Current Research F: Executive Summary

In Current Research F: Intermediate-Term Returns we return to more traditional tools to see what happens in the Intermediate-Term of 10 to 20 years.

Current Research E: Managing Downside Risk in Financial Markets came to an unsatisfactory conclusion. Even though authors Frank Sortino and Stephen Satchell presented an outstanding analysis technique, I was unable to build a satisfactory tool from the Forsey-Sortino Model that came with the book. I wanted stable statistical estimates in the intermediate-term of 10 to 20 years.

The model is built upon monthly returns.

Using monthly returns turns out to be unsatisfactory. It limits the predictive effects of valuations to only a few months. This weakness extends throughout a large portion of stock market research and invalidates it.

I am interested in the main portion of the stock market probability distribution. I am satisfied to work in the area in which the normal (Gaussian, bell shaped) distribution applies. In terms of dollar gains and losses, I assume that the distribution is lognormal.

I am unwilling to assign a confidence level greater than 90% (two-sided, 95% one-sided) to any finding.

The stock market has a distinctively non-normal distribution. Ed Easterling of Crestmont Research has shown that you can approximate single-year stock market returns by using two separate lognormal distributions: one during secular (long lasting) bull markets and another during secular (long lasting) bear markets.

Crestmont Research

NOTE: In their investment books, Nassim Taleb and Benoit Mandelbrot focus upon the infrequent events that make up the tails of the probability distribution function. My research focuses on the central portion of the probability distribution.

General Procedures

I extracted data with real, annualized, total returns (with zero expenses) at Years 10, 20 and 30 for sequences beginning in 1921-1980. I included P/E10 and the percentage earnings yield 100E10/P (that is, 100/[P/E10]).

I took advantage of Excel's plotting capability to make linear curve fits (i.e., I determined regression equations) and to report R-squared. R-squared is the square of the correlation. It tells us the percentage of the variance that can be explained by the line. It does not tell us about the variance itself.

I have made eyeball approximations for the confidence limits. This is a close-enough approximation because I am not claiming precision.

Initial Investigation

I made graphs of the real, annualized, total returns (with zero expenses) at Years 10 and 20 for sequences starting in 1923-1980 versus the percentage earnings yield 100E10/P based upon each month. In addition, I made a graph combining data from all twelve months and all years in 1923-1980.

This brute force approach was satisfactory. Equations were similar. The predictive relationship between returns and valuations was stable.

Individual Decades

Next, I looked at individual decades. The equations at years 10 and 20 varied considerably.

The reason that the Forsey-Sortino Model projections (in Current Research E) varied from one decade to another is that stock returns have varied from one decade to another.

I noticed a bending (or saturation) of the curves. I thinned the data, including only conditions with percentage earnings yields less than 10% (and P/E10 greater than or equal to 10). This got rid of the effects of the curvature, but the data still behaved badly.

Finally, I sorted equations into secular bull and bear market intervals as defined by Ed Easterling of Crestmont Research.

Sorting based on Ed Easterling's research did the best. Looking at R-squared, it performed exceptionally well except for 20-year projections from the 1933-1936 bull market.

The alternatives performed poorly at year 20 when starting from the 1930s. Nor did they perform well at years 10 and 20 when starting from the 1940s and the 1960s.

In terms of the months of a year, the relationship between returns and valuations is stable. In terms of decade to decade, returns vary. Separating bull markets from bear markets improves your forecasting ability.

Interpreting the Equations

I stuck earnings yield numbers into the equations to see what happens. I looked at 3.5%, 5.0% and 10.0%. The typical range historically has been P/E10=10 (earnings yield = 10%) for bargains and P/E10 = 20 (earnings yield = 5%) for overpriced stocks. Today's valuations are higher than the pre-bubble historical range. P/E10 is close to 28 or 29. The percentage earnings yield is close to 3.5%.

Thinning the data did not change predictions much. It increased predicted 1923-1980 and 1923-1930 returns when the earnings yield 100E10/P is 10% (and P/E10=10). But that was to have been expected. The reason for thinning was that the curve saturates at higher earnings yields. That is, the benefit of increasing the earnings yield tapers off at highly favorable valuations. Thinning the data improves the accuracy of equations at lower earnings yields (i.e., at higher valuations). It reduces the accuracy of equations at higher earnings yield (i.e., at lower valuations).

Projections varied a lot. This was in accordance with underlying uncertainties. The basic approach has the largest variation, thinned data approach is next and sorting based on Ed Easterling's research does best. At year 10, the total variations are in the neighborhood of 12%, just under 12% and 9%, respectively. At year 20, the total variations are in the neighborhood of just under 8%, 7% and 6%, respectively.

The really interesting effects were what happens to (secular) bull market and (secular) bear market projections. Year 10 projections are distinct. Year 20 projections are the same.

Sorting by Bulls and Bears

I divided the 1921-1980 data into two groups: one with secular (long lasting) bull markets and another with secular (long lasting) bear markets. I used Ed Easterling's divisions. The bull markets were in 1921-1928, 1933-1936 and 1942-1965. The bear markets were in 1929-1932, 1937-1941 and 1966-1980. [I selected a cutoff date of 1980. The 1966 bear market extended through 1981.]

100E10/P versus P/E10 Comparisons

I make plots using P/E10 as well as 100E10/P.

If you compare 100E10/P results with P/E10 results, you will notice that they are similar EXCEPT when 100E10/P = 3.5%. Lines drawn using 100E10/P place more emphasis on what happens at higher earnings yields (bargain prices, favorable valuations). Lines drawn based on P/E10 data place a greater emphasis on what happens at higher prices (unfavorable valuations).

The total range (all months in 1921-1980) of P/E10 was from 5.1 to 32.6. The range of 100E10/P was from 19.52% to 3.07%.

An earnings yield of 3.5% is at an extreme. But earnings yields of 5% and 10% are in the central region of the curve fit.

What happens is that the market changes from Bull to Bear or from Bear to Bull at the extremes. This explanation works when going starting at high valuations in a bull market. Multiples cease expanding before year 10. But if we start from high valuations in a bear market, multiples are already contracting. Possibly, they stop contracting as rapidly as at first. This corresponds to having a really sharp decline early, followed by a more gradual decline.

In addition, several bull and bear markets lasted less than 10 years.

These effects are present at both years 10 and 20.

Year 10 Bull Market versus Bear Market Comparisons

Here are the differences of the averages: Bull Market-Bear Market:

3.43% and 4.45% and 5.88%

This is in qualitative agreement with the dividend discount model and its variants.

In its most basic form: the investment return = the initial dividend yield + the rate of dividend growth. Smoothed earnings yield makes a good proxy for the initial dividend yield since (a) dividends come out of earnings and (b) using smoothed earnings avoids the problem of surprise dividend cuts.

Lower earnings yields (higher prices) translate into lower dividend yields. Higher earnings yields (lower prices) translate into higher dividend yields.

The overall trend that the differences between bull markets and bear markets increase as earnings yield increases makes sense because limits exist. That is, earnings yield is unlikely to stray far from its historical bounds for an extended amount of time. The normal range is 5% to 10% (P/E10 = 10 to 20). Outside of this range, returns are likely to disappoint (when P/E10>20) or please (when P/E10<10).

That is, if you start with a high earnings yield (low P/E10) in a bear market, the bear is almost over. If you start with a high earnings yield (low P/E10) in a bull market, the bull is just beginning.

If you start with a low earnings yield (high P/E10) in a bull market, the bull is almost over. If you start with a low earnings yield (high P/E10) in a bear market, the bear market has a long way to go.

Year 10 Baseline Comparisons

Identifying bull and bear markets appears to be helpful at Year 10. [The range of the data is in the neighborhood of plus and minus 7% and the number of degrees of freedom should be enough to bring the confidence limits down to plus and minus 1%.] There is still a lot of scatter in the likely outcomes.

Year 20 Baseline Comparisons

Identifying bull and bear markets does not help at Year 20. The best that we can say is that if you start in a bull market at a low earnings yield (high P/E10), you are likely to see it end and wind up in a bear market. If you start out at a low earnings yield (high P/E10) in a bear market, you are likely to recover somewhat by Year 20.

Summary

Separating projections based on secular (long lasting) bull markets from secular (long lasting) bear markets can be worthwhile, especially at Year 10.

You are likely to encounter both a secular bull market and a secular bear market by Year 20.

Repeatedly, the story at today's valuations (100E10/P = 3.5%) is bad news. We can expect to see the effects of the current secular bear market at year 10. The most likely outcome will be a net loss (of 3% annualized) between 2000 and 2010. The bull market that follows is likely to bring the overall annualized return to 1.7% (plus inflation) by year 20. That would almost match today's TIPS.

Repeatedly, the story is that markets reverse themselves at extreme valuations. We see this in projected returns by Year 10. Even then, there is still a lot of randomness even at Year 10. Outcomes can easily vary plus and minus 5% (annualized) about projections.

Have fun.

John Walter Russell
January 8, 2006