6、The historical return for each of a portfolio’s four positions is shown below. Using the population standard deviation, what is the coefficient of variation (CV) for these returns?

A)   1.89.

B)   1.97.

C)   3.12.

D)   1.56.

7、What is the coefficient of variation for a distribution with a mean of 10 and a variance of 4?

A)   25%.

B)   40%.

C)   20%.

D)   50%.

8、An investor is considering two investments. Stock A has a mean annual return of 16 percent and a standard deviation of 14 percent. Stock B has a mean annual return of 20 percent and a standard deviation of 30 percent. Calculate the coefficient of variation (CV) of each stock and determine if stock A has less dispersion or more dispersion relative to B.

A)        0.875           Stock A has less dispersion relative to the mean than stock B

B)        1.14          Stock A has less dispersion relative to the mean than stock B

C)        0.875           Stock A has more dispersion relative to the mean than stock B

D)        1.14          Stock A has more dispersion relative to the mean than stock B

答案和详解如下：

6、The historical return for each of a portfolio’s four positions is shown below. Using the population standard deviation, what is the coefficient of variation (CV) for these returns?

Position	Return
A	17.0%
B	12.2%
C	3.9%
D	–8.4%

A)   1.89.

B)   1.97.

C)   3.12.

D)   1.56.

The correct answer was D)

The coefficient of variation is equal to the standard deviation of returns divided by the mean return.

Position	Return	(R – 6.175%)2
A	17.0%	117.18
B	12.2%	36.30
C	3.9%	5.18
D	–8.4%	212.43
Mean	6.175%	Sum = 371.09
Std. Dev. = (371.09 / 4)0.5 = 9.63
CV = 9.63 / 6.175 = 1.56

7、What is the coefficient of variation for a distribution with a mean of 10 and a variance of 4?

A)   25%.

B)   40%.

C)   20%.

D)   50%.

The correct answer was C)

Coefficient of variation, CV = standard deviation / mean. The standard deviation is the square root of the variance, or 4^½ = 2. So, CV = 2/10 = 20%.

8、An investor is considering two investments. Stock A has a mean annual return of 16 percent and a standard deviation of 14 percent. Stock B has a mean annual return of 20 percent and a standard deviation of 30 percent. Calculate the coefficient of variation (CV) of each stock and determine if stock A has less dispersion or more dispersion relative to B.

CV (stock A)

Dispersion

A)        0.875           Stock A has less dispersion relative to the mean than stock B

B)        1.14          Stock A has less dispersion relative to the mean than stock B

C)        0.875           Stock A has more dispersion relative to the mean than stock B

D)        1.14          Stock A has more dispersion relative to the mean than stock B

The correct answer was A)

CV stock A = .14/.16 = 0.875

<CV stock B = .03/.20 = 1.5

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