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标题: Reading 7: Statistical Concepts and Market Returns-LOS e 习题 [打印本页]
作者: 1215    时间: 2011-3-1 14:29     标题: [2011]Session 2-Reading 7: Statistical Concepts and Market Returns-LOS e 习题

Session 2: Quantitative Methods: Basic Concepts
Reading 7: Statistical Concepts and Market Returns

LOS e: Define, calculate, and interpret measures of central tendency, including the population mean, sample mean, arithmetic mean, weighted average or mean (including a portfolio return viewed as a weighted mean), geometric mean, harmonic mean, median, and mode.

 

 

Consider the following statements about the geometric and arithmetic means as measures of central tendency. Which statement is least accurate?

A)
 The difference between the geometric mean and the arithmetic mean increases with an increase in variability between period-to-period observations.
B)
 The geometric mean may be used to estimate the average return over a one-period time horizon because it is the average of one-period returns.
C)
 The geometric mean calculates the rate of return that would have to be earned each year to match the actual, cumulative investment performance.

 

The arithmetic mean may be used to estimate the average return over a one-period time horizon because it is the average of one-period returns. Both remaining statements are true.

作者: 1215    时间: 2011-3-1 14:29

A stock had the following returns over the last five years: 15%, 2%, 9%, 44%, 23%. What is the respective geometric mean and arithmetic mean for this stock?

A)
 17.76%; 23.0%.
B)
 17.76%; 18.6%.
C)
 0.18%; 18.6%.

Geometric mean = [(1.15)(1.02)(1.09)(1.44)(1.23)]1/5 ? 1 = 1.17760 = 17.76%.

Arithmetic mean = (15 + 2 + 9 + 44 + 23) / 5 = 18.6%.

作者: 1215    时间: 2011-3-1 14:29

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)
4.96%   less than
C)
12.86%   greater than

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%.

作者: 1215    时间: 2011-3-1 14:30

An investor has a $12,000 portfolio consisting of $7,000 in stock A with an expected return of 20% and $5,000 in stock B with an expected return of 10%. What is the investor’s expected return on the portfolio?

A)
 12.2%.
B)
 15.0%.
C)
 15.8%.

Find the weighted mean where the weights equal the proportion of $12,000. (7,000 / 12,000)(0.20) + (5,000 / 12,000)(0.10) = 15.8%.

作者: 1215    时间: 2011-3-1 14:30

Michael Philizaire is studying for the Level I CFA examination. During his review of measures of central tendency, he decides to calculate the geometric average of the appreciation/deprecation of his home over the last five years. Using comparable sales and market data he obtains from a local real estate appraiser, Philizaire calculates the year-to-year percentage change in the value of his home as follows: 20, 15, 0, -5, -5. The geometric return is closest to:

A)
 11.60%.
B)
 4.49%.
C)
 0.00%.

The geometric return is calculated as follows:

[(1 + 0.20) × (1 + 0.15) × (1 + 0.0) (1 ? 0.05) (1 ? 0.05)]1/5 – 1,

or [1.20 × 1.15 × 1.0 × 0.95 × 0.95]0.2 – 1 = 0.449, or 4.49%.

作者: 1215    时间: 2011-3-1 14:31

The owner of a company has recently decided to raise the salary of one employee, who was already making the highest salary in the company, by 40%. Which of the following value(s) is (are) expected to be affected by this raise?

A)
 mean and median only.
B)
 median only.
C)
 mean only.

Mean is affected because it is the sum of all values / number of observations.  Median is not affected as it the midpoint between the top half of values and the bottom half of values.

作者: 1215    时间: 2011-3-1 14:31

An investor has a portfolio with 10% cash, 30% bonds, and 60% stock. Last year, the cash returns was 2.0%, the bonds’ return was 9.5%, and the stocks’ return was –32.5%. What was the return on the investor’s portfolio?

A)
 –33.33%.
B)
 –7.00%.
C)
 –16.45%.

Find the weighted mean. (0.10)(0.02) + (0.30)(0.095) + (0.60)(–0.325) = –16.45%.

作者: 1215    时间: 2011-3-1 14:31

Which measure of central tendency can be used for both numerical and categorical variables?

A)
 Mean.
B)
 Median.
C)
 Mode.

The mode is the only choice that makes sense since you cannot take an average or median of categorical data such as bond ratings (AAA, AA, A, etc.) but the mode is simply the most frequently occurring number or category.

作者: 1215    时间: 2011-3-1 14:32

For the last four years, the returns for XYZ Corporation’s stock have been 10.4%, 8.1%, 3.2%, and 15.0%. The equivalent compound annual rate is:

A)
 9.1%.
B)
 9.2%.
C)
 8.9%.

(1.104 × 1.081 × 1.032 × 1.15)0.25 ? 1 = 9.1%

作者: 1215    时间: 2011-3-1 14:32

What is the compound annual growth rate for stock A which has annual returns of 5.60%, 22.67%, and -5.23%?

A)
 7.08%.
B)
 6.00%.
C)
 8.72%.

Compound annual growth rate is the geometric mean. (1.056 × 1.2267 × 0.9477)1/3 – 1 = 7.08%

作者: 1215    时间: 2011-3-1 14:32

Find the mean, median, and mode, respectively, of the following data:

3, 3, 5, 8, 9, 13, 17

A)
 8; 8.28; 3.
B)
 3; 8.28; 8.
C)
 8.28; 8; 3.

Mean = (3 + 3 + 5 + 8 + 9 + 13 + 17) / 7 = 8.28; Median = middle of distribution = 8 (middle number); Mode = most frequent = 3.

作者: 1215    时间: 2011-3-1 14:32

An investor has a $15,000 portfolio consisting of $10,000 in stock A with an expected return of 20% and $5,000 in stock B with an expected return of 10%. What is the investor’s expected return on the portfolio?

A)
 16.7%.
B)
 12.2%.
C)
 7.9%.

Find the weighted mean where the weights equal the proportion of $15,000. [(10,000 / 15,000) × 0.20] + [(5,000 / 15,000 × 0.10] = 16.7%.

作者: 1215    时间: 2011-3-1 14:33

An investor has a portfolio with 10% cash, 30% bonds, and 60% stock. If last year’s return on cash was 2.0%, the return on bonds was 9.5%, and the return on stock was 25%, what was the return on the investor’s portfolio?

A)
 36.50%.
B)
 18.05%.
C)
 22.30%.

Find the weighted mean of the returns. (0.10 × 0.02) + (0.30 × 0.095) + (0.60 × 0.25) = 18.05%

作者: 1215    时间: 2011-3-1 14:33

Which of the following statements about a normal distribution is least accurate?

A)
 A normal distribution has excess kurtosis of three.
B)
 Approximately 68% of the observations lie within +/- 1 standard deviation of the mean.
C)
 The mean and variance completely define a normal distribution.

Even though normal curves have different sizes, they all have identical shape characteristics. The kurtosis for all normal distributions is three; an excess kurtosis of three would indicate a leptokurtic distribution. Both remaining choices are true.

作者: 1215    时间: 2011-3-1 14:33

An investor has the following assets:

What is the portfolio's expected return?

A)
 10.50%.
B)
 10.00%.
C)
 11.00%.

Expected return is the weighted average of the individual expected values. The expected return is: [(5,000) × (10.00) + (5,000) × (8.00) + (10,000) × (12.00)] / 20,000 = 10.50%.

作者: 1215    时间: 2011-3-1 14:33

A portfolio is equally invested in Stock A, with an expected return of 6%, and Stock B, with an expected return of 10%, and a risk-free asset with a return of 5%. The expected return on the portfolio is:

A)
 8.0%.
B)
 7.4%.
C)
 7.0%.

(0.333)(0.06) + (0.333)(0.10) + 0.333(0.05) = 0.07

作者: 1215    时间: 2011-3-1 14:33

Which of the following statements about the arithmetic mean is least accurate?

A)
 The arithmetic mean of a frequency distribution is equal to the sum of the class frequency times the midpoint of the frequency class all divided by the number of observations.
B)
 If the distribution is skewed to the left then the mean will be greater than the median.
C)
 The arithmetic mean is the only measure of central tendency where the sum of the deviations of each observation from the mean is always zero.

If the distribution is skewed to the left, then the mean will be less than the median.

作者: 1215    时间: 2011-3-1 14:34

Which of the following statements about the median is least accurate? It is:

A)
 more affected by extreme values than the mean.
B)
 equal to the 50th percentile.
C)
 equal to the mode in a normal distribution.

Median is less influenced by outliers since the median is computed as the “middle” observation. On the other hand, all of the data including outliers are used in computing the mean. Both remaining statements are true regarding the median.





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