Analysis of portfolio returns over a 20-year period showed the statistics below. (a) Calculate and compare the coefficients of variation.
Mean Standard Coefficient of
Investment Return Deviation Variation
Venture funds (adjusted) 18.2 11.3
All common stocks 12.1 14.3
Real estate 9.3 14.7
Federal short-term paper 4.7 2.1
(b) Why would we use a coefficient of variation, and why not just compare the standard deviations?
A. The standard deviations are relative and not absolute measures of dispersion.
B. The standard deviations are an "absolute", not relative, measure of dispersion. It is best to use the CV when comparing across variables that have different means.
C. Standard deviation can only be compared when the variables have different units of measure
(c) What do the data tell you about risk and return at that time period?
A. Venture funds have lower risk and greater return than common stocks based on the CV.
B. Federal short-term paper has the lowest standard deviation and hence the greatest risk; real estate, the lowest risk.
C. Federal short-term paper has the lowest CV and hence the greatest risk; real estate, the lowest risk.
D. Venture funds have greater risk and lower return than common stocks based on the CV.