Sortino Ratio: Calculation Steps
Calculating the Sortino Ratio is not too difficult assuming you have historical data for the Internal Rate of Return (IRR) of the portfolio and the IRR for a benchmark. Here at ITA Wealth Management our primary benchmark is Vanguard's Total Market Index Fund, or VTSMX. Eventually we plan to move to the ITA Index, a customized benchmark for each portfolio.
In Sortino's early work, he used the term, minimum acceptable return (MAR). In his more recent work, MAR is now referred to as Desired Target Return™, a more meaningful expression.
Here is the Sortino equation.
SR = (Portfolio IRR – DTR™)/DR where DR is the downside risk or semivariance.
The following steps outline how an investor determines the Sortino Ratio.
1. Subtract DTR™ from the Internal Rate of Return of the portfolio for each period. The question immediately arises as to what period to use. My recommendation is to go with a monthly period as that is what was advised by the authors of Captool, a software program I still use with several portfolios. Step #1 will give you the value of the numerator of the Sortino Ratio. The following steps will determine DR or the Downside Risk.
2. If the calculation for step #1 is negative, record the value. If the value is positive, set it equal to zero. We are only interested in volatility to the downside.
3. Square all calculations found in step #2 including the zero values.
4. Sum or add all values found in step #3.
5. Divide the sum or total found in step #4 by the total number of periods. Divide by all periods including those where the value is zero. Example: If four values are zero and six are negative, divide the sum by ten, not six.
6. Take the square root of the value found in step #5.
There you have it. Now program those instructions into a special worksheet as we have done with the TLH spreadsheet.