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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 Non-Predictive 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 year-end, from 1979 to 2004. In other words, as of year-end 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
R-squared = 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 10-Year 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 anti-enterprise 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.

YearS&P
Year End
Realized
Earnings
E/P:
Earnings
Yield
Y:
10 Year
Treasury
Subs
Yr Perf
Differential:
E/P - Y
Class*
1979107.914.6313.6%10.3%25.8%3.22%High
1980135.814.6410.8%12.4%-9.7%-1.65%Low
1981122.615.2712.5%14%14.8%-1.52%Med
1982140.613.569.6%10.4%17.3%-0.75%High
1983164.913.38.1%11.8%1.4%-3.74%Low
1984167.216.569.9%11.5%26.3%-1.61%Low
1985211.315.237.2%9%14.6%-1.78%Low
1986242.214.856.1%7.2%2%-1.09%Med
1987247.115.866.4%8.9%12.4%-2.44%Low
1988277.722.738.2%9.1%27.3%-0.95%High
1989353.423.76.7%7.9%-6.6%-1.23%Med
1990330.221.776.6%8.1%26.3%-1.47%Med
1991417.117.764.3%6.7%4.5%-2.44%Low
1992435.718.044.1%6.7%7.1%-2.55%Low
1993466.520.414.4%5.8%-1.5%-1.42%Med
1994459.327.325.9%7.8%34.1%-1.87%Low
1995615.935.185.7%5.6%20.3%0.14%High
1996740.7364.9%6.4%31%-1.56%Med
1997970.440.644.2%5.7%26.7%-1.55%Med
19981229.238.473.1%4.6%19.5%-1.52%Med
19991469.343.963%6.4%-10.1%-3.45%Low
20001320.353.74.1%5.1%-13%-1.04%Med
20011148.128.312.5%5.1%-23.4%-2.59%Low
2002879.830.043.4%3.8%26.4%-0.4%High
20031111.938.583.5%4.2%9%-0.78%High
20041211.957.774.8%4.2%5%0.55%High
20051272675.3%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 young-hearted 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(t-1) 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 r-squared, (0.122), and with one less variable, (Treasury Yield).

 

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