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

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

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

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 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

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

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 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.

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A leptokurtic distribution is more peaked than normal and has fatter tails. However, the excess kurtosis is greater than zero.

manchester88

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.

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A distribution with positive skewness has long right tails.

manchester88

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.

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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.