The coefficient of variation (COV) can determine the volatility of an investment. The COV is a ratio between the standard deviation of a data set to the expected mean. When used in the stock market, it helps to determine the amount of volatility in comparison to the expected return rate of investment. Dividing the volatility, or risk, by the absolute value of the investment's expected return, determines the COV.
Suppose a risk-averse investor is comparing the COV for three investment items and wants to determine which offers the best risk/reward ratio. The three different potential investment items are stock XYZ, broad market index DEF and bond ABC.
Assume stock XYZ has volatility, or standard deviation, of 15% and an expected return of 19%. The COV is 0.79 (15% ÷ 19%). Suppose the broad market index DEF has a standard deviation of 8% and an expected return of 19%. The coefficient of variation is 0.42 (8% ÷ 19%). The third investment, bond, ABC, has a volatility of 5% and an expected return of 8%. The coefficient of variation of bond ABC is 0.63 (5% ÷ 8%).
The risk-averse investor would choose to invest in the broad market index DEF because it offers the best risk/reward ratio and the lowest volatility percentage per unit of return. The investor would not look to invest in stock XYZ because it is more volatile than the index; however, both have the same expected return. Bond ABC carries the least risk, but the expected return is not favorable.