The research analyst for a stock brokerage firm wants to compare the dispersion in the price-earnings ratios for a group of common stock with their return on investment. For the price-earnings ratios, the mean is 10.9 and the standard deviation is 1.8. The mean return on investment is 25 percent and the standard deviation is 5.2 percent. What is the relative dispersion for the price earnings ratios and return on investment?
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A. B. C. D. E.E
The respective CVs are found from (s*100)/mean. Ratios: 1.8*100/10.9 = 16.5% and investment: 5.2*100/25 = 20.8%.
To calculate the relative dispersion, we need to compare the standard deviation to the mean for both the price-earnings ratios and the return on investment.
For the price-earnings ratios: Mean = 10.9 Standard Deviation = 1.8
Relative Dispersion for Price-Earnings Ratios = (Standard Deviation / Mean) * 100
Relative Dispersion for Price-Earnings Ratios = (1.8 / 10.9) * 100 ≈ 16.51%
For the return on investment: Mean = 25% Standard Deviation = 5.2%
Relative Dispersion for Return on Investment = (Standard Deviation / Mean) * 100
Relative Dispersion for Return on Investment = (5.2 / 25) * 100 ≈ 20.8%
Therefore, the correct answer is E. Ratios 16.5 percent, investment 20.8 percent.