ou purchased a share with a coefficient of variation equal to 0.125. The expected return on the shares is 20%. What is the variance of the share? (round final answer to 4 decimal places)
Question
ou purchased a share with a coefficient of variation equal to 0.125. The expected return on the shares is 20%. What is the variance of the share? (round final answer to 4 decimal places)
Solution
The coefficient of variation (CV) is a measure of relative variability. It is the ratio of the standard deviation to the mean (expected value).
The formula for the coefficient of variation is:
CV = Standard Deviation / Expected Return
In this case, we know that the CV is 0.125 and the expected return is 20% or 0.20.
We can rearrange the formula to solve for the standard deviation:
Standard Deviation = CV * Expected Return
Substituting the given values:
Standard Deviation = 0.125 * 0.20 = 0.025
The variance is the square of the standard deviation. So, to find the variance, we square the standard deviation:
Variance = (Standard Deviation)^2
Variance = (0.025)^2 = 0.000625
So, the variance of the share is 0.000625 (rounded to 4 decimal places).
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