Daily Speculations 

The Chairman
©2005 All content on site protected by copyright 
12/16/2005
A Christmas Present
The time has come to shed light on the P/E versus return speculations that are so dysfunctional and misleading, as a Christmas present to all our readers, despite the urgent pleas of the Minister of NonPredictive Studies that the results are too currently useful to qualify for inclusion in a site which is devoted to meals for a lifetime rather than meals for a day. On the other hand, the armchair investigators, those who come up with hypothetical defects of studies that rely on earnings, or are masters at throwing layers of noise on results, or look at charts, or look at results from the 1900s to come up with conclusions relevant for today, have the world so much in their grip that no matter what I say, people won't be swayed. So, Minister, let it be.
The question on the table is whether P/Es can be used to predict earnings. A raft of publicity has been disseminated recently about how P/Es are overstated, because they use predicted earnings, which tend to be greater than actual earnings, and thus lead to an underestimate of some kind. And that this is somehow bearish for the market. For example, if the earnings in the last 12 months are $60 per share and the price is 1200, the P/E is 20. But suppose the forecast is for earnings in the subsequent 12 months to be 75. Then the P/E based on forecasted earnings will be 1200/75 = 16. Great. P/E based on forecasted earnings is lower than using actual earnings. And if the forecasted P/E were then compared to the average realized P/E, there would be a bias to compare a number that is lower, based on a forecast, to one that tends to be higher, because it's based on an actual.
So what? What does this have to do with whether P/E itself is predictive of anything? Such a divergence always exists. Is it greater or less than usual and does it have anything to do with subsequent returns? Indeed, how about some direct study of this phenomenon. Do realize that stocks and bonds are substitutes for each other, and that the value of an ownership interest is related to the discounted value of what you get by virtue of owning it. To see how much earnings are worth in any period, the earnings must be compared to interest rates. Right now earnings in the S&P for the last 12 months are $67 a share. The price is 1272. That works out to a E/P of 5.27%. But bond yields on the 10 year bond using the most active current 10 year bonds are 4.43%. There's a difference of 0.84% in favor of stocks. Is that bullish or bearish?
To study this, let's be direct rather than sit in an armchair. Let's take the actual earnings for the past 12 months for the S&P that were reported as of the yearend, from 1979 to 2004. In other words, as of yearend 1979, let's look at the last 12 months earnings of S&P as they were reported. The last earnings reported would be those for the 12 months ended September 1979. We'll use the contemporaneous report of those earnings, available in the S&P Stock Guide available at the time. These are reported without adjustment in the S&P Statistical Service. We'll compare the earnings yield calculated from this earnings to the year end 1979 price to come up with an E/P ratio. This E/P ratio will be compared to the then current 10 year bond yield so that a contemporaneous yield differential is possible. For example in 1979 the earnings for the last 12 months were 14.63 , the price as of year end 1979 was 107.9, so the E/P was 13.6%. The 10 year bond yield was 10.3%. The differential was 3.2%.
In order to see how the differential level affects future returns, we divided the data into three groups based on the differential and examined the returns of the the groups. The groups are: Low (differential < 1.6%), Medium (differential between 1.6% and 1.0%), and High (differential > 1.0%). Returns for next 12 months for stocks, based on the actual earnings yield, less the bond yield, contemporaneously calculated 1979 to 2004, were as follows:
Yield Differential MEAN N T     High (> 1.00 %) 19% 7 5.4 Med (1.6% < x < 1.0%) 11% 9 2.0 Low < 1.60 %) 6% 10 1.0
The results are clear. When the yield differential was high ( above minus 1.0% in stocks' favor) the average return for stocks the next 12 months was 19%. When the differential was low ( in favor of bonds) the returns for stocks was a mere 6%. A good regression forecast of the return is:
Subsequent return = 16.5% + 4.0 * Earnings differential Rsquared = 0.12
To determine a forecast using this regression, calculate:
Current S&P (as of 12/16/05) stands at 1272.00
Realized Earnings = Reported Earnings for 12 months ended 9/30/05 = $67.00
Earnings Yield = E/P = Realized Earnings / S&P = 67/1272 = 5.27%
10.Year.Yield = Y = The Current Yield on 10Year government note = 4.43%
The Earnings Differential = E/P  Y = 5.27 percent  4.43 percent = 0.84 %
Substituting these numbers into the regression formula :
0.165 + 4.0 * 0.0084 = 19.9 percent
Therefore, the adjusted P/E model yields a forecast of about 19.9 percent for next
12 months.
Thus, using actual realized earnings, available without forecast, and comparing it to interest rates, a relatively accurate and statistically significant prediction of returns in S&P is possible for the last 26 years. Such a difference is in the High class right now, so the prediction is for a 19% return in 2006. No armchair speculations. No hateful antienterprise biases. No attempt to talk a book. Just the facts.
*To see a somewhat more accurate method for forecasting returns, see our work on the Fed Model. The Fed Model utilizes forward earnings (which tend to be higher than realized earnings) and thus encompass a greater amount of information for forecasting.
Year  S&P Year End  Realized Earnings 
E/P: Earnings Yield 
Y: 10 Year Treasury  Subs Yr Perf  Differential: E/P  Y  Class* 

1979  107.9  14.63  13.6%  10.3%  25.8%  3.22%  High 
1980  135.8  14.64  10.8%  12.4%  9.7%  1.65%  Low 
1981  122.6  15.27  12.5%  14%  14.8%  1.52%  Med 
1982  140.6  13.56  9.6%  10.4%  17.3%  0.75%  High 
1983  164.9  13.3  8.1%  11.8%  1.4%  3.74%  Low 
1984  167.2  16.56  9.9%  11.5%  26.3%  1.61%  Low 
1985  211.3  15.23  7.2%  9%  14.6%  1.78%  Low 
1986  242.2  14.85  6.1%  7.2%  2%  1.09%  Med 
1987  247.1  15.86  6.4%  8.9%  12.4%  2.44%  Low 
1988  277.7  22.73  8.2%  9.1%  27.3%  0.95%  High 
1989  353.4  23.7  6.7%  7.9%  6.6%  1.23%  Med 
1990  330.2  21.77  6.6%  8.1%  26.3%  1.47%  Med 
1991  417.1  17.76  4.3%  6.7%  4.5%  2.44%  Low 
1992  435.7  18.04  4.1%  6.7%  7.1%  2.55%  Low 
1993  466.5  20.41  4.4%  5.8%  1.5%  1.42%  Med 
1994  459.3  27.32  5.9%  7.8%  34.1%  1.87%  Low 
1995  615.9  35.18  5.7%  5.6%  20.3%  0.14%  High 
1996  740.7  36  4.9%  6.4%  31%  1.56%  Med 
1997  970.4  40.64  4.2%  5.7%  26.7%  1.55%  Med 
1998  1229.2  38.47  3.1%  4.6%  19.5%  1.52%  Med 
1999  1469.3  43.96  3%  6.4%  10.1%  3.45%  Low 
2000  1320.3  53.7  4.1%  5.1%  13%  1.04%  Med 
2001  1148.1  28.31  2.5%  5.1%  23.4%  2.59%  Low 
2002  879.8  30.04  3.4%  3.8%  26.4%  0.4%  High 
2003  1111.9  38.58  3.5%  4.2%  9%  0.78%  High 
2004  1211.9  57.77  4.8%  4.2%  5%  0.55%  High 
2005  1272  67  5.3%  4.4%  ?  0.84%  High 
Sources: S&P Security Price Index Record, Bloomberg *Differential Class determined as follows: Low : Differential < 1.6 % Med : 1.6% < Differential < 1.0% High : Differential > 1.0 %
Thanks to artful simulator Tom Downing for his calculations, regressions and contemporaneous data collection.
Comment from Sam Eisenstadt, a younghearted giant with a seemingly helpful solution:
Seasons Greetings!
I'm aware of your strong preference for the 'Fed Model'. With respect to the above post, I have a question. When looking at Earnings Yield minus Treasury Yield, aren't you in fact including market price on both sides of the equation? P(t) as part of the Earnings Yield and P(t+1)/P(t) as your dependent variable?
To avoid this problem using your numbers, I related E(t)/E(t1) to P(t+1)/P(t). I know this correlates future change in price to past change in earnings. For the period of your analysis, it produces the same rsquared, (0.122), and with one less variable, (Treasury Yield).