Target downside deviation and coefficient of variation

In short

• Standard deviation counts upside and downside surprises alike; investors mostly worry about the downside.
• Target downside deviation (target semideviation) uses only returns below a target B, but divides by the full sample's n − 1.
• Raising the target puts more observations below it and enlarges their shortfalls, so the semideviation rises.
• Coefficient of variation $CV = s/\bar X$ is risk per unit of mean return: lower is better.
• CV is scale-free, so it compares data sets with very different means or units; it breaks down when the mean is near zero or negative.