A project's coefficient of variation is 0.40.The project has a positive coefficient of correlation of 0.20.The expected value is $2,000.What is one standard deviation?

Question

Quizplus · Accepted Answer

Coefficient of variation (CV) = Standard deviation / Expected value
0.40 = Standard deviation / 2000
Standard deviation = 0.40 * 2000 = 800
Coefficient of correlation (r) = 0.20
We know that 
r = Covariance / (Standard deviation of X * Standard deviation of Y)
Here, we assume that Y is the expected value and X is the actual project value. Therefore,
r = Covariance / (standard deviation of X * 2000)
0.20 = Covariance / (standard deviation of X * 2000)
Covariance = 0.20 * standard deviation of X * 2000
We know that covariance = Correlation coefficient * (Standard deviation of X) * (Standard deviation of Y)
Therefore,
0.20 * standard deviation of X * 2000 = 0.40 * standard deviation of X * 2000 * (Standard deviation of X)
Standard deviation of X = 0.5 * 2000
Standard deviation of X = $1000
Hence, the answer is C.

A Project's Coefficient of Variation Is 0