Current Research
Previous Investigations
Current Research A: Fundamental Breakthroughs associated with TIPS
Latest update: June 16, 2005.
Current Research A: Fundamental Breakthroughs associated with TIPS
Current Research B: Keeping In Tune with the Human Element
Updated August 21, 2005.
Current Research B: Keeping In Tune with the Human Element
Current Research C: True Buy-and-Hold Investing
Dated: September 12, 2005.
Current Research C: True Buy-and-Hold Investing
Current Research D: Expanded Switching Algorithms
Dated: October 23, 2005.
Current Research D: Expanded Switching Algorithms
Current Research E: Managing Downside Risk in Financial Markets
Updated: January 1, 2006.
The Tools
I recently bought Managing Downside Risk in Financial Markets by Frank Sortino and Stephen Satchell. It describes methods that are light-years ahead of traditional Mean-Variance Optimization. It includes software.
Books
Managing Downside Risk in Financial Markets
I will be applying this software throughout this section. The software is the Forsey-Sortino model.
I will be using it extensively. I will be using it whenever I calculate upside potential and downside risk.
I will be using S&P500 data from Professor Robert Shiller’s web site.
Professor Shiller’s Web Site
I have placed a large quantity of selected data into my Yahoo Briefcase as Microsoft Word documents. They are in the Current Research E folder.
Yahoo Briefcase
Monthly Values of P/E10
When I ordered data by each month’s P/E10, I found that P/E10 had little predictive power, if any.
Upon reflection, this is to be expected. The model constructs synthetic years by repeatedly selecting twelve monthly returns at random (with replacement) and putting them together. In essence, this method of ordering tells us how well P/E10 does as a single-month predictor.
One-Year Values of P/E10
I listed the data according to dates. I made lists that kept the first value of P/E10 the same for intervals of one year for every month. That is, the list for January used the January value of P/E10 for the eleven months that followed. I updated the next year by using the new January value of P/E10. And so on.
I did this for the other months as well. I waited for the specified month to appear. Then I assigned that month’s value of P/E10 to the eleven months that followed. I changed to the new value of P/E10 when the specified month next appeared. And so on.
I collected summary data for the months of January and April. The results were very similar. I was satisfied to leave it at that. However, I have constructed ordered data for other months. They are in my Yahoo Briefcase folder (for Current Research E).
This did the trick. Using a single value of P/E10 for groups of twelve months in a row suddenly restored P/E10’s predictive power.
Two-Year Values of P/E10
I made lists that kept the first value of P/E10 the same for intervals of two years. However, I only made twelve (not twenty-four) lists, one for each month in the first year. This was a matter of convenience. Had the selection of two-year intervals have shown significant differences, I would have extended these conditions.
Using a two-year interval was similar to using a one-year interval. P/E10 displayed predictive power.
1921-1980 Data
I ordered all 720 months (sixty years). I grouped them in three equal parts: those with the 240 (20 years) lowest values of P/E10, those with the 240 (twenty years) middle values of P/E10 and those with the 240 (twenty years) highest values of P/E10.
Here are the means and plus and minus one standard deviation as displayed on the lognormal plot (using default values).
Monthly Ordering
Low P/E10: -12.8%, 8.2%, and 29.2%
Middle P/E10: -7.4%, 9.6%, and 26.6%
High P/E10: -5.2%, 9.5%, and 24.2%
Low P/E10: 5.12 to 11.48
Middle P/E10: 11.50 to 16.82
High P/E10: 16.83 to 32.56
January Single-Year Ordering
Low P/E10: -5.8%, 17.4%, and 40.5%
Middle P/E10: -10.5%, 6.7%, and 23.9%
High P/E10: -11.4%, 3.9%, and 19.3%
Low P/E10: 5.12 to 11.44
Middle P/E10: 11.47 to 16.72
High P/E10: 17.09 to 27.08
April Single-Year Ordering
Low P/E10: -3.7%, 20.3%, and 44.2%
Middle P/E10: -11.2%, 5.4%, and 22.0%
High P/E10: -12.6%, 2.2%, and 17.0%
Low P/E10: 5.30 to 11.10
Middle P/E10: 11.18 to 16.87
High P/E10: 16.94 to 27.57
January Two-Year Ordering
Low P/E10: -0.9%, 15.4%, and 31.8%
Middle P/E10: -10.5%, 12.7%, and 35.8%
High P/E10: -16.8%, -1.0%, and 14.7%
Low P/E10: 5.12 to 11.47
Middle P/E10: 11.50 to 16.71
High P/E10: 16.72 to 27.08
1921-1980 Summary
The results from monthly ordering appear to be random.
Single-year ordering strongly favors low values of P/E10. There is a general trend favoring lower valuations to higher valuations. We see these effects in both the January and April data.
The two-year ordering continues to show the trend in favor of lower valuations. Using two-year intervals improves the results at middle level valuations.
January 1981-June 2004 Data
I ordered all 282 months (twenty-three and one-half years). I grouped them in three almost equal parts: those with the 96 (eight years) lowest values of P/E10, those with the 96 (eight years) middle values of P/E10 and those with the 90 (seven and one-half years) highest values of P/E10. I kept the division as close to using complete years as possible to minimize seasonal effects.
Here are the means and plus and minus one standard deviation as displayed on the lognormal plot (using default values).
January Single-Year Ordering
Low P/E10: -4.4%, 10.1%, and 24.6%
Middle P/E10: 2.6%, 13.0%, and 23.4%
High P/E10: -8.8%, 5.9%, and 20.6%
Low P/E10: 7.39 to 14.92
Middle P/E10: 15.09 to 22.90
High P/E10: 24.76 to 43.77
January Two-Year Ordering
Low P/E10: -4.2%, 10.6%, and 25.3%
Middle P/E10: 3.2%, 13.3%, and 23.3%
High P/E10: -9.8%, 5.3%, and 20.4%
Low P/E10: 8.76 to 14.92
Middle P/E10: 15.09 to 20.32
High P/E10: 22.90 to 40.58
January 1981-June 2004 Data
The low P/E10 values all occurred in the earliest years (in the 1980s).
Both single-year ordering and two-year ordering speak badly about what happens when P/E10 is high.
Middle values of P/E10 did a little bit better than the lowest values of P/E10. However, the calendar separated the low P/E10 data from the rest. Those levels were grouped around the earliest years.
Comments
This concludes my initial survey using the Forsey-Sortino model. I have not even scratched the surface of its utility. For example, I have not introduced any Minimum Acceptable Returns (MAR), which is central to Downside Risk Management.
Introducing the Minimum Acceptable Return (MAR)
I repeated my procedures using one-year and two-year January P/E10 values. This time, I introduced Minimum Acceptable Return (MAR) requirements to see how they affect results.
The details are in this post.
Introducing the Minimum Acceptable Return (MAR)
Here are some highlights.
1921-1980 Summary
Single-year ordering strongly favors low values of P/E10. There is a general trend favoring lower valuations to higher valuations. The changes are gradual in terms of the downside. They are dramatic on the upside, especially when looking at the lowest P/E10 levels.
The two-year ordering continues to show the trend in favor of lower valuations. Here we see a consistent, strong effect in terms of exceeding the minimum acceptable return.
Using two-year intervals improves the performance at middle level valuations. It has similar means and upside potentials as at low valuations.
High valuations bring about lower returns, greater downside risk and limited upside potential.
January 1981-June 2004 Summary
The worse results occurred when P/E10 was high.
Middle values of P/E10 did better than the lowest values of P/E10. However, the low P/E10 values all occurred in the earliest years (in the 1980s). The calendar separated the low P/E10 data from the rest. Returns during the 1990s were higher than returns during the 1980s.
Since the early 1990s, lower levels of P/E10 have produced better results than high levels of P/E10.
Remarks
This is my second survey using the Forsey-Sortino model.
We had already learned to be wary of monthly return data. They strip away the effects of valuations. Single-year and two-year data restores the main effects at high and low valuations and produce similar trends. They differ in terms of the details associated with middle level valuations. Using two-year data groupings helps at middle level valuations.
To be precise, what we are learning has to do with Monte Carlo models. Conclusions do not necessarily translate into real world results. Still, relationships produced from the longer sequences probably are more representative of what happens in actual markets.
It makes sense that high valuations produce bad outcomes and low valuations produce good outcomes when holding periods are one year or longer. It makes sense that the ability to benefit at middle level valuations is better over a time period of two years than over a time period of one year.
In normal times, valuations have had a tremendous influence on upside potential. Using single-year data, we see this as strong only at low valuations. Two-year data (with a built-in longer holding period) demonstrate a strong result at middle level valuations as well.
Upside potential effects were dampened during the bubble. High valuations still reduced the upside potential, but not by much.
Monthly Returns
Already, our investigations into Managing Downside Risk in Financial Markets have led us to an unexpected conclusion: Much of academic investment research should be tossed out.
The critical flaw is the use of monthly returns.
Here is an explanation.
Monthly Returns
Ten Valuation Levels
I determined the effect of finer distinctions of P/E10 levels.
I determined how they affect single-year and two-year data.
Here are my conclusions:
We can use either single-year data or two-year data when using Means. Both produce similar results.
We must distinguish between single-year data and two-year data when examining the probability of exceeding a Minimum Acceptable Return (MAR).
We saw a distinction between single-year results and two-year results previous using three valuation levels. The middle level means were affected.
Ten Valuation Levels
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.
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.
Short Intervals
Longer Sequences
This time, I examine longer sequences. I compare 1-year, 2-year and 4-year sequences covering 1921-1980.
I find that 2-year sequences make an excellent choice.
I have also discovered that these sequences have a predictive time frame of the order of 2 to 4 years. That is, creating 2500 simulated years of data does not narrow down the confidence limits more than what is already inherent in the data.
Low, Medium, High Results
I ordered the data by P/E10. Then I broke them into three equal parts to make three portfolios for the Forsey-Sortino model.
Previously, we had found that single-year and two-year sequences behaved similarly at low and high values of P/E10. Two-year sequences performed better at middle level valuations. The lowest values of P/E10 always led to the best returns. The highest values of P/E10 always led to the worst returns.
The two-year sequence retained these features when using the offset. That is, ordering in two-year increments starting with the January 1920 P/E10 value produces results similar to those starting with the January 1921 P/E10 value.
The four-year sequences behaved similarly to the two-year sequences.
Detailed Two-Year and Four-Year High 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.
Two-Year 1921-1980 Sequences (original)
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.
Four-Year 1921-1980 Sequences (new)
This is the formula of the Mean return y as a function of x, the percentage earnings yield 100E10/P:
Portfolios: 4F21Jan1 to 4F21Jan10.
y = 2.8937x - 12.678 plus and minus 10%.
R-squared = 0.655.
When x = 4% (P/E10 = 25), y = -1.10%.
When x = 10% (P/E10 = 10), y = 16.26%.
Break point in MAR data is around 100E10/P = 9% or P/E10 = 11.
Detailed Two-Year and Four-Year High Comparisons
The results are very similar. The formulas are almost identical.
Comparison with 10-Year Stock Returns
From You Can't Count on 7%:
This is the regression equation for the 10-year stock return and the percentage earnings yield 100E10/P (using 1923-1972 data): y = 1.5247x-4.5509 where y is the annualized real return in percent and x is 100E10/P or 100/[P/E10]. The confidence limits are plus and minus 6%.
Comparisons
Ten-year confidence limits taken directly from the stock market are to plus and minus 6%. All of these single-year, two-year and four-year confidence limits are plus and minus 10% (very roughly).
The formulas differ significantly.
Assessment
These (single-year, two-year and four-year) data sets predict time intervals of 2 to 4 years. (If the variance obeyed a 1/N law, where N is the number of years, then the time interval would have been 2.79 years. It does not. But 1/N is OK as a first approximation.)
Conclusions
Two-year sequences make an excellent choice.
These sequences have a predictive time frame of the order of 2 to 4 years. They do not narrow down the confidence limits more than what is already inherent in the data.
This is consistent with our single-month findings. That is, using single-month data directly was appropriate for single-month predictions. Using single-year sequences is appropriate for single-year predictions. Using two-year and four-year sequences is appropriate for two to four year predictions.
Longer Sequences
Forsey-Sortino Baseline Portfolios
I have constructed baseline portfolios using the Forsey-Sortino Model.
The various formulas are all different. Apparently, this is because we use short (two-year) sequences. We will need to treat individual decades independently.
Forsey-Sortino Baseline Portfolios
Not There Yet
We found earlier that making stock market calculations based on monthly data is unsuitable except in the very short-term. It strips away 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.
I have made a series of predictions using the Forsey-Sortino Model based on 2-year sequences.
These new data do not provide us with what we are after. This is not simply a matter of randomness.
Not There Yet
Our Next Step
My next step takes me back to our standard calculator, Deluxe V1.1A08a. I will expand my investigations to include months other than January. The calculator already allows me to select price and dividend data from the other months. I will be pasting P/E10 and CPI data for other months into copies of the calculator. I will end up with a separate calculator for each month.
Keep in mind that my goal is better data analysis.
I have taken Professor Robert Shiller's data, arranged them by month and put them into my Yahoo Briefcase for public download. I made two Microsoft Word documents with tables and a self-extracting zip file of my spreadsheet. To make your own calculators, copy and paste special the P/E10 and CPI data onto rows 186 and 188. You must use the Paste Special command to transpose data copied from a column in order to paste them onto a row.
Yahoo Briefcase
Have fun.
John Walter Russell
January 1, 2006