Not There Yet

I have made a series of predictions using the Forsey-Sortino Model based on 2-year sequences.

Our goal is to build a better prediction tool. We are not there yet.

The Forsey-Sortino Model

I used 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 collected Forsey-Sortino Model results with Minimum Acceptable Returns (MAR) of 0% and 6.8% (approximately). I used Excel to calculate and plot straight-line graphs (i.e., regression equations) from the ten sets of data.

I constructed separate sequences for 1921-1940, 1941-1960 and 1961-1980. I refer to them as sequences 2jJan, 2kJan and 2mJan, respectively. I broke each into five parts because they had fewer data points. I collected Forsey-Sortino Model results with Minimum Acceptable Returns (MAR) of 0% and 6.8% (approximately). I used Excel to calculate and plot straight-line graphs (i.e., regression equations).

Means

2GJan (1921-1980) Means

P/E10 range: 27.08 to 5.12.
100E10/P range: 3.7% to 19.5%.

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

100E10/P = 3.5%, y = -2.75%.
100E10/P = 4.0%, y = -1.36%.
100E10/P = 5.0%, y = 1.43%.
100E10/P = 6.0%, y = 4.22%.
100E10/P = 7.0%, y = 7.01%.
100E10/P = 8.0%, y = 9.80%.
100E10/P = 10.0%, y = 15.38%.

2jJan (1921-1940) Means

P/E10 range: 27.08 to 5.12.
100E10/P range: 3.7% to 19.5%.

Mean: y = 2.8291x - 11.286 plus and minus 20%.
R-squared = 0.3887.

100E10/P = 3.5%, y = -1.38%.
100E10/P = 4.0%, y = 0.03%.
100E10/P = 5.0%, y = 2.86%.
100E10/P = 6.0%, y = 5.69%.
100E10/P = 7.0%, y = 8.52%.
100E10/P = 8.0%, y = 11.34%.
100E10/P = 10.0%, y = 17.01%.

2kJan (1941-1960) Means

P/E10 range: 18.34 to 10.10.
100E10/P range: 5.5% to 9.9%.

Mean: y = 4.7075x - 25.54 plus and minus 8%.
R-squared = 0.8063.

100E10/P = 3.5%, y = -9.06%.
100E10/P = 4.0%, y = -6.71%.
100E10/P = 5.0%, y = -2.00%.
100E10/P = 6.0%, y = 2.71%.
100E10/P = 7.0%, y = 7.41%.
100E10/P = 8.0%, y = 12.12%.
100E10/P = 10.0%, y = 21.54%.

2mJan (1961-1980) Means

P/E10 range: 24.06 to 8.85.
100E10/P range: 4.2% to 11.3%.

Mean: y = 1.5911x - 6.8546 plus and minus 5%.
R-squared = 0.3057.

100E10/P = 3.5%, y = -1.29%.
100E10/P = 4.0%, y = -0.49%.
100E10/P = 5.0%, y = 1.10%.
100E10/P = 6.0%, y = 2.69%.
100E10/P = 7.0%, y = 4.28%.
100E10/P = 8.0%, y = 5.87%.
100E10/P = 10.0%, y = 9.07%.

Downside Deviation

2GJan (1921-1980) Downside Deviation (MAR=0)

P/E10 range: 27.08 to 5.12.
100E10/P range: 3.7% to 19.5%.

Downside Deviation (MAR=0): y = -1.0641x + 16.12 plus and minus 7%.
R-squared = 0.365.

100E10/P = 3.5%, y = 12.40%.
100E10/P = 4.0%, y = 11.86%.
100E10/P = 5.0%, y = 10.80%.
100E10/P = 6.0%, y = 9.74%.
100E10/P = 7.0%, y = 8.67%.
100E10/P = 8.0%, y = 7.61%.
100E10/P = 10.0%, y = 5.48%.

2jJan (1921-1940) Downside Deviation (MAR=0)

P/E10 range: 27.08 to 5.12.
100E10/P range: 3.7% to 19.5%.

Downside Deviation (MAR=0): y = -1.8558x + 27.889 plus and minus 10%.
R-squared = 0.5545.

100E10/P = 3.5%, y = 21.39%.
100E10/P = 4.0%, y = 20.47%.
100E10/P = 5.0%, y = 18.61%.
100E10/P = 6.0%, y = 16.75%.
100E10/P = 7.0%, y = 14.90%.
100E10/P = 8.0%, y = 13.04%.
100E10/P = 10.0%, y = 9.33%.

2kJan (1941-1960) Downside Deviation (MAR=0)

P/E10 range: 18.34 to 10.10.
100E10/P range: 5.5% to 9.9%.

Downside Deviation (MAR=0): y = -1.5993x + 16.455 plus and minus 3%.
R-squared = 0.907.

100E10/P = 3.5%, y = 10.866%.
100E10/P = 4.0%, y = 10.06%.
100E10/P = 5.0%, y = 8.46%.
100E10/P = 6.0%, y = 6.86%.
100E10/P = 7.0%, y = 5.26%.
100E10/P = 8.0%, y = 3.66%.
100E10/P = 10.0%, y = 0.46%.

2mJan (1961-1980) Downside Deviation (MAR=0)

P/E10 range: 24.06 to 8.85.
100E10/P range: 4.2% to 11.3%.

Downside Deviation (MAR=0): y = -0.3064x + 8.7393 plus and minus 3%.
R-squared = 0.0429.

100E10/P = 3.5%, y = 7.67%.
100E10/P = 4.0%, y = 7.51%.
100E10/P = 5.0%, y = 7.21%.
100E10/P = 6.0%, y = 6.90%.
100E10/P = 7.0%, y = 6.59%.
100E10/P = 8.0%, y = 6.29%.
100E10/P = 10.0%, y = 5.68%.

Analysis

Initial Review

The Forsey-Sortino Model constructs 2500 simulated years for each set of data. In essence, each separate condition has enough data points to be very precise. Randomness remains. It comes from comparisons of groups of conditions.

The 2GJan equations are built from 10 sets of data, which I refer to as portfolios 2GJan1 through 2GJan10. I have constructed the 2GJan equations from the means and downside deviations of these ten portfolios. There are ten data points, each precisely determined from 2500 simulated years, that determine the equation for the mean. The randomness is from these sets of ten data points.

Similarly, there are ten data points that determine the equation for the downside deviation when MAR=0.

Similarly for the equations from portfolios 2jJan, 2kJan and 2mJan except that they have five data points each.

Except for the 1941-1960 data (portfolio 2kJan), the randomness inherent in the data (the spread of the confidence limits) is larger than the variation related to changes in the percentage earnings yield. Having multiple points (ten for 2GJan and five for 2jJan, 2kJan and 2mJan) reduces the variation required to show significance by factors of three or two, approximately.

We can reasonably conclude that Means increase and Downside Deviations (when MAR=0) decrease as the earnings yield 100E10/P increases (and P/E10 decreases).

A Closer Look at the Means

Here are the predictions at the extremes and in the middle:

2GJan (1921-1980) Mean and 100E10/P = 3.5%, y = -2.75%.
2jJan (1921-1940) Mean and 100E10/P = 3.5%, y = -1.38%.
2kJan (1941-1960) Mean and 100E10/P = 3.5%, y = -9.06%.
2mJan (1961-1980) Mean and 100E10/P = 3.5%, y = -1.29%.

2GJan (1921-1980) Mean and 100E10/P = 6.0%, y = 4.22%.
2jJan (1921-1940) Mean and 100E10/P = 6.0%, y = 5.69%.
2kJan (1941-1960) Mean and 100E10/P = 6.0%, y = 2.71%.
2mJan (1961-1980) Mean and 100E10/P = 6.0%, y = 2.69%.

2GJan (1921-1980) Mean and 100E10/P = 10.0%, y = 15.38%.
2jJan (1921-1940) Mean and 100E10/P = 10.0%, y = 17.01%.
2kJan (1941-1960) Mean and 100E10/P = 10.0%, y = 0.46%.
2mJan (1961-1980) Mean and 100E10/P = 10.0%, y = 9.07%.

Portfolio 2kJan (1941-1960) differs at the extremes (100E10/P = 3.5% and 10.0%). During these two decades, 100E10/P ranged from 5.5% to 9.9% (and P/E10 varied between 18.34 and 10.10). A general limitation of any extrapolation can explain the disagreement at an earnings yield of 3.5%. It cannot explain the disagreement at an earnings yield of 3.5%.

Instead, we end up focusing on the large spread that is associated with each equation. Portfolio 2kJan (1941-1960) varies plus and minus 8%. Dividing by two (because its equation is derived from on five data points, subtracting one to determine the number of degrees of freedom and taking the square root), the range of variation is still plus and minus 4%, which totals 8%. This almost works for 2mJan (1961-1980). It is close enough to be an unusual, but reasonable results. It does not work with portfolios 2GJan (1921-1980) and 2jJan (1921-1940).

A Closer Look at the Downside Deviations (MAR=0)

Here are the predictions at the extremes and in the middle:

2GJan (1921-1980) Downside Deviation (MAR=0) and 100E10/P = 3.5%, y = 12.40%.
2jJan (1921-1940) Downside Deviation (MAR=0) and 100E10/P = 3.5%, y = 21.39%.
2kJan (1941-1960) Downside Deviations (MAR=0) and 100E10/P = 3.5%, y = 10.866%.
2mJan (1961-1980) Downside Deviations (MAR=0) and 100E10/P = 3.5%, y = 7.67%.

2GJan (1921-1980) Downside Deviations (MAR=0) and 100E10/P = 6.0%, y = 9.74%.
2jJan (1921-1940) Downside Deviations (MAR=0) and 100E10/P = 6.0%, y = 16.75%.
2kJan (1941-1960) Downside Deviations (MAR=0) and 100E10/P = 6.0%, y = 6.86%.
2mJan (1961-1980) Downside Deviations (MAR=0) and 100E10/P = 6.0%, y = 6.90%.

2GJan (1921-1980) Downside Deviations (MAR=0) and 100E10/P = 10.0%, y = 5.48%.
2jJan (1921-1940) Downside Deviations (MAR=0) and 100E10/P = 10.0%, y = 9.33%.
2kJan (1941-1960) Downside Deviations (MAR=0) and 100E10/P = 10.0%, y = 0.46%.
2mJan (1961-1980) Downside Deviations (MAR=0) and 100E10/P = 10.0%, y = 5.68%.

This time, portfolio 2jJan (1921-1940) doesn’t fit.

Conclusions

These data do not provide us with what we are after: a stable prediction tool.

This is not simply a matter of randomness.

We found earlier that making stock market calculations based on monthly data is unsuitable except in the very short-term. It strips away the most of the effects of valuations.

We already have good prediction tools for the intermediate-term and the long-term based on annual returns. We anticipate building better tools and we expect the Forsey-Sortino Model to help. It is clearly better than many alternatives.

Putting this in context: we are trying to develop better prediction tools. We are not there yet.

Have fun.

John Walter Russell
December 30, 2005