Quant - Statistical Measures of Asset Returns Flashcards
The tenth percentile corresponds to observations in bin(s):
A.2.
B.1 and 2.
C.19 and 20.
B is correct. The tenth percentile corresponds to the lowest 10 percent of the observations in the sample, which are in bins 1 and 2.
The second quintile corresponds to observations in bin(s):
A.8.
B.5, 6, 7, and 8.
C.6, 7, 8, 9, and 10.
B is correct. The second quintile corresponds to the second 20 percent of observations. The first 20 percent consists of bins 1 through 4. The second 20 percent of observations consists of bins 5 through 8.
The fourth quartile corresponds to observations in bin(s):
A.17.
B.17, 18, 19, and 20.
C.16, 17, 18, 19, and 20.
C is correct. A quartile consists of 25 percent of the data, and the last 25 percent of the 20 bins are 16 through 20.
The median is closest to:
A.44.86.
B.46.88.
C.49.40.
B is correct. The center of the 20 bins is represented by the market capitalization of the highest value of the 10th bin and the lowest value of the 11th bin, which is 46.88.
Q. The interquartile range is closest to:
A.20.76.
B.23.62.
C.25.52.
IQR=Q3−Q1
Q1 is the median of the lower half of the dataset, and Q3 is the median of the upper half of the dataset.
B is correct. The interquartile range is the difference between the lowest value in the second quartile and the highest value in the third quartile. The lowest value of the second quartile is 34.72, and the highest value of the third quartile is 58.34. Therefore, the interquartile range is 58.34 − 34.72 = 23.62.
Exhibit 12 shows the annual MSCI World Index total returns for a 10-year period.
The fourth quintile return for the MSCI World Index is closest to:
A.20.65 percent.
B.26.03 percent.
C.27.37 percent.
B is correct.
The fund’s standard deviation of returns over the 10 years is closest to:
A.2.40 percent.
B.2.53 percent.
C.7.58 percent.
B is correct.
[F] [SST] //clear sigma
[F] [FIN] //clear finance reg.
[F] [REG] //clear normal reg.
[4.5] [Σ+]
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[g] [.] (the ‘s’)
(Calculator should show 2.527)
The target semideviation of the returns over the 10 years, if the target is 2 percent, is closest to:
A.1.42 percent.
B.1.50 percent.
C.2.01 percent.
B is correct.
Consider the mean monthly return and the standard deviation for three industry sectors, as shown in Exhibit 2:
Based on the coefficient of variation (CV), the riskiest sector is:
A.utilities.
B.materials.
C.industrials.
B is correct.
For a positively skewed unimodal distribution, which of the following measures is most accurately described as the largest?
A.
Median
B.
Mean
C.
Mode
B is correct.
Incorrect. For the positively skewed unimodal distribution, the mode is less than the median, which is less than the mean.
Correct. For a positively skewed unimodal distribution, the mode is less than the median, which is less than the mean.
Incorrect. For the positively skewed unimodal distribution, the mode is less than the median, which is less than the mean.
A risk manager would like to calculate the coefficient of variation of a portfolio. The following table reports the annual returns of the portfolio and of the risk-free rate over the most recent five years:
he coefficient of variation of the portfolio is closest to:
A.
0.74.
B.
0.90.
C.
1.00.
C is correct.
For a given expected return and standard deviation, investors are most likely to be attracted to return distributions that are:
A.
negatively skewed.
B.
positively skewed.
C.
normal.
B is Correct. For a given expected return and standard deviation, investors are most likely to be attracted by a positive skew because the mean return lies above the median. Relative to the mean return, positive skew amounts to limited, though frequent, downside returns compared with somewhat unlimited, but less frequent, upside returns.
Equity return distributions are best described as being:
A.
leptokurtic.
B.
platykurtic.
C.
mesokurtic.
A.
leptokurtic.
Which of the following statements is most accurate? The first quintile generally exceeds the:
A.
first quartile.
B.
median.
C.
first decile.
C is Correct. The first quintile is the 20th percentile (a percentile indicates the value below which a given percentage of observations in a group fall). The first decile is the 10th percentile, the first quartile is the 25th percentile, and the median is the 50th percentile. Although it is possible that these various percentiles or some subsets of them might be equal (for example, the 10th percentile possibly could be equal to the 20th percentile), in general, the order from smallest to largest would be: first decile, first quintile, first quartile, median.
A portfolio manager would like to calculate the compound rate of return on an investment. Which of the following mean returns will he most likely use?
A.
Geometric
B.
Harmonic
C.
Arithmetic
The geometric mean return represents the growth rate or compound rate of return on an investment.
The median of the returns on the index, if compared to the mean, will most likely be:
A. smaller.
B.
equal.
C.
greater.
A is Correct. The histogram clearly shows that the return distribution of the index is positively skewed (skewed to the right) and is unimodal (it has one most frequently occurring value). For a positively skewed unimodal distribution, the median is always less than the mean.
The following table shows the volatility of a series of funds that belong to the same peer group, ranked in ascending order:
The approximate value of the first quintile is closest to:
A.
10.70%.
B.
11.09%.
C.
10.84%.
A is correct.
The following 10 observations are a sample drawn from an approximately normal population:
The sample standard deviation is closest to:
A.
13.18.
B.
11.92.
C.
12.50.
A.
13.18.
