Question

What was the stock's coefficient of variation during this 5-year period? (Use the population standard deviation to calculate the coefficient of variation.) a. 0.69 b. 15.72 c. 4.22 d. 1.46 e. 10.80

Answer 1

d. 1.46

Explanation:

The question is incomplete:

Below are the stock returns for the past five years for Agnew

Industries:

Year Stock Return

2002 22%

2001 33 %

2000 1 %

1999 -12 %

1998 10%

The coefficient of variation (CV) can be expressed as the coefficient between the standard deviation over the mean of the stock returns:

`CV=\sigma/\mu`

The mean of the stock returns is:

`\mu=(1/n)\sum r_i=(1/5)*(0.22+0.33+0.01-0.12+0.10)=0.54/5\\\\\mu=0.108`

The standard deviation is:

`\sigma=√((1/n)\sum (r_i-\bar r)^2)\\\\\\\sum (r_i-\bar r)^2=(0.22-0.108)^2+(0.33-0.108)^2+(0.01-0.108)^2+(-0.12-0.108)^2+(0.10-0.108)^2\\\\\sum (r_i-\bar r)^2=0.0001+0.052+0.0096+0.0493+0.0125=0.1235\\\\\\\sigma=√(0.1235/5)= √(0.0247)= 0.1572`

Then, the coefficient of variation is:

`CV=\sigma/\mu=0.1572/0.108=1.455\approx 1.46`