CFA Level 1 － 模考试题(3)（PM）－Q21-25 holding, period, 考试题, style

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Question 21 

The holding period yield of a T-bill that has a bank discount yield of 4.70% and a money market yield of 4.86% and matures in 240 days is closest to: 

A) 2.5%.

B) 2.7%.

C) 2.3%.

D) 4.9%.

 

Question 22 

An investment has a mean return of 15% and a standard deviation of returns equal to 10%. Which of the following statements is least accurate? The probability of obtaining a return: 

A) greater than 25% is 0.32.

B) greater than 35% is 0.025.

C) less than 5% is 0.16.

D) between 5% and 25% is 0.68.

 

Question 23 

Given the following data:

  ♣ 40% of your prospects have only undergraduate degrees while 60% have MBAs. 

  ♣ 80% of the undergraduates buy your product while 50% of the MBAs do 

  ♣ You have just learned that prospect X purchased your product. 

Based on this information, the probability that prospect X has an MBA is closest to:

A) 36%.

B) 26%.

C) 60%.

D) 48%.

 

Question 24 

Johnson Inc. manages a growth portfolio of equity securities that has had a mean monthly return of 1.4% and a standard deviation of returns of 10.8%. Smith Inc. manages a blended equity and fixed income portfolio that has had a mean monthly return of 1.2% and a standard deviation of returns of 6.8%. The mean monthly return on Treasury bills has been 0.3%. Which of the following statements is most accurate? 

A) Based on the Sharpe ratio, the performance of the Johnson portfolio is preferable to the performance of the Smith portfolio.

B) Based on the Sharpe ratio, the performance of the Smith portfolio is preferable to the performance of the Johnson portfolio.

C) The Johnson portfolio has greater excess return per unit of risk than the Smith portfolio.

D) The Sharpe ratio shows that the Johnson and Smith portfolios have exhibited the same risk-adjusted performance.

 

Question 25 

Suppose the mean debt/equity ratio of all banks in the United States is 20 and the population variance is 25. A banking industry analyst uses a computer program to select a random sample of 50 banks from this population and compute the sample mean. The program repeats this exercise 1000 times and computes the sample mean each time. According to the central limit theorem, the sampling distribution of the 1000 sample means will have a standard error of the sample mean that is closest to:

A) 25.000.

B) 0.158.

C) 0.500.

D) 0.707.

 

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答案和详解如下：

Answer 21 

The correct answer was B) 2.7%. 

4.86 / (360/240) = 2.7%. 

This question tested from Session 2, Reading 6, LOS d, (Part 2)

 

Answer 22 

The correct answer was A) greater than 25% is 0.32. 

Sixty-eight percent of all observations fall within +/- one standard deviation of the mean of a normal distribution. Given a mean of 15 and a standard deviation of 10, the probability of having an actual observation fall within one standard deviation, between 5 and 25, is 68%. The probability of an observation greater than 25 is half of the remaining 32%, or 16%. This is the same probability as an observation less than 5. Because 95% of all observations will fall within 20 of the mean, the probability of an actual observation being greater than 35 is half of the remaining 5%, or 2.5%. 

This question tested from Session 3, Reading 10, LOS a

 

Answer 23 

The correct answer was D) 48%. 

Given a set of prior probabilities for an event, Bayes’ formula is used to update the probability of the event, in this case the probability that the prospect whom we already know purchased the product has an MBA. Bayes’ formula says to divide the "probability of new information given the event" by the "unconditional probability of new information," and multiply that result by the "prior probability of the event." In this case, P(prospect has an MBA) = 0.6 is divided by P(prospect buys the product), and the result is multiplied by P(an MBA buys the product) = 0.5. 

To find the unconditional probability of a prospect buying the product: 60% have MBAs, of whom 50% buy the product, and 40% are undergraduates, of whom 80% buy the product. So P(prospect buys the product) = (0.6)(0.5) + (0.4)(0.8) = 0.62. 

The updated probability is therefore (0.6/0.62) × 0.5 = 0.484 or 48.4%. 

This question tested from Session 2, Reading 8, LOS a

 

Answer 24 

The correct answer was B) Based on the Sharpe ratio, the performance of the Smith portfolio is preferable to the performance of the Johnson portfolio. 

The Sharpe ratio for the Johnson portfolio is (1.4 - 0.3)/10.8 = 0.1019.

The Sharpe ratio for the Smith portfolio is (1.2 - 0.3)/6.8 = 0.1324.

The Smith portfolio has the higher Sharpe ratio, or greater excess return per unit of risk. 

This question tested from Session 2, Reading 7, LOS h, (Part 2)

 

Answer 25 

The correct answer was D) 

0.707.

The central limit theorem tells us that for a population with a mean µ and a finite variance σ², the sampling distribution of the sample means for a sample of size n will be approximately normally distributed with a mean equal to µ and a variance equal to σ²/n, no matter the distribution of the population, assuming a large sample size. The standard error of the sample mean when the standard deviation of the population is known is: σ_{sample mean} = σ/√n = 5/√50 = 0.707 

This question tested from Session 3, Reading 10, LOS e

 

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