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Chartered Financial Analyst · Level I

CFA L1 Quantitative Methods: practice questions with answers

6 free exam-style questions on Quantitative Methods for CFA L1 Level I. Try each one, then open the answer to read the explanation. Fincora has 88 original questions on this syllabus area.

Question 1

An investor bought shares of Larkspur Foods at USD 40.00 each. During the next 12 months she received a dividend of USD 1.20 per share, and she then sold the shares at USD 43.50 each. Her holding period return is closest to:

  1. A 8.75%
  2. B 11.75%
  3. C 10.80%
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Answer: B. Holding period return = (ending price - beginning price + income) / beginning price = (43.50 - 40.00 + 1.20) / 40.00 = 4.70 / 40.00 = 11.75%.

Question 2

A random sample of 49 small-cap stocks has a mean annual return of 8% and a sample standard deviation of 21%. The population variance is unknown. Using a reliability factor of 2.01, the 95% confidence interval for the population mean return is closest to:

  1. A -34.21% to 50.21%
  2. B 1.97% to 14.03%
  3. C 7.14% to 8.86%
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Answer: B. Standard error of the sample mean = s / sqrt(n) = 21% / sqrt(49) = 21% / 7 = 3%. Confidence interval = sample mean +/- reliability factor x standard error = 8% +/- 2.01 x 3% = 8% +/- 6.03%, or 1.97% to 14.03%. With n = 49, the central limit theorem makes the sampling distribution of the mean approximately normal even if returns are not.

Question 3

Over a holding period of 42 months, a fund's continuously compounded return was 0.315; that is, ln(ending value / beginning value) = 0.315. There were no cash flows into or out of the fund. The fund's annualized return, stated with annual compounding, is closest to:

  1. A 9.00%
  2. B 9.42%
  3. C 10.58%
Show the answer

Answer: B. Continuously compounded returns are additive over time, so the annual continuously compounded return is 0.315 / 3.5 years = 0.0900.

Convert to annual compounding: e^0.0900 - 1 = 1.09417 - 1 = 9.42%.

Check: the holding period return is e^0.315 - 1 = 37.02%, and 1.3702^(1/3.5) - 1 = 9.42%.

Question 4

Compared with the standard normal distribution, Student's t-distribution is most accurately described as:

  1. A symmetric, with fatter tails, and approaching the standard normal distribution as the degrees of freedom increase.
  2. B positively skewed and bounded below by zero, approaching the standard normal distribution as the degrees of freedom increase.
  3. C symmetric, with thinner tails, and moving further away from the standard normal distribution as the degrees of freedom increase.
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Answer: A. Student's t-distribution is symmetric about zero and bell-shaped, like the standard normal, but it has fatter tails, so more probability lies in the tails. It is defined by a single parameter, the degrees of freedom (for a sample mean, n - 1). As the degrees of freedom increase, the tails become thinner and the t-distribution approaches the standard normal; this is why critical t-values are larger than z-values for small samples and almost equal to them for large ones. The chi-square and F-distributions, by contrast, are asymmetric (positively skewed) and bounded below by zero.

Question 5

An analyst regresses the monthly returns of the shares of a cable manufacturer on monthly changes in the price of copper, its main raw material, using 30 observations. The regression has a total sum of squares (SST) of 250 and a sum of squared errors (SSE) of 90, and the estimated slope coefficient is negative. The sample correlation between the share returns and the changes in the copper price is closest to:

  1. A -0.80
  2. B -0.64
  3. C 0.80
Show the answer

Answer: A. Coefficient of determination: R^2 = (SST - SSE) / SST = 1 - SSE / SST = 1 - 90 / 250 = 0.64.

In a simple linear regression with one independent variable, R^2 equals the square of the correlation between X and Y. So |r| = 0.64^0.5 = 0.80.

The correlation has the same sign as the slope coefficient, which is negative, so r = -0.80.

Question 6

Bank X offers a deposit rate of 7.20% per year compounded monthly. Bank Y offers 7.25% per year compounded semiannually. Which bank offers the higher effective annual rate (EAR), and what is that rate?

  1. A Bank X, with an EAR of about 7.44%.
  2. B Bank Y, with an EAR of about 7.38%.
  3. C Bank Y, with an EAR of about 7.25%.
Show the answer

Answer: A. EAR = (1 + stated rate / m)^m - 1, where m is the number of compounding periods per year.
Bank X: (1 + 0.072/12)^12 - 1 = 7.44%.
Bank Y: (1 + 0.0725/2)^2 - 1 = 7.38%.
Bank X has the lower stated rate but the higher EAR, because more frequent compounding adds more interest on interest. Stated rates with different compounding frequencies must be converted to EARs before they are compared.

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