S&P 500 Index Earnings Type	Annual Earnings on Index	P/E Ratio at 1136 S&P	Earnings Yield
Actual latest year (trailing four quarters) GAAP earnings	$60.83	18.7	5.4%
Latest year "operating"  earnings (removes "unusual" items)	$65.87	17.3	5.8%
Forecast forward GAAP earnings for the next year (next four quarters)	$66.62	17.1	5.8%
Forecast forward operating earnings for the next year (estimates summed by individual company)	$83.97	13.5	7.4%
Forecast forward operating earnings for the next year (estimate for the group of companies)	$69.84	16.3	6.1%
For Comparison here are S&P 500 Earnings in prior years:	Earnings	Historical P/E	Historical Earnings Yield
2009 Actual GAAP Earnings	$50.97	21.9	4.6%
2008 Actual GAAP Earnings	$14.88	60.7	1.6%
2007 Actual GAAP Earnings	$66.18	22.2	4.5%
2006 Actual GAAP Earnings	$81.51	17.4	5.7%
2005 Actual GAAP Earnings	$69.93	17.8	5.6%
2004 Actual GAAP Earnings	$58.55	20.7	4.8%
2003 Actual GAAP Earnings	$48.74	22.8	4.4%

The above numbers are all straight from the source  at Standard and Poors. (The numbers on the Standard and Poors site change weekly, our numbers were those that appeared as of May 15, 2010)

When you ask the "simple" question of "what is the earnings on the S&P 500?" index or "what is its P/E ratio?" you are given a number of quite different answers. We can help you fully  understand the different answers.

Standard and Poors itself in its "The Outlook" publication focuses on the forecast year (called  forward) operating earnings scenario, summed by individual company which is the highest earnings number and lowest P/E forecast. I find that to be overly aggressive as it ignores unusual losses. (Surely on a group of 500 companies a certain amount of so-called "unusual" losses is to be expected and should not be ignored). Also these company-by-company forecast operating earnings are higher than the forecast for the group of companies as a whole and this indicates an upward bias in the earnings forecast.

As of  May 15, 2010, the S&P 500 index was at 1136 and had a Price Earnings Ratio ("P/E") of  (a somewhat  unattractively high) 18.7 based on actual trailing reported earnings and a current Dividend yield of 1.96%.  The trailing P/E based on the past 12 months operating earnings (eliminates unusual one-time items) was moderately unattractively high at 17.3.  The forward S&P 500 P/E ratio based on projected reported actual accounting GAAP earnings in the next 12 months was about neutral in attractiveness at 17.0. The forward P/E based on forecast or forward operating earnings in the next 12 months (eliminates unusual one-time items) is neutral in attractiveness at 16.3 (based on an overall index forecast). And attractive but impossibly optimistic at 13.5 based on the summation of individual forecast operating earnings for the 500 companies. This summation of individual forecast operating earnings method appears to always show earnings that are higher than forecast for the entire group 500 of companies.

Most analysts might focus on forecast operating earnings for the index as a whole (P/E of 16.3) as the best estimate since it eliminates unusual gains and losses and is future oriented.

With the exception of the company-by-company operating earnings forecast at a P/E at 13.5, which we consider to be impossibly optimistic, all of the P/E estimates above indicate that the S&P 500 is either moderately over-valued or about neutral in valuation at this time.

Given that projected earnings tend to be optimistic and to ignore "unusual" losses, I normally prefer to use the actual trailing P/E, or equivalently the actual trailing GAAP earnings level. However, at this point in time both the trailing and forward P/Es based on actual and forecast reported GAAP accounting S&P 500 earnings have been driven higher due to the recent recession conditions.  In this case the the unusual losses were (if I may say) unusually large.

A more normalized view of S&P 500 earnings is needed. In estimating a normalized S&P 500 earnings number for the purposes of a long-term valuation, we are not really concerned with forecasting the actual earnings of the S&P 500 in the next year. Instead, we wish to use a normalized earnings level that we can use to apply a growth rate to and reach a reasonable estimate of where the S&P 500 earnings will be in ten years. That is because valuation depends mostly on long-term earnings not on next years earnings.

The long term average of S&P 500 index earnings in dollars relation to GDP in billions is 0.49%. Therefore based on 2009 United States GDP of 14,258, I calculate a normalized (essentially a non-recession level) view of current S&P 500 earnings as $70. This would imply the adjusted P/E of the S&P 500 is currently about 1136/70 = 16.2.

This assumption of a a normalized or starting earnings level of $70 is equal to the 2005 actual GAAP earnings, lower than the peak earnings of $81.51  from 2006 and moderately higher than the 2007 level of $66. Also it is (coincidently) just equal to the projected next 12 months operating earnings for the S&P 500 which from the table above is $70.  It is important to understand that this starting earnings level is a very major determinant in our calculation of the fair value of the S&P 500 index and that it is a difficult number to estimate.

The S&P 500 index represents a portfolio of 500 stocks. For each $1136 (the index value)  purchased, the underlying companies in the portfolio are earning an adjusted or normalized earnings level of $70 and currently pays an annualized dividend of $1136 * 0.0196 = $22.27 

It is important that we not base the analysis on an unrealistic level of S&P 500 earnings such as might be caused by a one-time peak in earnings or the recent unusual losses.

When we buy the S&P 500 index, we can therefore think of it as being an investment or "stock" that (as of May 15, 2010) costs $1136 and currently earns (on an adjusted or normalized basis) $70 per year and pays a current dividend of $22 per year. It is worth thinking about whether or not this "stock" is a good investment at or around its recent level of $1136.

We know that the S&P 500 index was at 1136 on May 15, 2010. We can estimate what the S&P theoretically "should" be  trading at based on the value of its current earnings and dividends and the projected growth in those earnings and dividends. This intrinsic value approach calculates the value of the projected earnings and dividends for a ten year period and then assumes that the index is sold at some projected future P/E ratio.

In addition to the beginning earnings and dividend level, three additional factors are required to calculate the fair value at which the S&P 500 should be trading at. These are, 1. The forecast average annual growth rate in earnings and dividends over the next ten years. 2. The forecast P/E ratio at which the S&P index will be trading in ten years time. 3. The estimated rate of return required by investors.

The S&P 500 portfolio average earnings should (in the longer term) grow at a rate close to the growth rate of the U.S. economy in nominal (after inflation) terms. I believe a prudent estimate for this growth rate is  4% to 6% and I would focus on 5%.  We have a short article that both explains why (quoting Warren Buffett) and also demonstrates that earnings tend to grow at about the same rate as nominal GDP growth in the long run.

The following graph illustrates that S&P 500 earnings have trended up at about the same rate as GDP growth (although slightly lower) over the long-term, although certainly with substantial volatility around the trend in individual years and over short periods of years.

This graph also clearly illustrates that the U.S. GDP (In nominal dollars, not inflation adjusted dollars)  has trended up steadily and has never failed to grow over say a three year period, except in the case of the depression. Those who are betting on a major and long-term decline in U.S. GDP and/or betting on a permanent decline in earnings on the S&P 500 index are betting against history.

Note that we use a logarithmic scale on this chart. Logarithmic scales should always be used when the time period is more than about 30 years because otherwise the lines will turn up exponentially.

The next chart presents the same data but starting in 1980 and using a regular arithmetic scale so that we can more closely examine the graph over more recent years.

The last point on the chart is the earnings  and GDP in the 12 months ended December 2009. The earnings dipped sharply in 2007 and 2008 after reaching a peak in 2006, there has been a partial earnings recovery in 2009. The GDP figure is showing a small dip in 2009. Note that the GDP figures here are in nominal dollars, whereas reports of GDP growth usually refer to real, inflation adjusted dollars.

This chart shows that while GDP rose fairly steadily since 1980, the S&P 500 earnings growth significantly lagged the GDP growth from 1980 bottoming with the recession in 1992. Thereafter the S&P 500 earnings rose at about the same rate as GDP or a bit higher before plunging after 2006. A best fit trend line since 1980 would likely place the 2009 S&P 500 earnings at about $50 (which with a P/E of 15 would put the fair value of the S&P 500 index at (gulp) 750 and even with an 18 P/E it would only be 900). A best fit S&P 500 earnings trend line since 1992 would place the 2009 S&P 500 earnings at no more than about about $70 (implying at a 15 P/E a fair value S&P 500 of 1050 or at an 18 P/E, a fair value S&P 500 index of 1,260.)

The high S&P 500 earnings of $82 in 2006 were clearly well above the trend line.

Our representative normalized earnings value of $70 selected above is at the high end of the S&P 500 earnings trend since 1992. This shows that our normalized stating earnings level of $70 is not wildly optimistic, is certainly not overly pessimistic, but appears to be perhaps a moderately optimistic estimate.

Having determined and discussed the earnings level on the S&P 500 index we also need to make an assumption about the P/E level that is likely to apply to the index in the longer term.

The average for the S&P 500 P/E ratio since 1935 is 15.6. But the average since 1988 has been 23.15. However the Justifiable P/E changes with earnings expectations and the market's required return on equities. I have conservatively calculated that the current Justifiable P/E is about 14.3 assuming that with today's low interest rates investors require about a 7% expected return and assuming that competition will drive available returns down to the required 7% level. The article also indicates that if companies can deliver in perpetuity an 8% ROE when investors only require 7% (perhaps due to a lack of corporate competition) then a P/E of 21.4 can be justified but we considered that to violate equilibrium conditions.   However, I have given some weight to the much higher historical S&P 500 P/E  figure since 1988. The range used in our table below is 13 to 17.

I would estimate that a minimum (pre-tax) return required by stock investors is in the range of 7% to 9%. The higher return required by investors then the lower the price or level that investors should be willing to pay for the index today, all else being equal. 

The following table calculates the value that the S&P 500  will be  at in ten years given various forecasts for the earnings growth and given various scenarios for the forecast P/E ratio that will apply at that time. The last column of the table then shows the fair or present value that we should be willing to pay today for the cash flows that would result from ten years of dividends plus the assumed cash from selling the index in ten years time. The present value is calculated based on various scenarios for the required return or discount rate.

S&P 500 Current Annual Earnings Estimate	S&P 500 Current  Annual Dividends	Earnings and Dividend Growth forecast	S&P 500 P/E forecast in 10 years	Resulting S&P 500 index in 10 years	Required Return	Resulting S&P 500 index Fair Value Today	Resulting Fair P/E today
70	22	4.0%	13	1,347	7%	874	12.5
70	22	4.0%	15	1,554	7%	979	14.0
70	22	4.0%	17	1,761	7%	1,084	15.5
70	22	4.0%	13	1,347	9%	740	10.6
70	22	4.0%	15	1,554	9%	828	11.8
70	22	4.0%	17	1,761	9%	916	13.1
70	22	4.5%	13	1,413	7%	912	13.0
70	22	4.5%	15	1,631	7%	1,023	14.6
70	22	4.5%	17	1,848	7%	1,133	16.2
70	22	4.5%	13	1,413	9%	773	11.0
70	22	4.5%	15	1,631	9%	865	12.4
70	22	4.5%	17	1,848	9%	956	13.7
70	22	5.0%	13	1,482	7%	952	13.6
70	22	5.0%	15	1,710	7%	1,068	15.3
70	22	5.0%	17	1,938	7%	1,184	16.9
70	22	5.0%	13	1,482	9%	806	11.5
70	22	5.0%	15	1,710	9%	903	12.9
70	22	5.0%	17	1,938	9%	999	14.3

 

Conclusions

Given my assumed current normalized earnings level of $70 and the actual dividend of $22, by changing the expected earnings growth rate, the return required by the investor and the assumed P/E ratio that will apply in ten years I can calculate that today's S&P 500 index should be anywhere from 740 (assumes that our starting normalized earnings level of $70 is accurate, that the market P/E falls to 13, earnings grow at only 4% annually and equity investors require an expectation of making 9%) to 1,184 (assumes our starting normalized earnings level of $70 is accurate, a terminal market P/E of 17 will apply in ten years, earnings grow at 5% per year and investors only require an expectation of earning 7% on equities).

My own fair-value estimate is 944 based on the average of the two high-lighted rows  This assumes that investors require a minimum 8% expected return, that the S&P earnings and dividend will grow at 4.5%  (3% GDP growth plus 1.5% inflation) and that the long run S&P 500 P/E ratio is 15. Higher S&P 500  index values are implicitly assuming that the current normalized starting earnings level is higher than $70, that earnings growth will exceed 4.5% annually, that the justifiable long-run P/E exceeds 15, and/or that investors require less than an 8% (pre-tax) return.

Our range of investor required returns of 7% to 9% is very attractive compared to the recent 10-year U.S. government bond yield of about 3.4%. It's also attractive compared to long -term corporate bond yields which we understand are about 5%.

It's interesting to note that my fair value S&P 500 of 944 implies that I require the P/E to be as low as 944/$70 = 13.5, which seems low, when I am assuming that the long-term faior P/E is 15/. The reason for this is that if I wish to male 8% (the average of my 7% and 9% scenarios and if the S&P is going to grow at 5% and give dividends of 2% then I need the P/E to rise over my holding period.

Possibly it would be more consistent to go with the higher end of my range with a faire value of 1023 and an expected earnings of 7% and with an expectation of the P/E to be flat at 15.

The overall conclusion is that a fair value of the S&P 500 index based on estimated normalized annual earnings is  probably within the range of 865 to 1023, with a mid-point estimate of 944. Since this is based on many estimated numbers it should be taken as a rough indication and certainly not as an exact determination. 

Buying the S&P 500 index when it is at about 1136 (the level when this article was written) should be expected (but certainly not guaranteed) to result in an average return of under 7% (about 6%) per year if held for the next 10 years.  The expected standard deviation around this expected 6% is also large so that the actual return over the next 10 years might be expected to fall within a range of say 4% to 8% per year with some chance of being outside that range. And that return includes dividends and is before trading costs and taxes. And in any given year, the return will range wildly and should be expected to be negative in some years.

I note that the reported S&P 500 P/E ratio was well above 20 for most of the last 8 years. Either the earnings were distorted (downward) or the index was overvalued. Hind-sight suggests that the index was over-valued for much of the past dozen years.

It is impossible to predict where the S&P 500 index will go in the next year. But it is possible to estimate its fair value and therefore whether or not it is currently over-valued based on reasonable growth expectations and a reasonable expectation around the initial earnings (or equivalently the  initial P/E level) and around the terminal P/E ratio. Caution is warranted because the S&P 500 can sometimes spend years in an over-valued or an under-valued-state. But ultimately, as we have seen in the early 2000's crash, and the crash of 2008, valuation does correct itself.  (and sometimes over-corrects to the downside)

Readers should see also a similar article on the Dow Jones Industrial Average and as well a similar analysis of the Toronto Stock Exchange index.

Shawn C. Allen, CFA, CMA, MBA, P.Eng.

President, InvestorsFriend Inc. 
www.investorsfriend.com

Updated May 15, 2010 

Note that at present it seems more difficult to calculate a fair value estimate of the S&P 500 index because earnings were negative in late 2008 and it becomes very difficult to select a representative level for the current earnings on the index. With all the variables at play here it is possible to "torture the results"  until they confess to some pre-conceived notion of a fair value of the index. I have tried hard here not to torture the numbers. I have presented a table of results so that readers can select their own fair value estimate for various assumptions around growth, required return and the terminal P/E level. Also one could scale the fair value results up if you prefer to use a  higher estimate for "current" earnings on the index. 

Past Results from this Analysis.

Before placing any weight on the analysis above, you may be interested to review a summary of the fair values that we calculated in the past and whether or not our long-term analysis provided any hint of the market crash (Arguably the June 1, 2008 analysis provided some hint, especially for investors that felt that a 9% return was required for which we indicated a fair value of the S&P 500 index was 982 in that case and the index was sitting at 1400).

Keep in mind that with the past analysis we also provided a range of valuations and readers were free to select a different fair valuation from our table above.

Date	S&P Level	Fair Value we Calculated	Apparent Performance as of May 15,'10 with Index at 1136 (and note that this was meant to be a long-term tool not short-term)
August 5, 2009	1003 Actual	886 Fair Value	In the early going, the market remains well above our fair value from August (our fair value now looks low)
Feb. 20, 2009	770 Actual	896 Fair Value	It appears we were correct, the index was under-valued on Feb 20, 2009
Oct. 5, 2008	1099 Actual	991 Fair Value
June 1, 2008	1400 Actual	1158 Fair Value	It appears that we were correct that the index was significantly over valued, though our own fair value now looks high as well
March 25, 2008	1358 Actual	1221 Fair Value	It appears that we were correct that the index was over valued, though our own fair value - based on the higher earnings at that time - now looks far too high as well
Feb 10, 2008	1331 Actual	1388 Fair Value	It appears our fair value was too optimistic at that time
August 19, 2007	1446 Actual	1373 Fair Value	It appears our fair value was too optimistic at that time although we were directionally correct that the index was over valued
Feb 10, 2007	1438 Actual	1295 Fair Value	It appears that we were correct that the index was over valued, though our own fair value now looks high as well
Sept. 9, 2006	1299 Actual	1189 Fair Value	It appears that we were correct that the index was over valued, though our own fair value now looks high as well
April 7, 2006	1295 Actual	1215 Fair Value	It appears that we were correct that the index was over valued, though our own fair value now looks high as well
Feb. 28, 2005	1191 Actual	925 Fair Value	It appears that we were correct that the index was  over valued.
Sept. 4, 2004	1104 Actual	961 Fair Value	Directionally we were right but it was more over-valued than we thought. But we did recognize that our 961 might be high and stated: Investors should be sobered by the fact that if investors require a 9% rate of return and if the earnings only grow at 5% (say 3% GDP plus 2% inflation) and if the S&P commands a P/E of only 14 in ten years then the fair value of the S&P today is calculated as only 731, which is 34% below the current value!

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