manchester88

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.

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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.

manchester88

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.

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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.

manchester88

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.

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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.

manchester88

A distribution that is more peaked than normal is:

A) skewed.

B) leptokurtic.

C) platykurtic.

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A distribution that is more peaked than normal is leptokurtic. A distribution that is flatter than normal is platykurtic.

manchester88

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.

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A distribution with positive excess kurtosis is one that is more peaked than a normal distribution.

manchester88

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.

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Positive values of kurtosis do not indicate a distribution that has fat tails. Positive values of excess kurtosis (kurtosis > 3) indicate fat tails.

manchester88

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.

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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.

manchester88

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.

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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.

manchester88

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.

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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.

manchester88

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.

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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%.