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标题: Quantitative Methods 【Reading 7】Sample [打印本页]
作者: jawz    时间: 2012-3-22 13:15     标题: [2012 L1] Quantitative Methods 【Session 2 - Reading 7】Sample

Fifty mutual funds are ranked according to performance. The five best performing funds are assigned the number 1, while the five worst performing funds are assigned the number 10. This is an example of a(n):
A)
ordinal scale.
B)
interval scale.
C)
nominal scale.


The ordinal scale of measurement categorizes and orders data with respect to some characteristic. In this example, the ordinal scale tells us that a fund ranked “1” performed better than a fund ranked “10,” but it does not tell us anything about the difference in performance.
作者: jawz    时间: 2012-3-22 13:15

Which measure of scale has a true zero point as the origin?
A)
Nominal scale.
B)
Ordinal scale.
C)
Ratio scale.


Ratio scales are the strongest level of measurement; they quantify differences in the size of data and have a true zero point as the origin.
作者: jawz    时间: 2012-3-22 13:15

Which of the following statements regarding the terms population and sample is least accurate?
A)
A sample includes all members of a specified group.
B)
A sample's characteristics are attributed to the population as a whole.
C)
A descriptive measure of a sample is called a statistic.


A population includes all members of a specified group. A sample is a portion, or subset of the population of interest.
作者: jawz    时间: 2012-3-22 13:16

Which of the following statements about statistical concepts is least accurate?
A)
A frequency distribution is a tabular display of data summarized into a relatively small number of intervals.
B)
A sample contains all members of a specified group, but a population contains only a subset.
C)
A parameter is any descriptive measure of a population characteristic.


A population is defined as all members of a specified group, but a sample is a subset of a population.
作者: jawz    时间: 2012-3-22 13:16

A summary measure that is computed to describe a population characteristic from a sample is called a:
A)
census.
B)
parameter.
C)
statistic.


When sampling from a portion of the population, you compute a statistic to make inferences about the population.
作者: jawz    时间: 2012-3-22 13:17

Which one of the following alternatives best describes the primary use of inferential statistics? Inferential statistics are used to:
A)
summarize the important characteristics of a large data set based on statistical characteristics of a smaller sample.
B)
make forecasts, estimates or judgments about a large set of data based on statistical characteristics of a smaller sample.
C)
make forecasts based on large data sets.


Inferential statistics are used mainly to make forecasts, estimates or judgements about a large set of data based on statistical characteristics of a smaller set of data.
作者: jawz    时间: 2012-3-22 13:17

Which one of the following alternatives best describes the primary use of descriptive statistics? Descriptive statistics are used to:
A)
obtain data about the characteristics of any data set that can be used to assess the likelihood of the occurrence of future events.
B)
arrive at estimates regarding a large set of data regarding the statistical characteristics of a smaller sample.
C)
summarize important characteristics of large data sets.


Descriptive statistics are used mainly to summarize important characteristics of large data sets.
作者: jawz    时间: 2012-3-22 13:17

What is the main difference between descriptive statistics and inferential statistics? Descriptive statistics are:
A)
used to summarize data while inferential statistics are used to obtain precise information about a large data set.
B)
used to make forecasts about the likelihood of upcoming events while inferential statistics are used to summarize any data set.
C)
used to summarize a large data set while inferential statistics involves procedures used to make forecasts or judgments about a large data set by examining a smaller sample.


Descriptive statistics are used to summarize a large data set while inferential statistics are based on procedures used to make forecasts or judgments about a large data set by examining a smaller set of data.
作者: jawz    时间: 2012-3-22 13:17

Which of the following statements regarding various statistical measures is least accurate?
A)
The correlation coefficient is calculated by dividing the covariance of two random variables by the product of their standard deviations.
B)
Variance equals the sum of the squared deviations from the mean times the probability that that each outcome will occur.
C)
The coefficient of variation is calculated by dividing the mean by the standard deviation.


The coefficient of variation equals the standard deviation divided by the mean.
作者: jawz    时间: 2012-3-22 13:19

Which of the following is an example of a parameter?
A)
Population variance.
B)
Sample standard deviation.
C)
Sample mean.


A parameter is any descriptive measure of a population characteristic. The population variance describes a population while the sample standard deviation and sample mean are each descriptive measures of samples.
作者: jawz    时间: 2012-3-22 13:19

A summary measure of a characteristic of an entire population is called a:
A)
statistic.
B)
parameter.
C)
census.


A parameter measures a characteristic of the underlying population.
作者: jawz    时间: 2012-3-22 13:19

Which of the following statements regarding frequency distributions is least accurate? Frequency distributions:
A)
summarize data into a relatively small number of intervals.
B)
organize data into overlapping groups.
C)
work with all types of measurement scales.


Data in a frequency distribution must belong to only one group or interval. Intervals are mutually exclusive and non-overlapping.
作者: jawz    时间: 2012-3-22 13:20

Which of the following best describes a frequency distribution? A frequency distribution is a grouping of:
A)
selected data into intervals (classes) so that the number of observations in each of the non-overlapping intervals (classes) can be seen and tallied.
B)
data into intervals (classes) so that the number of observations in each of the non-overlapping intervals (classes) can be seen and tallied.
C)
independent intervals (classes) so that they can be seen and tallied.


A frequency distribution is a tabular presentation of statistical data that aids the analysis of large data sets.
作者: jawz    时间: 2012-3-22 13:20

How is the relative frequency of an interval computed?
A)
Dividing the frequency of that interval by the sum of all frequencies.
B)
Dividing the sum of the two interval limits by 2.
C)
Subtracting the lower limit of the interval by the upper limit.


The relative frequency is the percentage of total observations falling within each interval. It is found by taking the frequency of the interval and dividing that number by the sum of all frequencies.
作者: jawz    时间: 2012-3-22 13:21

In a frequency distribution histogram, the frequency of an interval is given by the:
A)
height multiplied by the width of the corresponding bar.
B)
width of the corresponding bar.
C)
height of the corresponding bar.


In a histogram, intervals are placed on the horizontal axis, and frequencies are placed on the vertical axis. The frequency of a particular interval is given by the value on the vertical axis, or the height of the corresponding bar.
作者: jawz    时间: 2012-3-22 13:21

Which of the following indicates the frequency of an interval in a frequency distribution histogram?
A)
Height of the corresponding bar.
B)
Horizontal logarithmic scale.
C)
Width of the corresponding bar.


In a histogram, intervals are placed on horizontal axis, and frequencies are placed on the vertical axis. The frequency of the particular interval is given by the value on the vertical axis, or the height of the corresponding bar.
作者: jawz    时间: 2012-3-22 13:21

Which of the following statements about histograms and frequency polygons is least accurate?
A)
A frequency polygon is constructed by plotting the midpoint of each interval on the horizontal axis.
B)
A histogram connects points with a straight line.
C)
A histogram and a frequency polygon both plot the absolute frequency on the vertical axis.


In constructing a frequency polygon, the midpoint of each interval is plotted on the horizontal axis and the frequency of each interval is plotted on the vertical axis. Points are then connected with straight lines. A histogram is a bar chart of data that has been grouped into a frequency distribution – because it is a bar chart, there are no individual points to connect.
作者: jawz    时间: 2012-3-22 13:22

Consider the following statements about the geometric and arithmetic means as measures of central tendency. Which statement is least accurate?
A)
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.
B)
The difference between the geometric mean and the arithmetic mean increases with an increase in variability between period-to-period observations.
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: jawz    时间: 2012-3-22 13:22

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)
0.18%; 18.6%.
C)
17.76%; 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: jawz    时间: 2012-3-22 13:22

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 ReturnGeometric compared to Arithmetic
  
A)
4.96%   greater than
B)
12.86%   greater than
C)
4.96%   less 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: jawz    时间: 2012-3-22 13:23

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: jawz    时间: 2012-3-22 13:23

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: jawz    时间: 2012-3-22 13:23

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: jawz    时间: 2012-3-22 13:23

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)
–16.45%.
B)
–33.33%.
C)
–7.00%.


Find the weighted mean. (0.10)(0.02) + (0.30)(0.095) + (0.60)(–0.325) = –16.45%.
作者: burning0spear    时间: 2012-3-22 13:28

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: burning0spear    时间: 2012-3-22 13:29

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


(1.104 × 1.081 × 1.032 × 1.15)0.25 − 1 = 9.1%
作者: burning0spear    时间: 2012-3-22 13:29

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: burning0spear    时间: 2012-3-22 13:29

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

3, 3, 5, 8, 9, 13, 17
A)
8; 8.28; 3.
B)
8.28; 8; 3.
C)
3; 8.28; 8.


Mean = (3 + 3 + 5 + 8 + 9 + 13 + 17) / 7 = 8.28; Median = middle of distribution = 8 (middle number); Mode = most frequent = 3.
作者: burning0spear    时间: 2012-3-22 13:30

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


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: burning0spear    时间: 2012-3-22 13:30

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: burning0spear    时间: 2012-3-22 13:30

Which of the following statements about a normal distribution is least accurate?
A)
Approximately 68% of the observations lie within +/- 1 standard deviation of the mean.
B)
A normal distribution has excess kurtosis of three.
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: burning0spear    时间: 2012-3-22 13:31

An investor has the following assets:
What is the portfolio's expected return?
A)
10.00%.
B)
11.00%.
C)
10.50%.


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: burning0spear    时间: 2012-3-22 13:31

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


(0.333)(0.06) + (0.333)(0.10) + 0.333(0.05) = 0.07
作者: burning0spear    时间: 2012-3-22 13:31

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: burning0spear    时间: 2012-3-22 13:32

Which of the following statements about the median is least accurate? It is:
A)
equal to the 50th percentile.
B)
more affected by extreme values than the mean.
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.
作者: burning0spear    时间: 2012-3-22 13:32

What are the median and the third quintile of the following data points, respectively?
9.2%, 10.1%, 11.5%, 11.9%, 12.2%, 12.8%, 13.1%, 13.6%, 13.9%, 14.2%, 14.8%, 14.9%, 15.4%
A)
13.1%; 13.6%.
B)
13.1%; 13.7%.
C)
12.8%; 13.6%.


The median is the midpoint of the data points. In this case there are 13 data points and the midpoint is the 7th term.
The formula for determining quantiles is: Ly = (n + 1)(y) / (100). Here, we are looking for the third quintile (60% of the observations lie below) and the formula is: (14)(60) / (100) = 8.4. The third quintile falls between 13.6% and 13.9%, the 8th and 9th numbers from the left. Since L is not a whole number, we interpolate as: 0.136 + (0.40)(0.139 − 0.136) = 0.1372, or 13.7%.
作者: burning0spear    时间: 2012-3-22 13:32

What does it mean to say that an observation is at the sixty-fifth percentile?
A)
65% of all the observations are below that observation.
B)
65% of all the observations are above that observation.
C)
The observation falls within the 65th of 100 intervals.


If the observation falls at the sixty-fifth percentile, 65% of all the observations fall below that observation.
作者: burning0spear    时间: 2012-3-22 13:33

Consider the following set of stock returns: 12%, 23%, 27%, 10%, 7%, 20%,15%. The third quartile is:
A)
23%.
B)
21.5%.
C)
20.0%.


The third quartile is calculated as: Ly = (7 + 1) (75/100) = 6. When we order the observations in ascending order: 7%, 10%, 12%, 15%, 20%, 23%, 27%, “23%” is the sixth observation from the left.
作者: burning0spear    时间: 2012-3-22 13:33

The following data points are observed returns.  

4.2%, 6.8%, 7.0%, 10.9%, 11.6%, 14.4%, 17.0%, 19.0%, 22.5%, 28.1%

What return lies at the seventh decile (70% of returns lie below this return)?
A)
17.0%.
B)
18.4%.
C)
19.0%.


The formula for the seventh decile is Ly = (n + 1)(7 / 10) = 7.70 or between the seventh and eighth return from the left. The seventh return is 17%, while the eighth return is 19%. Interpolating, we find that the seventh decile is 17% + 0.7(19% – 17%) = 18.4%.
作者: burning0spear    时间: 2012-3-22 13:33

When creating intervals around the mean to indicate the dispersion of outcomes, which of the following measures is the most useful? The:
A)
variance.
B)
median.
C)
standard deviation.


The standard deviation is more useful than the variance because the standard deviation is in the same units as the mean. The median does not help in creating intervals around the mean.
作者: burning0spear    时间: 2012-3-22 13:34

For the past three years, Acme Corp. has generated the following sample returns on equity (ROE): 4%, 10%, and 1%. What is the sample variance of the ROE over the last three years?
A)
21.0%.
B)
4.6%.
C)
21.0(%2).


[(4 − 5)2 + (10 − 5)2 + (1 − 5)2] / (3 − 1) = 21(%2).
作者: burning0spear    时间: 2012-3-22 13:34

There is a 40% chance that an investment will earn 10%, a 40% chance that the investment will earn 12.5%, and a 20% chance that the investment will earn 30%. What is the mean expected return and the standard deviation of expected returns, respectively?
A)
15.0%; 5.75%.
B)
15.0%; 7.58%.
C)
17.5%; 5.75%.


Mean = (0.4)(10) + (0.4)(12.5) + (0.2)(30) = 15%
Var = (0.4)(10 − 15)2 + (0.4)(12.5 − 15)2 + (0.2)(30 − 15)2 = 57.5
Standard deviation = √57.5 = 7.58
作者: burning0spear    时间: 2012-3-22 13:34

Cameron Ryan wants to make an offer on the condominium he is renting. He takes a sample of prices of condominiums in his development that closed in the last five months. Sample prices are as follows (amounts are in thousands of dollars): $125, $175, $150, $155 and $135. The sample standard deviation is closest to:
A)
370.00.
B)
38.47.
C)
19.24.


Calculations are as follows:
作者: burning0spear    时间: 2012-3-22 13:35

Assume a sample of beer prices is negatively skewed. Approximately what percentage of the distribution lies within plus or minus 2.40 standard deviations of the mean?
A)
95.5%.
B)
58.3%.
C)
82.6%.


Use Chebyshev’s Inequality to calculate this answer. Chebyshev’s Inequality states that for any set of observations, the proportion of observations that lie within k standard deviations of the mean is at least 1 – 1/k2. We can use Chebyshev’s Inequality to measure the minimum amount of dispersion whether the distribution is normal or skewed. Here, 1 – (1 / 2.42) = 1 − 0.17361 = 0.82639, or 82.6%.
作者: burning0spear    时间: 2012-3-22 13:35

In a skewed distribution, what is the minimum proportion of observations between +/- two standard deviations from the mean?
A)
95%.
B)
84%.
C)
75%.


For any distribution we can use Chebyshev’s Inequality, which states that the proportion of observations within k standard deviations of the mean is at least 1 – (1 / k2).
1 – (1 / 22) = 0.75, or 75%.
Note that for a normal distribution, 95% of observations will fall between +/- 2 standard deviations of the mean.
作者: burning0spear    时间: 2012-3-22 13:35

Regardless of the shape of a distribution, according to Chebyshev’s Inequality, what is the minimum percentage of observations that will lie within +/– two standard deviations of the mean?
A)
68%.
B)
89%.
C)
75%.


According to Chebyshev’s Inequality, for any distribution, the minimum percentage of observations that lie within k standard deviations of the distribution mean is equal to:
1 – (1 / k2), with k equal to the number of standard deviations. If k = 2, then the percentage of distributions is equal to 1 – (1 / 4) = 75%.
作者: burning0spear    时间: 2012-3-22 13:36

In a skewed distribution, what is the minimum amount of observations that will fall between +/- 1.5 standard deviations from the mean?
A)
44%.
B)
56%.
C)
95%.


Because the distribution is skewed, we must use Chebyshev’s Inequality, which states that the proportion of observations within k standard deviations of the mean is at least 1 – (1 / k2).
1 – (1 / 1.52) = 0.5555, or 56%.
作者: burning0spear    时间: 2012-3-22 13:36

According to Chebyshev’s Inequality, for any distribution, what is the minimum percentage of observations that lie within three standard deviations of the mean?
A)
94%.
B)
89%.
C)
75%.


According to Chebyshev’s Inequality, for any distribution, the minimum percentage of observations that lie within k standard deviations of the distribution mean is equal to: 1 – (1 / k2). If k = 3, then the percentage of distributions is equal to 1 – (1 / 9) = 89%.
作者: burning0spear    时间: 2012-3-22 13:36

Which of the following statements about statistical concepts is least accurate?
A)
The coefficient of variation is useful when comparing dispersion of data measured in different units or having large differences in their means.
B)
For a normal distribution, only 95% of the observations lie within ±3 standard deviations from the mean.
C)
For any distribution, based on Chebyshev’s Inequality, 75% of the observations lie within ±2 standard deviations from the mean.


For a normal distribution, 95% of the observations lie within ±2 standard deviations of the mean while 99% of the observations lie within plus or minus three standard deviations of the mean. Both remaining statements are true. Note that 75% of observations for any distribution lie within ±2 standard deviations of the mean using Chebyshev’s inequality.
作者: burning0spear    时间: 2012-3-22 13:37

A higher Sharpe ratio indicates:
A)
a higher excess return per unit of risk.
B)
lower volatility of returns.
C)
a lower risk per unit of return.


The Sharpe ratio is excess return (return − Rf) per unit of risk (defined as the standard deviation of returns).
作者: burning0spear    时间: 2012-3-22 13:37

A portfolio of options had a return of 22% with a standard deviation of 20%. If the risk-free rate is 7.5%, what is the Sharpe ratio for the portfolio?
A)
0.725.
B)
0.568.
C)
0.147.


Sharpe ratio = (22% – 7.50%) / 20% = 0.725.
作者: burning0spear    时间: 2012-3-22 13:37

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%. Based on the Sharpe ratio, the:
A)
performance of the Smith portfolio is preferable to the performance of the Johnson portfolio.
B)
Johnson and Smith portfolios have exhibited the same risk-adjusted performance.
C)
performance of the Johnson portfolio is preferable to the performance of the Smith 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.
作者: burning0spear    时间: 2012-3-22 13:38

Portfolio A earned an annual return of 15% with a standard deviation of 28%. If the mean return on Treasury bills (T-bills) is 4%, the Sharpe ratio for the portfolio is:
A)
0.54.
B)
1.87.
C)
0.39.


(15 − 4) / 28 = 0.39
作者: burning0spear    时间: 2012-3-22 13:38

Which of the following statements regarding the Sharpe ratio is most accurate? The Sharpe ratio measures:
A)
excess return per unit of risk.
B)
peakedness of a return distrubtion.
C)
total return per unit of risk.


The Sharpe ratio measures excess return per unit of risk. Remember that the numerator of the Sharpe ratio is (portfolio return − risk free rate), hence the importance of excess return. Note that peakedness of a return distribution is measured by kurtosis.
作者: manchester88    时间: 2012-3-22 13:39

The mean monthly return on U.S. Treasury bills (T-bills) is 0.42%. The mean monthly return for an index of small stocks is 4.56%, with a standard deviation of 3.56%. What is the Sharpe measure for the index of small stocks?
A)
1.16%.
B)
16.56%.
C)
10.60%.


The Sharpe ratio measures excess return per unit of risk. (4.56 – 0.42) / 3.56 = 1.16%.
作者: manchester88    时间: 2012-3-22 13:39

Portfolio A earned a return of 10.23% and had a standard deviation of returns of 6.22%. If the return over the same period on Treasury bills (T-bills) was 0.52% and the return to Treasury bonds (T-bonds) was 4.56%, what is the Sharpe ratio of the portfolio?
A)
1.56.
B)
0.56.
C)
0.91.


Sharpe ratio = (Rp – Rf) / σp, where (Rp – Rf) is the difference between the portfolio return and the risk free rate, and σp is the standard deviation of portfolio returns. Thus, the Sharpe ratio is: (10.23 – 0.52) / 6.22 = 1.56. Note, the T-bill rate is used for the risk free rate.
作者: manchester88    时间: 2012-3-22 13:40

A portfolio has a return of 14.2% and a Sharpe’s measure of 3.52. If the risk-free rate is 4.7%, what is the standard deviation of returns?
A)
3.9%.
B)
2.6%.
C)
2.7%.


Standard Deviation of Returns = (14.2% – 4.7%) / 3.52 = 2.6988.
作者: manchester88    时间: 2012-3-22 13:40

Given a population of 200, 100, and 300, the coefficient of variation is closest to:
A)
30%.
B)
40%.
C)
100%.


CV = (σ/mean)
mean = (200 + 100 + 300)/3 = 200
σ = √[(200 - 200)2 + (100 - 200)2 + (300 - 200)2 / 3] = √6666.67 = 81.65
(81.65/200) = 40.82%
作者: manchester88    时间: 2012-3-22 13:40

The mean monthly return on (U.S. Treasury bills) T-bills is 0.42% with a standard deviation of 0.25%. What is the coefficient of variation?
A)
60%.
B)
84%.
C)
168%.


The coefficient of variation expresses how much dispersion exists relative to the mean of a distribution and is found by CV = s / mean, or 0.25 / 0.42 = 0.595, or 60%.
作者: manchester88    时间: 2012-3-22 13:41

An investor is considering two investments. Stock A has a mean annual return of 16% and a standard deviation of 14%. Stock B has a mean annual return of 20% and a standard deviation of 30%. Calculate the coefficient of variation (CV) of each stock and determine if Stock A has less dispersion or more dispersion relative to B. Stock A's CV is:
A)
1.14, and thus has more dispersion relative to the mean than Stock B.
B)
1.14, and thus has less dispersion relative to the mean than Stock B.
C)
0.875, and thus has less dispersion relative to the mean than Stock B.


CV stock A = 0.14 / 0.16 = 0.875
CV stock B = 0.30 / 0.20 = 1.5
Stock A has less dispersion relative to the mean than Stock B.
作者: manchester88    时间: 2012-3-22 13:41

The mean monthly return on a sample of small stocks is 4.56% with a standard deviation of 3.56%. What is the coefficient of variation?
A)
78%.
B)
128%.
C)
84%.


The coefficient of variation expresses how much dispersion exists relative to the mean of a distribution and is found by CV = s / mean. 3.56 / 4.56 = 0.781, or 78%.
作者: manchester88    时间: 2012-3-22 13:41

If stock X's expected return is 30% and its expected standard deviation is 5%, Stock X's expected coefficient of variation is:
A)
0.167.
B)
6.0.
C)
1.20.


The coefficient of variation is the standard deviation divided by the mean: 5 / 30 = 0.167.
作者: manchester88    时间: 2012-3-22 13:42

What is the coefficient of variation for a distribution with a mean of 10 and a variance of 4?
A)
40%.
B)
25%.
C)
20%.



Coefficient of variation, CV = standard deviation / mean. The standard deviation is the square root of the variance, or 4½ = 2. So, CV = 2 / 10 = 20%.
作者: manchester88    时间: 2012-3-22 13:42

If the historical mean return on an investment is 2.0% and the standard deviation is 8.8%, what is the coefficient of variation (CV)?
A)
1.76.
B)
6.80.
C)
4.40.


The CV = the standard deviation of returns / mean return or 8.8% / 2.0% = 4.4.
作者: manchester88    时间: 2012-3-22 13:43

Consider the following graph of a distribution for the prices for various bottles of California-produced wine. Which of the following statements about this distribution is least accurate?
A)
Approximately 68% of observations fall within one standard deviation of the mean.
B)
The graph could be of the sample $16, $12, $15, $12, $17, $30 (ignore graph scale).
C)
The distribution is positively skewed.


This statement is true for the normal distribution. The above distribution is positively skewed. Note: for those tempted to use Chebyshev’s inequality to determine the percentage of observations falling within one standard deviation of the mean, the formula is valid only for k > 1.
The other statements are true. When we order the six prices from least to greatest: $12, $12, $15, $16, $17, $30, we observe that the mode (most frequently occurring price) is $12, the median (middle observation) is $15.50 [(15 + 16)/2], and the mean is $17 (sum of all prices divided by number in the sample). Time-Saving Note: Just by ordering the distribution, we can see that it is positively skewed (there are large, positive outliers). By definition, mode < median < mean describes a positively skewed distribution.
作者: manchester88    时间: 2012-3-22 13:44

A distribution with a mode of 10 and a range of 2 to 25 would most likely be:
A)
positively skewed.
B)
normally distributed.
C)
negatively skewed.


The distance to the left from the mode to the beginning of the range is 8. The distance to the right from the mode to the end of the range is 15. Therefore, the distribution is skewed to the right, which means that it is positively skewed.
作者: manchester88    时间: 2012-3-22 13:44

Which of the following statements regarding skewness is least accurate?
A)
A distribution that is not symmetrical has skew not equal to zero.
B)
A positively skewed distribution is characterized by many small losses and a few extreme gains.
C)
In a skewed distribution, 95% of all values will lie within plus or minus two standard deviations of the mean.


For a normal distribution, the mean will be equal to its median and 95% of all observations will fall within plus or minus two standard deviations of the mean. For a skewed distribution, because it is not symmetrical, this may not be the case. Chebyshev’s inequality tells us that at least 75% of observations will lie within plus or minus two standard deviations from the mean.
作者: manchester88    时间: 2012-3-22 13:44

If a distribution is skewed:
A)
the magnitude of positive deviations from the mean is different from the magnitude of negative deviations from the mean.
B)
it will be more or less peaked reflecting a greater or lesser concentration of returns around the mean.
C)
each side of a return distribution is the mirror image of the other.


Skewness is caused by the magnitude of positive deviations from the mean being either larger or smaller than the magnitude of negative deviations from the mean. Each side of a skewed distribution is not a mirror image of the other. Peakedness of a distribution is measured by kurtosis.
作者: manchester88    时间: 2012-3-22 13:46

Which of the following statements concerning skewness is least accurate? A distribution with:
A)
a distribution with skew equal to 1 is not symmetrical.
B)
positive skewness has a long left tail.
C)
negative skewness has a large number of outliers on its left side.


A distribution with positive skewness has long right tails.
作者: manchester88    时间: 2012-3-22 13:47

Which of the following statements concerning kurtosis is least accurate?
A)
A distribution that is more peaked than a normal distribution is leptokurtic.
B)
A leptokurtic distribution has fatter tails than a normal distribution.
C)
A leptokurtic distribution has excess kurtosis less than zero.


A leptokurtic distribution is more peaked than normal and has fatter tails. However, the excess kurtosis is greater than zero.
作者: manchester88    时间: 2012-3-22 13:47

Which of the following statements about kurtosis is least accurate? Kurtosis:
A)
measures the peakedness of a distribution reflecting a greater or lesser concentration of returns around the mean.
B)
is used to reflect the probability of extreme outcomes for a return distribution.
C)
describes the degree to which a distribution is not symmetric about its mean.


The degree to which a distribution is not symmetric about its mean is measured by skewness. Excess kurtosis which is measured relative to a normal distribution, indicates the peakedness of a distribution, and also reflects the probability of extreme outcomes.
作者: manchester88    时间: 2012-3-22 13:47

Which of the following statements concerning a distribution with positive skewness and positive excess kurtosis is least accurate?
A)
It has a lower percentage of small deviations from the mean than a normal distribution.
B)
The mean will be greater than the mode.
C)
It has fatter tails than a normal distribution.


A distribution with positive excess kurtosis has a higher percentage of small deviations from the mean than normal. So it is more “peaked” than a normal distribution. A distribution with positive skew has a mean > mode.
作者: manchester88    时间: 2012-3-22 13:48

A distribution of returns that has a greater percentage of small deviations from the mean and a greater percentage of large deviations from the mean compared to a normal distribution:
A)
is positively skewed.
B)
has positive excess kurtosis.
C)
has negative excess kurtosis.


A distribution that has a greater percentage of small deviations from the mean and a greater percentage of large deviations from the mean will be leptokurtic and will exhibit positive excess kurtosis. The distribution will be taller (more peaked) with fatter tails than a normal distribution.
作者: manchester88    时间: 2012-3-22 13:48

A distribution that is more peaked than normal is:
A)
skewed.
B)
leptokurtic.
C)
platykurtic.


A distribution that is more peaked than normal is leptokurtic. A distribution that is flatter than normal is platykurtic.
作者: manchester88    时间: 2012-3-22 13:48

A distribution that has positive excess kurtosis is:
A)
more skewed than a normal distribution.
B)
less peaked than a normal distribution.
C)
more peaked than a normal distribution.


A distribution with positive excess kurtosis is one that is more peaked than a normal distribution.
作者: manchester88    时间: 2012-3-22 13:49

Which of the following statements about skewness and kurtosis is least accurate?
A)
Positive values of kurtosis indicate a distribution that has fat tails.
B)
Kurtosis is measured using deviations raised to the fourth power.
C)
Values of relative skewness in excess of 0.5 in absolute value indicate large levels of skewness.


Positive values of kurtosis do not indicate a distribution that has fat tails. Positive values of excess kurtosis (kurtosis > 3) indicate fat tails.
作者: manchester88    时间: 2012-3-22 13:49

In the most recent four years, an investment has produced annual returns of 4%, –1%, 6%, and 3%. The most appropriate estimate of the next year’s return, based on these historical returns, is the:
A)
geometric mean.
B)
harmonic mean.
C)
arithmetic mean.


Given a series of historical returns, the arithmetic mean is statistically the best estimator of the next year’s return. For estimating a compound return over more than one year, the geometric mean of the historical returns is the most appropriate estimator.
作者: manchester88    时间: 2012-3-22 13:50

If a distribution is positively skewed:
A)
the mean is greater than the median.
B)
the mode is greater than the median.
C)
the mode is greater than the mean.


For a positively skewed distribution, the mode is less than the median, which is less than the mean (the mean is greatest). Remember that investors are attracted to positive skewness because the mean return is greater than the median return.
作者: manchester88    时间: 2012-3-22 13:50

A distribution with a mean that is less than its median most likely:
A)
is negatively skewed.
B)
is positively skewed.
C)
has negative excess kurtosis.


A distribution with a mean that is less than its median is a negatively skewed distribution. A negatively skewed distribution is characterized by many small gains and a few extreme losses. Note that kurtosis is a measure of the peakedness of a return distribution.
作者: manchester88    时间: 2012-3-22 13:51

Consider the following graph of a distribution for the prices of various bottles of champagne.


Which of the following statements regarding the distribution is least accurate?
A)
The distribution is negatively skewed.
B)
Point A represents the mode.
C)
The mean value will be less than the mode.


The graph represents a negatively skewed distribution, and thus Point A represents the mean. By definition, mean < median < mode describes a negatively skewed distribution.
Both remaining statements are true. Chebyshev’s Inequality states that for any set of observations (normally distributed or skewed), the proportion of observations that lie within k standard deviations of the mean is at least 1 – 1 / k2. Here, 1 – (1 / 1.32) = 1 − 0.59172 = 0.40828, or 40%.
作者: manchester88    时间: 2012-3-22 13:51

In a positively skewed distribution, the:
A)
median equals the mean.
B)
mean is greater than the median.
C)
mean is less than the median.


In a right-skewed distribution, there are large positive outliers. These outliers increase the mean of the distribution but have little effect on the median. Therefore, the mean is greater than the median.
作者: manchester88    时间: 2012-3-22 13:52

If a distribution is positively skewed, then generally:
A)
mean < median < mode.
B)
mean > median < mode.
C)
mean > median > mode.


When a distribution is positively skewed the right side tail is longer than normal due to outliers. The mean will exceed the median, and the median will generally exceed the mode because large outliers falling to the far right side of the distribution can dramatically influence the mean.
作者: manchester88    时间: 2012-3-22 13:52

Twenty Level I CFA candidates in a study group took a practice exam and want to determine the distribution of their scores. When they grade their exams they discover that one of them skipped an ethics question and subsequently filled in the rest of his answers in the wrong places, leaving him with a much lower score than the rest of the group. If they include this candidate’s score, their distribution will most likely:
A)
have a mode that is less than its median.
B)
have a mean that is less than its median.
C)
be positively skewed.


With the low outlier included, the distribution will be negatively skewed. For a negatively skewed distribution, the mean is less than the median, which is less than the mode.
作者: manchester88    时间: 2012-3-22 13:52

In a negatively skewed distribution, what is the order (from lowest value to highest) for the distribution’s mode, mean, and median values?
A)
Median, mode, mean.
B)
Mode, mean, median.
C)
Mean, median, mode.


In a negatively skewed distribution, the mean is less than the median, which is less than the mode.
作者: ikoreaii    时间: 2012-3-22 13:55

In a positively skewed distribution, what is the order (from lowest value to highest) for the distribution’s mode, mean, and median values?
A)
Mean, median, mode.
B)
Mode, mean, median.
C)
Mode, median, mean.


In a positively skewed distribution, the mode is less than the median, which is less than the mean.
作者: terpsichorefan    时间: 2013-3-15 01:00

thanks for sharing!



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