Earnings Yield Versus Next 12 Month Change in the S&P 500, 1945-May,2007

Valuation: What seems obvious on Wall Street often turns out not to be true. Such is the case with traditional measures of value, the most well-known being the ratio of price to earnings, or its inverse, the earnings yield. One would think that buying the S&P500 when the PE falls (or the earnings yield rises) to a certain value then selling when the other historical extreme is reached would be profitable.

In the long haul, earnings drive stock prices and if prices inflate much more rapidly than earnings, then an expansion in the PE results. To claim this could continue indefinitely is absurd. However, it is equally absurd to try to pin a precise "fair value" on the S&P500 to which the market must revert by a given date. It simply is not that exact a science and since the PE is in the end a psychological variable, it can reach a new higher (or lower) plateau and stay there for awhile. During the 1990s, the earnings yield shrank to historically unprecedented levels, yet the market has performed remarkably well for several years, skewing the numbers. The very week performance of the market following the record low earnings yield of 2000 brought the historical relationship back into line.

A visual inspection of the earnings yield at the start of each rolling 12 month period, divided into quartiles, versus the subsequent 12 month return, shows a stepwise and positive relationship:

Earnings Yield By Quartile Versus Next 12 Months Change in the S&P 500, 1945- May,2007:

Correlation between the earnings yield and the next 12 month change in the S&P 500, January, 1946-May, 2007, n = 724:
		Last 12 months' change:			Next 12 months' change:
Percentiles:	n	From:		To:
Min-25%	184	2.18%		5.31%	4.50%
25-50%	184	5.31%		6.28%	7.11%
50-75%	184	6.28%		9.04%	10.97%
75-Max	185	9.04%		16.50%	12.54%
		Correlation:			21.8%
All:	737		Average:		8.79%

The higher the earnings yield, the greater the subsequent 12 month change in the S&P500. Each higher quartile of earnings yield had a higher subsequent 12 month return. The market had a below average return when the earnings yield was below average. The market only had an average rate of return over 10 percent when the earnings yield was above average (6.3% or higher).

Earnings Yield Versus Next 10 Year's Rate of Return, 1945- May, 2007 (May, 1997, was the last known subsequent 10 year return).

This historical relationship is even more robust as the time frame examined is stretched to 10 years. If one divides the earnings yield into quartiles then calculates the average next 10 year return (annualized, including dividends), a clear, strong, stepwise pattern emerges:

Earnings yield versus next 10 year average annual S&P 500 total return (including dividends), January, 1945-May, 2007, n = 630:
		Earnings yield			Next 10 year return (annualized):
Percentiles:	n	From:		To:
Min-25%	158	3.81%		5.61%	8.50%
25-50%	157	5.61%		6.92%	10.17%
50-75%	157	6.92%		9.71%	13.92%
75-Max	158	9.71%		16.50%	16.55%
		Correlation:			66.1%
All:	630		Average:		12.29%[1]

Note that the correlation is very strong (for statistically noisy financial data series): 661. This means that roughly two-thirds of the subsequent 10-year returns of the stock market is predicted by this single variable, beginning earnings yield.

Note that even for a holding period as long as 10 years, the valuation of the market at the buying point is a major determinant of your total rate of return. Only when the starting earnings yield is in the top 3 quartiles (5.61% or above - corresponding to a price-earnings ratio of 17.8 or below) can you expect an average total return (including dividends) for the next 10 years of 10% or above. Starting earnings yields in the highest quartile (9.71% or above, or a price-earnings of 10.3 or below), the average subsequent 10 year return was a whopping 16.6% a year.

What is not true is that periods of high valuation mean the market will definitely fall. High valuations (as indicated by low earnings yields) only are correlated with below average but still positive returns. Some of this is skewed by the higher returns (10% average) seen in the 10 years following the lowest 10% of earnings yields 5.6% or lower). This is probably a function of market momentum; the market can surge for years following even silly valuation levels as the stock market gets ahead of reported earnings.

Note that this does not mean that one has to wait 10 years to invest; it is rare an investor has to wait longer than 1-3 years for the earnings yield to dip into this range, usually following a panic or severe economy slowdown. Nor does it mean one should not invest at all during peak earnings yield periods, since even 8.52% - the average rate of return of the second-to-lowest quartile - is better than the long-term returns of bonds or cash. It simply means that for marginal dollars, such as an inheritance or a bonus that could be invested at optimal levels, waiting for the market's earnings yield to rise to a historically high level may pay off greatly.

One error commonly made even by analysts who should do better is to compare the long term historical track record of price-earnings ratios based on trailing cash earnings on the S&P 500 as calculated here with "forward" or estimated earnings. In other words, a market strategist might say that based on his estimated earnings for the S&P 500, the market is trading at "only" 15 times next year's earnings and since the market price-earnings ratio has averaged about 15 (15.7 during this time frame), the market is fairly priced. This type of reasoning is misleading and should be avoided (unless one's objective is to mislead clients into a false sense of complacency). There are no reliable estimates of forward estimates, since to gather those, one would have to calculate some average of analyst estimated next 12 month earnings at each point in time not as they subsequently turned out because there is often a marked difference. Yes, cash earnings as reported can and are manipulated, but they aren't nearly as subject to revision after the fact and, since earnings tend to grow over time, the trailing price-earnings will almost always be higher (and the earnings yield lower) than the forward price-earnings based on analysts' estimates. If an analyst wants to make a rough estimate of where the market should be, she should either assume her estimate is correct, then use historical averages to make an estimate for where the market should be fairly priced a year hence. So if the market is trading at 17 times trailing earnings, and she believes S&P 500 earnings will grow 10% this year, then the fair value of the market would still be below its current level if the 15.7x historical price-earnings were applied to even this 10% greater earnings which would be trailing earnings in 1 year. There are many reasons the market might continue to trade at above its historical trailing price-earnings but if it is cited, it should be used consistently.

An even more egregious error is to calculate a multiple of operating earnings (earnings stripped of various items such as depreciation and amortization that generally depress earnings) then compare this to the historical trailing cash earnings price-earnings. Again, the only way to say whether the market is over or under valued by this measure is to get a series of consistently defined operating earnings as they were known at each time point in the past and then calculate a historical price-earnings ratio based on this.

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^[1] The 11.25% average annual S&P 500 return is different than the average return below 9% given in the other data sets for 2 reasons: 1.) dividends were included in the 10 year average; and 2.) the periods were different since the 10-year data series ended in 1997, not 2006, as for the annual data.