CFA Level 1 － 模考试题(3)（PM）－Q26-30 考试题, style, class

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Question 26 

Joe Mayer, CFA, projects that XYZ Company's return on equity varies with the state of the economy in the following way:

State of Economy	Probability of Occurrence	Company Returns
Good	.20	20%
Normal	.50	15%
Poor	.30	10%

The standard deviation of XYZ's expected return on equity is closest to:

A) 3.5%.

B) 12.3%.

C) 1.3%.

D) 1.5%.

 

Question 27 

Twenty students take an exam. The percentages of questions they answer correctly are ranked from lowest to highest as follows:

32	49	57	58	61
62	64	66	67	67
68	69	71	72	72
74	76	80	82	83

In a frequency distribution from 30% to 90% that is divided into six equal-sized intervals, the absolute frequency of the sixth interval is:

A) 2.

B) 4.

C) 1.

D) 3.

 

Question 28 

Mei Tekei just celebrated her 22nd birthday. When she is 27, she will receive a $100,000 inheritance. Tekei needs funds for the down payment on a co-op in Manhattan and has found a bank that will give her the present value of her inheritance amount, assuming an 8.0% stated annual interest rate with continuous compounding. Will the proceeds from the bank be sufficient to cover her down payment of $65,000? 

A) Yes, Tekei will receive $68,058.

B) No, Tekei will only receive $49,182.

C) No, Tekei will only receive $61,878.

D) Yes, Tekei will receive $67,028.

 

Question 29 

A researcher is testing the hypothesis that a population mean is equal to zero. From a sample with 64 observations, the researcher calculates a sample mean of -2.5 and a sample standard deviation of 8.0. At which levels of significance should the researcher reject the hypothesis? 

 1% significance  5% significance   10% significance

A) Reject             Fail to reject        Fail to reject

B) Fail to reject         Fail to reject         Reject

C) Reject              Reject              Reject

D) Fail to reject         Reject              Reject

 

Question 30 

Trina Romel, mutual fund manager, is taking over a poor-performing fund from a colleague. Romel wants to calculate the return on the portfolio. Over the last five years, the fund’s annual percentage returns were: 25, 15, 12, -8, and –14. Determine if the geometric return of the fund will be less than or greater than the arithmetic return and calculate the fund’s geometric return: 

     Geometric Return    Geometric compared to Arithmetic

A)        4.96%               greater than

B)        12.86%              greater than

C)        12.86%              less than

D)        4.96%               less than

 

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答案和详解如下：

Answer 26 

The correct answer was A) 3.5%. 

In order to calculate the standard deviation of the company returns, first calculate the expected return, then the variance, and the standard deviation is the square root of the variance. 

The expected value of the company return is the probability weighted average of the possible outcomes: (0.20)(0.20) + (0.50)(0.15) + (0.30)(0.10) = 0.145.  The variance is the sum of the probability of each outcome multiplied by the squared deviation of each outcome from the expected return: (0.2)(0.20 - 0.145)² + (0.5)(0.15 - 0145)² + (0.3)(0.1-0.145)² = 0.000605 + 0.0000125 + 0.0006075 = 0.001225.  The standard deviation is the square root of 0.001225 = 0.035 or 3.5%. 

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

 

Answer 27 

The correct answer was D) 3. 

The intervals are 30% ≤ x < 40%, 40% ≤ x < 50%, 50% ≤ x < 60%, 60% ≤ x < 70%, 70% ≤ x < 80%, and 80% ≤ x ≤ 90%. There are 3 scores in the range 80% ≤ x ≤ 90%. 

This question tested from Session 2, Reading 7, LOS b

 

Answer 28 

The correct answer was D) Yes, Tekei will receive $67,028. 

Because the rate is 8% compounded continuously, the effective annual rate is e^0.08 - 1 = 8.33%. To find the present value of the inheritance, enter N=5, I/Y=8.33, PMT=0, FV=100,000 CPT PV = 67,028. 

Alternatively, 100,000e^-0.08(5) = 67,032. 

This question tested from Session 3, Reading 9, LOS k, (Part 2)

 

Answer 29 

The correct answer was D) Fail to reject         Reject             Reject This is a two-tailed test using a z-statistic. The test statistic =  = −2.5. For a two-tailed z-test, the critical values are ±1.645 for a 10% significance level, ±1.96 for a 5% significance level, and ±2.58 for a 1% significance level. The researcher should reject the hypothesis at the 10% and 5% significance levels, but fail to reject the hypothesis at the 1% significance level. 

This question tested from Session 3, Reading 11, LOS a, (Part 2)

 

Answer 30 

The correct answer was D)

The geometric return is calculated as follows:

[(1 + 0.25)(1 + 0.15)(1 + 0.12)(1 - 0.08)(1 – 0.14)]^1/5 – 1,

or [1.25 × 1.15 × 1.12 × 0.92 × 0.86]^0.2 – 1 = 0.4960, or 4.96%.

The geometric return will always be less than or equal to the arithmetic return. In this case the arithmetic return was 6%. 

This question tested from Session 2, Reading 7, LOS d

 

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