Sortino ratio

The Sortino ratio ( English Sortino ratio ) is a measure of the risk-adjusted return on an investment. It's a modification of the Sharpe Ratio . While the Sharpe Ratio takes into account the usual volatility of investments, the Sortino Ratio only takes into account that part of the volatility that is generated by downward movements. The upward movements are considered favorable and are included in the calculation with the value zero. As a result, the volatility component reacts to the frequency of the downward movements, i.e. it takes into account a possible asymmetrical distribution of returns.

calculation

The Sortino ratio is calculated as follows:

${\displaystyle S={{{\bar {r}}-r_{MAR}} \over {\sigma _{d}}}}$

This includes the expected return, the average return on an investment used as a benchmark, for example the risk-free interest rate from government bonds , and the so-called downside deviation or downside volatility . ${\displaystyle {\bar {r}}}$ ${\displaystyle r_{MAR}}$ ${\displaystyle \sigma _{d}}$

For historical returns , the Sortino ratio can be calculated from ${\displaystyle r_{i},1\leq i\leq n,}$

${\displaystyle \sigma _{d}={\sqrt {{1 \over {n}}\sum _{i=1}^{n}\left(\min \left(r_{i}-r_{MAR},0\right)\right)^{2}}}}$

${\displaystyle {\bar {r}}={\left(\prod _{i=1}^{n}(1+r_{i})\right)}^{1 \over n}-1}$

In calculating the volatility component only yields take into account the (English the smallest accepted yield minimum acceptable return ) not exceed. Nevertheless, is divided by , i.e. the number of all returns in the period under review. Since the downside deviation is not a statistical key figure in the strict sense of the word, unlike the standard deviation of a sample, it is divided by instead of . ${\displaystyle \sigma _{d}}$ ${\displaystyle r_{MAR}}$ ${\displaystyle n}$ ${\displaystyle n}$ ${\displaystyle n-1}$

In this case is the geometric mean return. ${\displaystyle {\bar {r}}}$

In some cases, the mean arithmetic return is also used for calculation. Then

${\displaystyle {\bar {r}}={{1 \over {n}}\sum _{i=1}^{n}{r_{i}}}}$

Usually, the Sortino ratio is determined from monthly returns and annualized by multiplication with . ${\displaystyle {\sqrt {12}}}$

meaning

The Sortino ratio was developed by Frank A. Sortino . It is used in particular as a key figure for assessing hedge fund investments that want to generate an absolute return in all market phases .

See also

• Modern portfolio theory