The Sortino Ratio is similar to Sharpe Ratio except it uses downside risk (Downside Deviation) in the denominator. It was developed in early 1980's by Frank Sortino. Since upside variability is not necessary a bad thing, Sortino ratio is sometimes more preferable than Sharpe ratio.
er = excess return
= monthly downside deviation
n = periods in a year
Monthly,
Annualized,
Arithmetic Sortino Ratio is calculated similarly, except the arithmetic excess return is the numerator instead of the geometric excess return. When annualize, use multiplication for the numerator instead of compounding.