# Sortino Ratio

## What is the 'Sortino Ratio'

The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.

## BREAKING DOWN 'Sortino Ratio'

The Sortino ratio is a useful way for investors, analysts and portfolio managers to evaluate an investment's return for a given level of bad risk. Since this ratio uses the downside deviation as its risk measure, it addresses the problem of using total risk, or standard deviation, as upside volatility is beneficial to investors.

A ratio such as the Sharpe ratio punishes the investment for good risk, which provides positive returns for investors. However, determining which ratio to use depends on whether the investor wants to focus on standard deviation or downside deviation.

## Sortino Ratio Calculation Example

Just like the Sharpe ratio, a higher Sortino ratio is better. When looking at two similar investments, a rational investor would prefer the one with the higher Sortino ratio because it means that the investment is earning more return per unit of bad risk that it takes on. The formula for the Sortino ratio is as follows:

Here, R equals the asset's or portfolio's annualized return, r(f) equals the risk-free rate, and DD equals the asset's or portfolio's downside deviation.

For example, assume Mutual Fund X has an annualized return of 12% and a downside deviation of 10%. Mutual Fund Z has an annualized return of 10% and a downside deviation of 7%. The risk-free rate is 2.5%. The Sortino ratios for both funds would be calculated as:

Mutual Fund X Sortino = (12% - 2.5%) / 10% = 0.95

Mutual Fund Z Sortino = (10% - 2.5%) / 7% = 1.07

Even though Mutual Fund X is returning 2% more on an annualized basis, it is not earning that return as efficiently as Mutual Fund Z, given their downside deviations. Based on this metric, Mutual Fund Z is the better investment choice.

While using the risk-free rate of return is common, investors can also use expected return in calculations. To keep the formulas accurate, the investor should be consistent in terms of the type of return.

For an in-depth knowledge of this ratio, read Mitigating Downside With the Sortino Ratio and 5 Ways to Rate Your Portfolio Manager.