Reading 7: Statistical Concepts and Market Returns-LOS i, (P 2010, face, interpret, variation, center

bmaggie

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

LOS i, (Part 1): Define, calculate, and interpret the coefficient of variation.

 

 

 

Given a population of 200, 100, and 300, the coefficient of variation is closest to:

A) 40%.

B) 30%.

C) 100%.

bmaggie

Given a population of 200, 100, and 300, the coefficient of variation is closest to:

A) 40%.

B) 30%.

C) 100%.

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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%

bmaggie

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) 84%.

B) 168%.

C) 60%.

bmaggie

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) 84%.

B) 168%.

C) 60%.

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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%.

bmaggie

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) 0.875, and thus has less dispersion relative to the mean than Stock B.

B) 1.14, and thus has more dispersion relative to the mean than Stock B.

C) 1.14, and thus has less dispersion relative to the mean than Stock B.

bmaggie

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) 0.875, and thus has less dispersion relative to the mean than Stock B.

B) 1.14, and thus has more dispersion relative to the mean than Stock B.

C) 1.14, and thus has less dispersion relative to the mean than Stock B.

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CV stock A = 0.14 / 0.16 = 0.875

CV stock B = 0.03 / 0.20 = 1.5

Stock A has less dispersion relative to the mean than Stock B.

bmaggie

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) 128%.

B) 84%.

C) 78%.

bmaggie

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) 128%.

B) 84%.

C) 78%.

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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%.

bmaggie

If stock X's expected return is 30% and its expected standard deviation is 5%, Stock X's expected coefficient of variation is:

A) 6.0.

B) 0.167.

C) 1.20.

bmaggie

If stock X's expected return is 30% and its expected standard deviation is 5%, Stock X's expected coefficient of variation is:

A) 6.0.

B) 0.167.

C) 1.20.

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The coefficient of variation is the standard deviation divided by the mean: 5 / 30 = 0.167.