts the number on the stack)
From the lesson Holding period return
3A portfolio returns 20%, −10% and 5% over three years. Its geometric mean annual return is closest to:
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The answer is A.

A. 1.20 × 0.90 × 1.05 = 1.134, and 1.134^(1/3) − 1 = 4.28%.
B. Divides the total return of 13.4% by 3, which ignores compounding.
C. The arithmetic mean: (20 − 10 + 5) ÷ 3. The trap
On your calculator
1. 1.2×0.9×1.05=y^x31/x=−1= 0.0428
y^x power · 1/x reciprocal
1. 1.2ENTER0.9×1.05×31/xy^x1− 0.0428
ENTER enter (on the HP, puts the number on the stack) · 1/x reciprocal · y^x power
From the lesson Arithmetic and geometric mean returns

Module 2 Types of Financial Returns

4The coupons on a floating-rate note are best described as a:

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The answer is C.

A. Coupons are cash paid to the holder. A price return is a change in the price.
B. The trap. They are coupons, but the rate resets, so the amount paid changes. The trap
C. The payment moves with the reference rate, so it is a variable capital distribution.

From the lesson Types of returns: assets, instruments and indicators
5Over long periods, the main source of total return on long-term government bonds has been:

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The answer is B.

A. The trap. Bond prices move with interest rates, but they contribute little over the long run. The trap
B. Coupons (capital distributions) make up most of the return.
C. A domestic investor in home-country government bonds has no currency return.

From the lesson Long-run asset class returns and their components
6Which of the following is best described as a micro (unsystematic) risk?

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The answer is C.

A. One of the three systematic factors that affect all assets.
B. The trap. Rates hit some sectors harder, but they move all asset prices, so it is systematic. The trap
C. This is sector risk: specific to one industry and diversifiable.

From the lesson Macro and micro risk and the risk-return trade-off

Module 3 Benchmarking Returns

7A pension fund's external managers do not control when the sponsor adds or withdraws money. To evaluate the managers, the sponsor should most appropriately use the:

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The answer is B.

A. The money-weighted rate of return is distorted by the sponsor's deposits and withdrawals, which the managers did not choose. The trap
B. It removes the size and timing of cash flows, isolating what the managers did with the money.
C. The arithmetic mean of period returns does not deal with cash flows or compounding.

From the lesson Money-weighted vs time-weighted rate of return
8An index starts the year at 1,250.00 and ends at 1,310.00. Its constituents paid income equal to 18.75 index points. The index's total return is closest to:
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The answer is C.

A. This is the price return, 60.00 ÷ 1,250.00. It leaves out the income. The trap
B. Divides by the ending level: 78.75 ÷ 1,310.00. Always divide by the starting level.
C. (1,310.00 − 1,250.00 + 18.75) ÷ 1,250.00 = 78.75 ÷ 1,250.00 = 6.30%.
On your calculator
1. 1310−1250+18.75=÷1250= 0.063
1. 1310ENTER1250−18.75+1250÷ 0.063
ENTER enter (on the HP, puts the number on the stack)
From the lesson Index value, price return and total return
9A price-weighted index of three shares priced 24, 56 and 160 stands at 100.00 with a divisor of 2.40. The share priced 160 splits 4-for-1. The new divisor is closest to:
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The answer is B.

A. Divides the old divisor by the split ratio, 2.40 ÷ 4. The divisor follows the sum of prices, not the ratio.
B. The new sum is 24 + 56 + 40 = 120. 120 ÷ D = 100, so D = 1.20.
C. Leaves the divisor unchanged, so the index would fall from 100 to 50 with no change in value. The trap
On your calculator
1. 24+56+40=÷100= 1.2
1. 24ENTER56+40+100÷ 1.2
ENTER enter (on the HP, puts the number on the stack)
From the lesson Price-weighted and equal-weighted indexes

Module 4 Time Value of Money in Finance

10A 10-year zero-coupon bond with a face value of USD 1,000 yields 3.8% (annual compounding). Its price is closest to:
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The answer is A.

A. 1,000 ÷ 1.038¹⁰ = 688.69.
B. Discounts nine periods instead of ten: 1,000 ÷ 1.038⁹.
C. Uses simple interest, 1,000 ÷ (1 + 0.038 × 10). With annual compounding, discount once for each of the ten years. The trap
On your calculator
1. 2NDCLR TVM
2. 10N3.8I/Y1000FV
3. CPTPV −688.69
2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · FV future value · CPT compute · PV present value
1. fCLEAR FIN
2. 10n3.8i1000FV
3. PV −688.69
f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · FV future value · PV present value
From the lesson Pricing bonds: zero-coupon, coupon and perpetual
11A borrower takes a 30-year USD 400,000 mortgage at 5.4% a year, paid monthly. The monthly payment is closest to:
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The answer is B.

A. Interest only: 400,000 × 0.054 ÷ 12. The payment must also repay principal. The trap
B. N = 360, I/Y = 0.45, PV = 400,000, FV = 0 gives PMT = 2,246.12.
C. Computes an annual payment at 5.4% over 30 years and divides by 12.
On your calculator
1. 2NDCLR TVM with P/Y set to 1
2. 360N0.45I/Y400000PV
3. CPTPMT −2,246.12
2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · PV present value · CPT compute · PMT payment
1. fCLEAR FIN
2. 360n0.45i400000PV
3. PMT −2,246.12
f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PV present value · PMT payment
From the lesson Annuities and level-payment loans

Module 5 Statistical Characteristics of Asset Returns

12Eight quarterly returns (%) are 4.0, −2.0, 1.0, 3.0, 25.0, 2.0, 0.0 and 1.0. The median is closest to:
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The answer is B.

A. Takes the 4th sorted value only. With an even count the median averages the 4th and 5th.
B. Sorted: −2, 0, 1, 1, 2, 3, 4, 25. The 4th and 5th values are 1 and 2, so (1 + 2) ÷ 2 = 1.50.
C. The mean, 34 ÷ 8, which the 25.0 outlier pulls up. The trap
On your calculator
1. 1+2=÷2= 1.5
1. 1ENTER2+2÷ 1.5
ENTER enter (on the HP, puts the number on the stack)
From the lesson Mean, median, mode and what outliers do to them
13Four monthly returns are 5%, −3%, 9% and 1%. The sample standard deviation is closest to:
Show the answer

The answer is C.

A. The mean absolute deviation: (2 + 6 + 6 + 2) ÷ 4.
B. Divides by n instead of n − 1: √(80 ÷ 4) = √20. The trap
C. The mean is 3. Squared deviations: 4, 36, 36, 4 = 80. 80 ÷ 3 = 26.67, and √26.67 = 5.16.
On your calculator
1. 2NDDATA2NDCLR WORK
2. 5ENTER↓↓3+|-ENTER↓↓9ENTER↓↓1ENTER
3. 2NDSTAT2NDSET until 1-V shows
4. ↓↓↓ Sx = 5.16, the sample figure
2ND second function (the shifted label above a key) · DATA data worksheet · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · +|- change sign · STAT statistics worksheet · SET change the setting
1. fCLEAR Σ
2. 5Σ+3CHSΣ+9Σ+1Σ+
3. gs 5.16
f gold shift key · CLEAR Σ clear the statistics registers · Σ+ add a data point · CHS change sign · g blue shift key · s standard deviation
From the lesson Range, mean absolute deviation, variance and standard deviation

Module 6 Statistical Distributions

14An analyst forecasts earnings per share of INR 2.40 (probability 0.3), INR 2.00 (probability 0.5) or INR 1.50 (probability 0.2). Expected EPS is closest to:
Show the answer

The answer is B.

A. A simple average of the three forecasts: 5.90 ÷ 3. It ignores the probabilities. The trap
B. 0.3 × 2.40 + 0.5 × 2.00 + 0.2 × 1.50 = 0.72 + 1.00 + 0.30 = 2.02.
C. The most optimistic forecast, not a probability-weighted average.
On your calculator
1. 2NDDATA2NDCLR WORK
2. 2.4ENTER↓30ENTER↓2ENTER↓50ENTER↓1.5ENTER↓20ENTER
3. 2NDSTAT2NDSET until 1-V shows
4. ↓↓ X̄ = 2.02, the probabilities typed as percent frequencies
2ND second function (the shifted label above a key) · DATA data worksheet · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · STAT statistics worksheet · SET change the setting
1. fCLEAR Σ
2. 2.4ENTER0.3Σ+
3. 2ENTER0.5Σ+
4. 1.5ENTER0.2Σ+
5. gx̄w 2.02
f gold shift key · CLEAR Σ clear the statistics registers · ENTER enter (on the HP, puts the number on the stack) · Σ+ add a data point · g blue shift key · x̄w weighted mean
From the lesson Unconditional expected value, variance and standard deviation
15An analyst models the number of up days in a 40-day period as binomial, with a 0.55 probability of an up day. The variance of the number of up days is closest to:
Show the answer

The answer is B.

A. The standard deviation, √9.90.
B. 40 × 0.55 × 0.45 = 9.90.
C. The mean, np = 22.00, offered as the variance. The trap
On your calculator
1. 40×0.55×0.45= 9.9
1. 40ENTER0.55×0.45× 9.9
ENTER enter (on the HP, puts the number on the stack)
From the lesson Discrete distributions: uniform, binomial and Poisson

Module 7 Estimation and Hypothesis Testing

16A sample of 64 monthly returns has a standard deviation of 24%. The standard error of the sample mean is closest to:
Show the answer

The answer is B.

A. Divides by n: 24 ÷ 64. The trap
B. 24 ÷ √64 = 24 ÷ 8 = 3.00%.
C. Divides the variance by n: 576 ÷ 64.
On your calculator
1. 24÷64√x= 3
√x square root
1. 24ENTER64g√x÷ 3
ENTER enter (on the HP, puts the number on the stack) · g blue shift key · √x square root
From the lesson The central limit theorem and the standard error of the mean
17An equity index has 100 monthly returns with a mean of 0.80% and a sample standard deviation of 4.50%. The 95% confidence interval for the mean monthly return is closest to:
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The answer is B.

A. Uses the standard deviation instead of the standard error: 0.80 ± 1.96 × 4.50. The trap
B. Standard error 4.50 ÷ √100 = 0.45; margin 1.96 × 0.45 = 0.882; 0.80 ± 0.882 = −0.08% to 1.68%.
C. Uses the standard error as the margin, leaving out Z: 0.80 ± 0.45.
On your calculator
1. 4.5÷100√x×1.96=STO1 0.882, the margin of error
2. 0.8−RCL1= −0.082
3. 0.8+RCL1= 1.682
√x square root · STO store · RCL recall a stored number
1. 4.5ENTER100g√x÷1.96×STO1 0.882, the margin of error
2. 0.8RCL1− −0.082
3. 0.8RCL1+ 1.682
ENTER enter (on the HP, puts the number on the stack) · g blue shift key · √x square root · STO store · RCL recall a stored number
From the lesson Confidence intervals for a mean return

Module 8 Portfolio Return and Risk

18A portfolio is 50% in asset X (standard deviation 20%) and 50% in asset Y (standard deviation 12%). The covariance of their returns is 0.006. The portfolio standard deviation is closest to:
Show the answer

The answer is B.

A. Drops the covariance term: √(0.25 × 0.04 + 0.25 × 0.0144) = 11.66%.
B. 0.25 × 0.04 + 0.25 × 0.0144 + 2 × 0.25 × 0.006 = 0.0166, and √0.0166 = 12.88%.
C. Averages the standard deviations: 0.5 × 20% + 0.5 × 12%. That holds only if the correlation is +1. The trap
On your calculator
1. 0.5x²×0.04+(0.5x²×0.0144)+(2×0.5×0.5×0.006)= 0.0166
2. √x 0.1288
x² square · √x square root
1. 0.5ENTER×0.04×0.5ENTER×0.0144×+2ENTER0.5×0.5×0.006×+ 0.0166
2. g√x 0.1288
ENTER enter (on the HP, puts the number on the stack) · g blue shift key · √x square root
From the lesson Portfolio expected return, variance and the role of correlation
19When investors can lend and borrow at a risk-free rate, the optimal risky portfolio on the efficient frontier is the portfolio with the:

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The answer is B.

A. That describes the global minimum-variance portfolio, a different point. The trap
B. The line from the risk-free rate touches the frontier where the Sharpe ratio is highest (the tangency portfolio).
C. Without short selling, that is the single highest-return asset, rarely the best risk-adjusted choice.

From the lesson The minimum-variance portfolio and the efficient frontier

Module 9 Simulating Prices and Returns

20A pension fund simulates its funding surplus. The team has already chosen the inputs and produced 5,000 sets of asset returns and interest rates. Its next task, turning each set into a surplus figure with the formulas chosen at the start, belongs to which step?

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The answer is C.

A. Setup chose the inputs and wrote the formulas; it does not apply them to scenarios.
B. Generation produced the 5,000 input sets; it does not compute the outputs. The trap
C. The calculation engine runs the setup formulas on each scenario and produces one output for each.

From the lesson Historical, bootstrap or Monte Carlo: the four-step engine
21A historical simulation produces 230 daily profit-and-loss scenarios for a portfolio. The 10th to 13th largest losses are USD 412,000, USD 398,000, USD 371,000 and USD 366,000. Using linear interpolation, the one-day 95% value at risk is closest to:
Show the answer

The answer is B.

A. Rounds the rank 11.5 up to 12 and takes the 12th loss; the question asks for interpolation.
B. k = 0.05 × 230 = 11.5, halfway between the 11th and 12th losses: (398,000 + 371,000) ÷ 2 = 384,500.
C. Rounds the rank down to 11 instead of interpolating. The trap
On your calculator
1. 398000+371000=÷2= 384,500
1. 398000ENTER371000+2÷ 384,500
ENTER enter (on the HP, puts the number on the stack)
From the lesson Historical simulation and historical value at risk

Module 10 Simple Linear Regression in Finance

22Cov(X, Y) = 0.0018, Var(X) = 0.0024 and Var(Y) = 0.0030. The slope of the regression of Y on X is closest to:
Show the answer

The answer is C.

A. Divides the covariance by the variance of Y: 0.0018 ÷ 0.0030. The trap
B. That is the correlation: 0.0018 ÷ √(0.0024 × 0.0030).
C. Slope = Cov(X, Y) ÷ Var(X) = 0.0018 ÷ 0.0024 = 0.75.
On your calculator
1. 0.0018÷0.0024= 0.75
1. 0.0018ENTER0.0024÷ 0.75
ENTER enter (on the HP, puts the number on the stack)
From the lesson The regression line: slope, intercept and least squares
23A residual plot shows residuals that spread wider as X increases. This most likely indicates a violation of:

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The answer is B.

A. A curved or U-shaped pattern signals non-linearity, not a widening spread. The trap
B. A fan means the error variance changes with X: heteroskedasticity, so homoskedasticity is violated.
C. Normality is judged from the distribution of the residuals (histogram), not from a fan shape.

From the lesson The four regression assumptions and what residual plots reveal

Module 11 Financial Data Science

24An analyst worries that a large set of online product reviews contains many fake posts. This concern relates to big data's:

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The answer is C.

A. Variety is about the many forms data take, not whether they are genuine. The trap
B. Velocity is about how fast data are created and delivered.
C. Doubt over whether the posts are credible and reliable is a veracity problem.

From the lesson Big data, the four Vs and alternative data
25A model is trained on 10 years of past bond data in which each bond is marked "defaulted" or "did not default". This is an example of:

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The answer is A.

A. The outcome of each bond is labeled, so the algorithm learns to predict it.
B. Unsupervised learning has no labels. The trap
C. An expert system follows hand-coded if-then rules; it does not learn from data.

From the lesson AI and machine learning: supervised, unsupervised, reinforcement, deep

Keep going

Study the topic module by module in the Quantitative Methods lessons, look up a word in the Level I glossary, or run a timed practice set that tracks your score by topic.