CFA Institute CFA Institute Certifications CFA-LEVEL-1 Questions & Answers

• Question 3221:

  To test whether small-cap stocks perform worse than large stocks under the Fama-French three-factor

  model, you set up the following hypothesis:

  Ho: Expected excess returns of small stocks = 0

  H1: Expected excess returns of small stocks < 0

  The excess returns are returns adjusted for risk using the Fama-French three-factor model. In this setup,

  which of the following is/are true?

  I. You must employ a right-tailed test.

  II. The rejection region for the z-statistic on the excess return extends from negative infinity to the critical value associated with the significance level.

  III.

  It is harder to reject the null than in the case where the alternative is specified as H1: Excess returns are non-zero.

  A.

  II only

  B.

  I and III

  C.

  II and III

  D.

  none of these answers

  E.

  I only

  Correct Answer: A

  Since the rejection region for the null is to the left of the maintained null value of zero, you must employ a left-tailed test. In that case, the rejection region for the z-statistic on the excess return extends from negative infinity to the critical value associated with the significance level. Also note that it is harder to reject the null under a two-tailed test than under a one-tailed test since the critical value for any given significance level is higher (in magnitude) for a two-tailed test.

• Question 3222:

  What is the relationship between the variance and the standard deviation?

  A. Variance is the square root of the standard deviation

  B. None of these answers

  C. No constant relationship between the variance and the standard deviation

  D. Variance is twice the standard deviation

  E. Variance is the square of the standard deviation

  Correct Answer: E

  The variance is the mean of the squared deviations from the mean. The standard deviation is the positive square root of the variance.

• Question 3223:

  A bell-shaped, symmetrical frequency distribution has a mean of 5 and a standard deviation of 2.5. The percentage of observations less than zero is about:

  A. cannot be calculated

  B. 5%

  C. 10%

  D. 2.5%

  Correct Answer: D

  Note that the mean is 2 standard deviations above zero. The fraction of observations in a bell-shaped, symmetrical frequency distribution which lie outside the 2-sigma range around the mean is about 5%. Since the distribution is symmetrical about the mean, the percentage of observations less than zero is approximately equal to 5%/2 = 2.5%.

• Question 3224:

  A random variable, X, has a mean of 10 and a standard deviation of 15. Another random variable, Y, is defined by Y = 2X + 3. Then, which of the following is/are true? I. The mean of Y is 33. II. The variance of Y is 30. III. The standard deviation of Y is 33. IV. X and Y are perfectly correlated.

  A. II and IV

  B. I, II and IV

  C. II only

  D. III and IV

  E. IV only

  F. III only

  G. I only

  Correct Answer: E

  The mean of Y is 2*10 + 3 = 23. The standard deviation of Y is 2*15 = 30. Its variance is then equal to 30^2 = 900. Finally, since Y is a linear multiple of X, X and Y are perfectly correlated (positively, in this case)

• Question 3225:

  A systematic sampling method should not be used when:

  A. the data are commingled.

  B. the data are systematically biased.

  C. the data are already arranged in the form of a predetermined pattern.

  D. the data are divided into open-ended classes.

  Correct Answer: C

  If the data are already arranged in the form of a predetermined pattern, using systematic sampling can introduce a systematic pattern in the sample itself, which would lead to erroneous inferences about the entire population.

• Question 3226:

  The R-square in a univariate regression measures:

  A. the significance of the regression.

  B. the variance of the error term.

  C. the amount of variance in the dependent variable caused by the variance in the independent variable.

  D. the correlation between the dependent and the independent variables.

  Correct Answer: C

  It should be noted that in a univariate regression, the square root of R-square equals the correlation coefficient. The significance of a univariate or a multivariate regression is measured by the F-statistic.

• Question 3227:

  John buys a house that costs $175,000 and agrees to pay for it with a 15 year mortgage at 7% per year, compounded monthly. What is John's monthly payment on the loan?

  A. $972.22

  B. $552.12

  C. $12,218.50

  D. $12,250.06

  E. $1,572.95

  Correct Answer: E

  On the BAII Plus, press 180 N, 7 divide 12 = I/Y, 175000 PV, 0 FV, CPT PMT. On the HP12C, press 180 n, 7 ENTER 12 divide i, 175000 PV, 0 FV, PMT. Make sure the BAII Plus has the P/Y value set to 1.

• Question 3228:

  Each salesperson in a large department store chain is rated either below average, average, or above average with respect to sales ability. Each salesperson is also rated with respect to his or her potential for advancement either fair, good, or excellent. These traits are the 500 salespeople were cross classified into the following table.

  Sales Ability Potential for Advancement Fair Good Excellent Below Average 161222 Average 456045 Above Average 9372135

  What is the probability that a salesperson selected at random will have average sales ability and good potential for advancement?

  A. 0.09

  B. None of these answers

  C. 0.12

  D. 0.525

  E. 0.30

  Correct Answer: C

  Prob. of selecting a person with average sales ability: (45 + 60 + 45)/500 = 3/10. Prob. of selecting good potential amongst those with average sales ability: 60/150. Therefore: 3/10*6/15 = 0.12.

• Question 3229:

  You are given a risk-free rate of 3% per year, a portfolio return of 8% per year, and a standard deviation of portfolio return of 22% per year. What is the Sharpe measure of risk-adjusted performance?

  A. 0.250.

  B. 0.234.

  C. 0.227.

  D. 0.222.

  Correct Answer: C

  The Sharpe measure of risk-adjusted performance is equal to (rbar_p - rbar_f)/sigma_p, where rbar_p is the mean portfolio return, rbar_f is the mean risk-free return, and sigma_p is the standard deviation of portfolio return. In our case, we have (8% - 3%) / 22% = 5/22 = 0.227.

• Question 3230:

  A large group of inductees was given a mechanical aptitude and a finger dexterity test. The mean score on the mechanical aptitude test was 200, with a standard deviation of 10. The mean and standard deviation for the finger dexterity test were 30 and 6 respectively. What is the relative dispersion in the two groups?

  A. Mechanical 5 percent, finger 20 percent

  B. Mechanical 500 percent, finger 200 percent

  C. Mechanical 20 percent, finger 10 percent

  D. Mechanical 50 percent, finger 200 percent

  E. None of these answers

  Correct Answer: A

  The respective CVs are found from (s*100)/mean. Mechanical: 10*100/200 = 5% and Finger: 6*100/30 = 20%.