The coefficient of variationexpresses how much dispersion exists relative to the mean of a distribution and allows for direct comparison of dispersion across different data sets.
CV = [standard deviation of returns]/[Expected rate of return]
Example:
Investment A has an ER of 7% and a s of .05.
Investment B has an ER of 12% and a s of .07.
Which is riskier?
A’s CV is .05/.07 = .714
B’s CV is .07/.12 = .583
A has .714 units of risk for each unit of return while B has .583 units of risk for each unit of return. A is riskier, it has more risk per unit of return.
n: Define, calculate, and interpret the Sharpe measure of risk-adjusted performance.
The Sharpe measure seeks to measure excess return per unit of risk. The numerator of the Sharpe measure recognizes the existence of a risk-free return. Portfolios with large Sharpe ratios are preferred to portfolios with smaller ratios because it is assumed that rational investors prefer return and dislike risk. The Sharpe ratio is also called the reward-to-variability ratio.