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

• Question 3191:

  You are evaluating 5 portfolio managers (A, B, C, D, and E) whose Sharpe ratios are 0.25, 0.41, 0.92, 0.78, and 0.51, respectively. Which manager would most risk-averse investors prefer?

  A. C.

  B. A.

  C. E.

  D. None of these answers is correct.

  Correct Answer: A

  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. Thus, the manager with the highest Sharpe ratio is generating the largest return in excess of the risk free rate, per unit of risk assumed. This is manager C, with a Sharpe ratio of 0.92.

• Question 3192:

  What degree of relationship do values of the correlation coefficient (r) with magnitudes close to 1.00 indicate?

  A. Weak

  B. Strong

  C. Moderate

  D. None

  Correct Answer: B

  The closer to 1, the stronger the relationship.

• Question 3193:

  A researcher has a sample of 700 observations from a population whose standard deviation is known to be 1,235.6. The mean of the sample is calculated to be 219.2. The null hypothesis is stated as Ho: mean = 150 and the alternative is non-directional. The p-value in this case equals ________.

  A. 10.16%

  B. 13.88%

  C. 6.94%

  D. 12.82%

  Correct Answer: B

  The z-statistic under the null equals (219.2 - 150)/(1235.6/(700^.5)) = 1.48. Since the alternative is non-directional, you must use a two-tailed test and ask the question, "What is the probability of observing a z-statistic at least as large in magnitude as 1.48?" The answer to this will give you the p- value for this sample under the two-tailed test. The right-tailed probability of observing a z-statistic which is at least as big as 1.48 equals 1.0 - 0.9306 = 0.0694 = 6.94%. The left- tailed probability of observing a z-statistic which is at least as small as - 1.48 also equals 6.94% since the standard normal distribution is symmetrical about zero. Therefore, the p-value of this two-tailed test in this sample equals 6.94%*2 = 13.88%.

• Question 3194:

  In a sample of 2,000 persons, 1,600 favored more strict environmental protection measures. What is the estimated population proportion?

  A. 0.82 or 82%

  B. 0.20 or 20%

  C. 0.16 or 16%

  D. None of these answers

  E. 0.80 or 80%

  Correct Answer: E

  Population proportion is given by 1600/2000 = 0.80

• Question 3195:

  What is the Net Present Value of this series of annual cash flows using an interest rate of 15% per year: Year 0: <$10,000>, Year 1: $5,000, Year 2: $5,000, Year 3: $7,500? (Note that the <> are used to indicate a negative number).

  A. $2,981.21

  B. $5,077.49

  C. $3,059.92

  D. $3,224.98

  E. $3,104.37

  Correct Answer: C

  On the BAII Plus, press CF 2nd CLRWork 10000 +/- ENTER DownArrow 5000 ENTER DownArrow DownArrow 5000 ENTER DownArrow DownArrow 7500 ENTER DownArrow DownArrow 2nd Quit. Then press NPV 15 ENTER DownArrow CPT. On the HP12C, press these keys: 10000 CHS BlueShift CFo 5000 BlueShift CFj 5000 BlueShift CFj 7500 BlueShift CFj Then press 15 i, YellowShift NPV. The "DownArrow" represents the downward-pointing arrow on the top row of the BAII Plus keyboard.

• Question 3196:

  Which of the following is/are true?

  I. There are as many values above the mean as below it.

  II. The sum of the differences between the observations in a sample and the mean of the sample equals zero.

  III. The mean is greatly affected by "outliers."

  IV.

  The mean is harder to estimate with reliability for open-ended data.

  A.

  I, II and III

  B.

  III only

  C.

  II and III

  D.

  II only

  E.

  I only

  F.

  IV only

  G.

  I and III

  H.

  II, III and IV

  Correct Answer: H

  I would be correct if "mean" is replaced by "median" i.e. there are as many values above the median as below it. Note that one of the advantages of using the median instead of the mean is that the mean is greatly affected by outliers since it represents an average of all the observations while the median is not affected in this fashion.

• Question 3197:

  Which of the following are true regarding covariance?

  I. Covariance of returns on two assets is 0 when the returns are unrelated.

  II. Covariance will be negative if, when the return on one asset is below expected value, the other return will also be below its expected value.

  III. The covariance of returns of an asset with itself is the asset's return variance.

  IV.

  Covariance is the probability weighted average of the cross product of the deviation of each random variable from its expected value.

  A.

  All but II.

  B.

  All but I.

  C.

  All but IV.

  D.

  All but III.

  Correct Answer: A

  I, III, and IV are all true. II is false. To make II true, we would have to restate it as "Covariance will be negative if, when the return on one asset is below expected value, the other return will be above its expected value."

• Question 3198:

  The U.S. Federal Aviation Administration reported that passenger revenues on international flights increased from $528 million in 1972 to $5,100 million in 1995. What is the geometric mean annual percent increase in international passenger revenues?

  A. None of these answers

  B. 27.9

  C. 9.96

  D. 103.6

  E. 10.4

  Correct Answer: E

  There are 24 years involved. The geometric mean is = [(1 + 5100/528)^1/23]-1. In words, it is the 23rd square root of (1 + 5100/528) minus 1. So we have GM = (1 + 9.66)^(1/23) - 1 = 0.1036 = 10.4%

• Question 3199:

  A researcher has a sample of 400 observations from a population whose standard deviation is known to be

  136. The mean of the sample is calculated to be 17.2. The null hypothesis is stated as Ho: mean = 4. The p-value under the alternative hypothesis H1: mean > 4 equals ________.

  A. 3.92%

  B. 5.2%

  C. 1.96%

  D. 2.6%

  Correct Answer: D

  The z-statistic under the null is calculated to be (17.2 - 4)/(136/(400^.5)) = 1.94. The right-tailed probability of observing a z-statistic at least as big as 1.94 equals 1.0 - 0.9738 = 0.026 = 2.6%. This is the p-value of the right-tailed test in this sample.

• Question 3200:

  You are given a portfolio mean return of 15%, and a standard deviation of portfolio return is 20%, and a Sharpe ratio of 0.51. What is the risk-free rate?

  A. None of these answers is correct.

  B. 4.0%.

  C. 5.0%.

  D. 4.2%.

  Correct Answer: A

  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 (15% - x%) / 20% = 0.51. Solving for x, we obtain x = 0.15 - 0.51

  * 0.20 = 0.15 - 0.102 = 0.048 = 4.8%.