Sortino Ratio

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.

Portfolio Performance: 12 November 2010

Portfolio Performance Data Table

Not only did many of the portfolios lose ground, as measured by IRR, most also showed a decline in the Sortino and Retirement Ratios. This again demonstrates just how difficult it is to outperform a broad market index such as Vanguard's VTSMX fund. Below is the table of performance. Overall, we are still doing quite well in meeting our goals, but it has been a difficult fall for investors.

There are still a few portfolios that are not in balance. The specifics are exposed when the individual portfolios are updated. Perhaps a further decline in the market will move more limit orders into the Buy zone.

Pay particular attention to columns 9, 11, and 12. Column 9 measures the difference between the performance of the portfolio and the VTSMX benchmark. In columns 11 and 12, we are looking for positive values and the larger the better.

Portfolio Performance - 11/12/2010

Portfolio Last Update Launch Date Tracking Tool Port. IRR ITA Index Diff Port. vs. ITA Index VTSMX IRR Diff. Port. vs. VTSMX Index IR SR RR
AA-Mosaic 09/301/2010 07/21/1999 Captool 1.95% NA NA -0.42% 2.37% 0.05 NA NA
Curie 11/12/2010 12/26/2007 TLH SS 3.8% -0.5% 4.2% -2.0% 5.8% NA 8.4 2.4
Mosaic2 09/30/2010 07/19/1999 Captool 4.37% NA NA -0.61% 4.98% 0.15 NA NA
Newton 11/12/2010 06/02/2008 TLH SS 8.4% 4.7% 3.8% 5.1% 3.3% NA 8.3 8.3
Passive Port. 10/29/2010 12/01/2000 Captool 4.9% NA NA 2.0% 2.9% 0.69 NA NA
Schrodinger 11/12/2010 12/01/2000 TLH SS 4.9% 10.9% -6.0% 2.2% 2.7% NA 10.1 10.1
Jane 09/30/10 02/14/1997 Captool 8.69% NA NA 3.07% 5.62% 0.53 NA NA
Einstein 11/12/2010 06/30/2008 TLH SS 13.9% 20.9% -7.0% 9.0% 4.9% NA 5.2 5.2
Gauss 09/30/2010 02/19/1997 Captool 8.86% NA NA 3.04% 5.82% 0.22 NA NA
Kepler 11/12/2010 11/01/2008 TLH SS 22.4% 32.6% -10.3% 19.3% 3.0% NA 4.5 4.5
Scrappy 09/30/2010 08/14/2008 Captool 10.53% NA NA -4.12% 14.65% NA NA NA
Bohr 11/12/2010 08/14/2008 TLH SS 11.7% 14.1% -2.4% 2.5% 9.3% NA 9.3 7.8
Kenilworth 11/12/2010 08/18/2010 TLH SS 36.0% 25.5% 10.5% 48.4% -12.4% NA -1.2* -1.2*
Projects 10/29/2010 12/01/2000 Captool 5.1% NA NA 0.02% 4.9% 1.32 NA NA
Washington 10/29/2010 06/18/1999 Captool 2.9% NA NA 3.1% -0.2% 0.27 NA NA
Maxwell 11/12/2010 12/25/2000 TLH SS 0.3% 2.0% -1.7% 3.3% -3.0% NA -1.6 -1.6
Adams 10/29/2010 06/18/1999 Captool 2.3% NA NA 3.1% -0.8% 0.70 NA NA
Euclid 11/12/2010 06/30/1999 TLH SS 0.7% 0.9% -0.2% 3.3% -2.7% NA -0.9 -0.9
Jefferson 10/29/2010 03/13/2008 Captool 5.9% NA NA 6.6% -0.7% NA NA NA
Madison 11/12/2010 03/13/2008 TLH SS 5.5% 1.9% 3.6% 7.3% -1.7% NA -1.4 -1.4

Next week the Bohr, Curie, and Schrodinger portfolios are scheduled for updates and review.