Forsey-Sortino Baseline Portfolios

These are my baseline portfolios using the Forsey-Sortino Model.

The Forsey-Sortino Model

I took advantage of the Forsey-Sortino model. It comes with the book, Managing Downside Risk in Financial Markets, by Frank Sortino and Stephen Satchell.

The Portfolios

I constructed a group of two-year sequences beginning in each year from 1921-1980. I assigned the January value of P/E10 for two sets of sequences, starting with both January 1920 and January 1921. I used each month from 1921-1980 twice, one time for each of the two possible P/E10 values that applied.

I refer to the list of these sequences as 2GJan. I broke it into ten parts, sorted according to P/E10. I refer to the individual parts as 2GJan1 through 2GJan10.

I constructed two other sets of sequences. One set covered the years 1981-2004+. I refer to this as 2HJan. I broke it into ten parts, sorted according to P/E10, which I call 2HJan1 through 2HJan10.

The other covered the years 1991-2003. I refer to it as 2iJan. I broke it into six parts, sorted according to P/E10, which I call 2iJan1 through 2iJan6.

I set the Minimum Acceptable Return (roughly) equal to 0.0% and 6.8%. These correspond to matching inflation and matching the real, annualized (very) long-term total return of the stock market.

I collected data with the Probability of Exceeding the Minimum Acceptable Return (Prob>MAR). I collected Downside Deviation data based on a MAR of 6.8%. The formula for Downside Deviation is similar to that of a Standard Deviation, except that it uses the MAR in place of the mean and it excludes all values greater than the MAR.

Portfolios 2GJan

Here is the formula for the Mean y as a function of x, the Percentage Earnings Yield 100E10/P.

y = 2.7888x - 12.513 plus 15% and minus 5%.
R-squared = 0.6428.

Here is the formula for y, the Downside Deviation for MAR = 6.8%, as a function of x, the Percentage Earnings Yield 100E10/P.

y = -1.335x + 21.463 plus and minus 5%.
R-squared = 0.3957.

In both cases, the Prob>MAR data saturated. The breakpoint in MAR data was around 100E10/P = 8% or P/E10 = 12.5.

Portfolios: 2HJan (1981-2004 through June)

These portfolios were unsatisfactory. As mentioned in an earlier article, data from the 1980s all had the lowest values of P/E10. The final result seemed to have an overshoot at a 4% earnings yield (P/E10 = 25).

Here is the formula for the Mean y as a function of x, the Percentage Earnings Yield 100E10/P.

y = 0.9832x+ 3.1704 plus and minus 15%.
R-squared = 0.12.

Break point (possibly, overshoot) when 100E10/P = 4.0% to 4.5% or P/E10 = 22 to 25.

Portfolios: 2iJan (1991-2003)

These portfolios were satisfactory. I eliminated the decade of the 1980s and I constrained the data to complete years. These data were homogenous.

I limited myself to six segments because of the limited amount of data.

Here is the formula for the Mean y as a function of x, the Percentage Earnings Yield 100E10/P.

y = 5.402x - 11.819 plus and minus 4%.
R-squared = 0.7527.

Here is the formula for y, the Downside Deviation for MAR = 6.8%, as a function of x, the Percentage Earnings Yield 100E10/P.

y = -4.2174x + 24.216 plus and minus 3%.
R-squared = 0.8692.

In both cases, the Prob>MAR data saturated. The breakpoint in MAR data is around 100E10/P = 4.5% or P/E10 = 22.

Observations

Our baselines are portfolios 2GJan for 1921-1980 and 2iJan for 1991-2003.

Portfolio 2HJan (1981-2004+) was unsatisfactory.

All of the formulas are different. We have seen this before. Apparently, this is because we use short (two-year) sequences. We will need to treat decades separately.

Have fun.

John Walter Russell
December 22, 2005