Short Intervals

I examined using a single ten-year interval. It is unsatisfactory.

This is in contrast to longer time intervals. Limited sampling from the 1921-1980 time interval, which is what I examined initially, appears to be satisfactory.

Data Groupings

I ordered the 1971-1980 data in accordance with P/E10. I looked at extensive single-year groupings. I also took a quick look at two-year groupings.

With single-year groupings, I assigned the January value of P/E10 to the subsequent eleven months. I repeated this for all of the other months. I continued the process of assigning the first month’s P/E10 value to the eleven months that followed until I had a one-year sequence for each month from January 1971 through December 1980.

There is a large amount of data overlap. Ten years produces 1440 inputs for the model.

I refer to these portfolios as 1A1mw7180 to 1A10mw7180. The first 1 is for a single-year, A is a unique identifier for the sequence, mw is for moving window, and 7180 is for the years 1971-1980.

With two-year groupings, I assigned the January P/E10 value to the subsequent 23 months. Then I assigned the P/E10 level of the following month (January, two years later) to the next 23 months and so forth. I did this for two-year sequence beginning with January in all of the odd years from 1971-1979. This was a very quick process. It resulted in five sequences.

I refer to these portfolios as 2D7180 and 2D7180a to e. The 2 is for two-year sequences, D is a unique identifier for the sequence and 7180 is for the years 1971-1980. Individual letters identify the five individual sequences. When there is no letter, the reference is for the entire group of five sequences.

Data Collection

I collected an extensive amount of data using the Forsey-Sortino model. It comes with the book, Managing Downside Risk in Financial Markets, by Frank Sortino and Stephen Satchell. Their methods are light-years ahead of traditional Mean-Variance Optimization.

I determined the mean, mean plus and minus one standard deviation, probability of exceeding the Minimum Acceptable Return (MAR) for levels of 0% and 2% (approximately), below target deviation, upside potential and upside ratio for all individual segments.

I have placed these data into my Yahoo Briefcase under the folder for Current Research E and the files 1971-1980 1-yr Graphs D5 and 1971-1980 2-yr Graphs D6.

Yahoo Briefcase

Results

I plotted Means and the Probability>MAR for a Minimum Acceptable Return (MAR) of approximately 0% versus the percentage earnings yield 100E10/P of each segment. I plotted straight-line graphs using Excel.

Single-Year 1971-1980 Sequences

This is the formula of the Mean return y as a function of x, the percentage earnings yield 100E10/P:
Portfolios: 1A1mw7180 to 1A10mw7180 (1971-1980 data).
y = 2.9303x - 25.755 plus and minus 10%.
R-squared = 0.4635.
When x = 4% (P/E10 = 25), y = -14.03%.
When x = 10% (P/E10 = 10), y = 3.55%.

There was no saturation of the Probability of exceeding the Minimum Acceptable Return MAR. The data (roughly) fit a straight-line.

Single-Year 1921-1980 Sequences

Listing by single-year P/E10 groupings of 1921-1980 data:
Portfolios: 1CJan1 to 1CJan10.
y = 2.9436x - 13.57 plus and minus 10%.
R-squared = 0.6446
When x = 4% (P/E10 = 25), y = -1.80%.
When x = 10% (P/E10 = 10), y = 15.87%.

There was no saturation of the Probability of exceeding the Minimum Acceptable Return MAR. The data (roughly) fit a straight-line.

Two-Year 1971-1980 Sequences

This is the formula of the Mean return y as a function of x, the percentage earnings yield 100E10/P:
Portfolios: 2D7180 and 2D7180a to e.
y = 4.9542x - 38.807 plus and minus 20%.
R-squared = 0.4217.
When x = 4% (P/E10 = 25), y = -18.99%.
When x = 10% (P/E10 = 10), y = 10.74%.

There was no saturation of the Probability of exceeding the Minimum Acceptable Return MAR. The data (roughly) fit a straight-line.

Two-Year 1921-1980 Sequences

Listing by two-year P/E10 groupings of 1921-1980 data:
Portfolios: 2BJanL1 to 2BJanL10.
y = 2.7924x - 12.552 plus and minus 10%.
R-squared = 0.6545
When x = 4% (P/E10 = 25), y = -1.38%.
When x = 10% (P/E10 = 10), y = 15.37%.

There was saturation of the Probability of exceeding the Minimum Acceptable Return MAR at an 8% earnings yield. The data were (roughly) flat above 8% (P/E10 = 12.5). They (roughly) fit a straight-line at lower percentage earnings yields.

Using a Single Decade: Summary

There needs to be an offset adjustment for each decade.

With single-year sequences, the slope of the mean return versus the percentage earnings yield 100E10/P for a single decade was the same as for the entire 1921-1980 period. The offsets differed.

Two-year sequences lost their saturation attribute. That is, a plot of the probability of exceeding a Minimum Acceptable Return MAR remained linear when restricting the data to a single decade.

Conclusion

Using data from a single-decade is unsatisfactory.

Such a conclusion is not unique to the S&P500. It is typical of a new asset class as well. Its actual behavior can remain uncertain for an extended period of time. Caution is advised.

Have fun.

John Walter Russell
December 16, 2005