Reading 7: Statistical Concepts and Market Returns-LOS j, (P 2010, interpret, meaning, return, center

bmaggie

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

LOS j, (Part 1): Define and interpret skewness, and explain the meaning of a positively or negatively skewed return distribution.

 

 

 

A distribution with a mode of 10 and a range of 2 to 25 would most likely be:

A) normally distributed.

B) positively skewed.

C) negatively skewed.

bmaggie

A distribution with a mode of 10 and a range of 2 to 25 would most likely be:

A) normally distributed.

B) positively skewed.

C) negatively skewed.

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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.

bmaggie

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 any distribution, based on Chebyshev’s Inequality, 75% of the observations lie within ±2 standard deviations from the mean.

C) For a normal distribution, only 95% of the observations lie within ±3 standard deviations from the mean.

bmaggie

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 any distribution, based on Chebyshev’s Inequality, 75% of the observations lie within ±2 standard deviations from the mean.

C) For a normal distribution, only 95% of the observations lie within ±3 standard deviations from the mean.

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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.

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bmaggie

Which of the following statements regarding skewness is least accurate?

A) A distribution that is not symmetrical has skew not equal to zero.

B) In a skewed distribution, 95% of all values will lie within plus or minus two standard deviations of the mean.

C) A positively skewed distribution is characterized by many small losses and a few extreme gains.

bmaggie

Which of the following statements regarding skewness is least accurate?

A) A distribution that is not symmetrical has skew not equal to zero.

B) In a skewed distribution, 95% of all values will lie within plus or minus two standard deviations of the mean.

C) A positively skewed distribution is characterized by many small losses and a few extreme gains.

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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.

bmaggie

If a distribution is skewed:

A) it will be more or less peaked reflecting a greater or lesser concentration of returns around the mean.

B) each side of a return distribution is the mirror image of the other.

C) the magnitude of positive deviations from the mean is different from the magnitude of negative deviations from the mean.

bmaggie

If a distribution is skewed:

A) it will be more or less peaked reflecting a greater or lesser concentration of returns around the mean.

B) each side of a return distribution is the mirror image of the other.

C) the magnitude of positive deviations from the mean is different from the magnitude of negative deviations from the mean.

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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.

bmaggie

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) be positively skewed.

C) have a mean that is less than its median.

bmaggie

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) be positively skewed.

C) have a mean that is less than its median.

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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.