Under what circumstances will the coefficient of variation of a security’s returns and the standard deviation of that security’s returns give the same relative measure of risk when compared with the risk of another security?
Standard deviation, as applied to investment returns, is a quantitative statistical measure of the variation of specific returns to the average of those returns. The coefficient of variation is a better measure of risk, quantifying the dispersion of an asset’s returns in relation to the expected return, and, thus, the relative risk of the investment. Hence, the coefficient of variation allows the comparison of different investments.
The coefficient of variation and the standard deviation of a security's return will give the same relative measure of risk when compared to the risk of another security when both securities have the same level of expected returns.