S&P 500 Index Earnings Type	Annual Earnings on Index	P/E Ratio at 1159 S&P	Earnings Yield
Actual latest year (trailing four quarters) GAAP earnings	$83.90	13.8	7.2%
Latest year "operating"  earnings (removes "unusual" items)	$90.89	12.8	7.8%
Forecast forward GAAP earnings for the next year (next four quarters)	$93.75	12.4	8.1%
Forecast forward operating earnings for the next year (estimates summed by individual company)	$105.45	11.0	9.1%
Forecast forward operating earnings for the next year (estimate for the group of companies)	$99.34	11.7	8.6%
For Comparison here are S&P 500 Earnings in prior years:	Earnings	Historical P/E	Historical Earnings Yield
2010 Actual GAAP Earnings	$76.97	16.3	6.1%
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%

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  August 25, 2011, the S&P 500 index was at 1159 and had a Price Earnings Ratio ("P/E") of  (a moderately attractively low) 13.8 based on actual trailing reported earnings and a current Dividend yield of 2.30  The trailing P/E based on the past 12 months operating earnings (eliminates unusual one-time items) was even more attractive at 12.8.  The forward S&P 500 P/E ratio based on projected reported actual accounting GAAP earnings in the next 12 months was also attractive at 12.4. The forward P/E based on forecast or forward operating earnings in the next 12 months (eliminates unusual one-time items) was quite attractive at 11.7 (based on an overall index forecast). And even more attractive but impossibly optimistic (due to ignoring all unusual losses) at 11.0 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 14.5) as the best estimate since it eliminates unusual gains and losses and is future oriented.

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.  This figure is $84, for a P/E of 13.8.

This representative earnings level of $84 is moderately higher than the peak earnings of $81.51  from 2006 and noticeably higher than the earnings in 2007, 2008 and 2009. 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 therefore represents a portfolio of 500 stocks. For each $1159 (the index value)  purchased, the underlying companies in the portfolio are earning an adjusted or normalized earnings level of $84 and currently pays an annualized dividend of $1159 * 0.0230 = $26.66 

When we buy the S&P 500 index, we can therefore think of it as being an investment or "stock" that (as of August 25, 2011) costs $1159 and currently earns $84 per year and pays a current dividend of $26.66 per year. It is worth thinking about whether or not this "stock" is a good investment at or around its recent level of $1159.

We know that the S&P 500 index was at 1159 on August 25, 2011. 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 nominal 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. The last point on the graph is the estimated figures for 2011 (as of late 2010).

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 currently estimated for 2011. The earnings dipped sharply in 2007 and 2008 after reaching a peak in 2006, there has been a total earnings recovery during 2009 and 2010 and including the 2011 estimate. The GDP figure is showing a small dip in 2009 with a full recovery in 2010 and forecasts continued growth in 2011. 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 and then recovering strongly in 2009 and 2010. A best fit trend line since 1980 would likely place the 2011 S&P 500 earnings at about $65 (which with a P/E of 15 would put the fair value of the S&P 500 index at (gulp) 975 and even with with an 18 P/E it would be only 1170). 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 $80 (implying at a 15 P/E a fair value S&P 500 of 1200 or at an 18 P/E, a fair value S&P 500 index of 1,440.)

The trailing GAAP earnings value of $84 noted above is only moderately above the S&P 500 earnings trend since 1992. 

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 1936 is 15.9 (this eliminates from the average any P/E greater than 50 which only occurred in Q4 2008 through Q3 2009 when the earnings plunged to abnormally low levels). But the average (on the same basis) since 1988 has been 22.1. 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 second 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.

The last column in the table indicates the average annual return that would be made if the S&P 500 is purchased at its recent level of 1159 and if earnings and dividends grow at the indicated rate and the index trades at the indicated P/E ratio in ten years time.

 

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	Return per Year Buying at S&P 1159
84	27	4.0%	13	1,616	7%	1,053	12.5	5.9%
84	27	4.0%	15	1,865	7%	1,180	14.0	7.2%
84	27	4.0%	17	2,114	7%	1,306	15.6	8.4%
84	27	4.0%	13	1,616	9%	893	10.6	5.9%
84	27	4.0%	15	1,865	9%	998	11.9	7.2%
84	27	4.0%	17	2,114	9%	1,103	13.1	8.4%
84	27	5.0%	13	1,779	7%	1,148	13.7	6.9%
84	27	5.0%	15	2,052	7%	1,287	15.3	8.2%
84	27	5.0%	17	2,326	7%	1,426	17.0	9.5%
84	27	5.0%	13	1,779	9%	972	11.6	6.9%
84	27	5.0%	15	2,052	9%	1,088	13.0	8.2%
84	27	5.0%	17	2,326	9%	1,204	14.3	9.5%
84	27	6.0%	13	1,956	7%	1,251	14.9	7.9%
84	27	6.0%	15	2,256	7%	1,404	16.7	9.3%
84	27	6.0%	17	2,557	7%	1,557	18.5	10.5%
84	27	6.0%	13	1,956	9%	1,058	12.6	7.9%
84	27	6.0%	15	2,256	9%	1,185	14.1	9.3%
84	27	6.0%	17	2,557	9%	1,313	15.6	10.5%

 

 

Conclusions

Given the current earnings level of $84 and the current dividend of $27, 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 893 (assumes that our starting earnings level of $84 is reflective, that the market P/E falls to 13, earnings grow at only 4% annually and equity investors require an expectation of making 9%) to 1,557 (assumes our starting normalized earnings level of $84 is reflective, 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 1188 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 5%  (3% GDP growth plus 2.0% 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 $84, that earnings growth will exceed 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 indeed compared to the recent 10-year U.S. government bond yield of about 2.2%. It's also attractive compared to long-term A rated corporate bond yields which we understand are under 5%.

It's interesting to note that my fair value S&P 500 of 1188 implies that I require the P/E to be as low as 1188/$84 = 14.1, which seems low, when I am assuming that the long-term fair P/E is 15. The reason for this is that if I wish to make 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%, for a total return of 7% at a constant P/E,  then I need the P/E to rise over my holding period to give me the additional 1%.

The last column in the table shows that under the indicated assumptions, if money is invested today in the S&P 500 and held for ten years and if the earnings and dividends grow at the rate indicated and the P/E ratio in ten years is as indicated then the average returns per year would range from 5.9% to 10.5% per year. With the 10-year treasury bond currently yielding about 2.2% these estimated returns are quite attractive. Of course the earnings growth on the S&P 500 could be lower than 4% and the terminal P/E ratio could be lower than 13, in which cases a lower return would result. One can always come up with losing scenarios, but based on historical earnings growth and P/E ratios it would appear that over a ten year holding period, stocks are likely to significantly out-perform government bonds.

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 1088 to 1287, with a mid-point estimate of 1188. 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 1159 (the level when this article was written) should be expected (but certainly not guaranteed) to result in an average return of about 8.2% per year if held for the next 10 years, assuming 5% annual growth and a terminal P/E ratio of 15.  The expected standard deviation around this expected 8.2% is also large so that the actual return over the next 10 years might be expected to fall within a range of about 6% to 10% 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.

Another way to calculate the expected return on the S&P 500 index is by using the dividend growth model. This assumes that the dividend will grow at the rate of the ROE on retained earnings times the proportion of earnings that are retained.  The S&P 500 currently has an ROE of about 14%. (This is calculated as ROE = P/B divided by P/E and uses the $594 book value reported by S&P for March 2011.) The dividend payout ratio calculated from the dividend and earnings in the table above is 27/84 = 32%. That means the earnings retention ratio is 68%. If the S&P 500 companies can continue to make the same ROE of 14% on their existing equity plus on retained earnings then the dividend should grow at 68% of that or 9.5%. Adding the current dividend yield of 2.30% would suggest an expected return of about 12%. However, a 14% ROE on future as well as past retained earnings may be optimistic. If we use a 10% ROE the expected return on this basis is about 9%. And this assumes that the P/E remains constant at 13.8. 

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 and early 2009, valuation does correct itself.  (and sometimes over-corrects to the downside).

You can easily invest in the S&P 500 index by buying the ishares S&P 500 index Exchange Traded Fund under symbol IVV on the New York Stock Exchange. And if you are really bullish you can buy the double bull Proshares Ultra S&P 500 symbol SSO. Or if you are bearish there is the single bear ETF, Proshares short S&P 500 symbol SH, or the double bear Proshares Ultrashort S&P 500 symbol SDS. Be cautious and understand what you are buying.

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 August 25, 2011 (ETF symbols added November 23, 2011)

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.

The table below shows that our analysis appears to have been directionally correct. Based on where the S&P 500 index is today we were correct that it was over-valued from 2004 through to October 2008. (With one exception we were wrong to see the market as fairly valued in February 20080. Our analysis correctly saw the market as under-valued in the Spring and Summer of 2009. We correctly saw that it was again over-valued by Spring 2010 and substantially over-valued in early 2011.

 

Date	S&P Level at that Date	Fair Value we Calculated	Average Capital Gain Per Year	Apparent Performance as of August 25,'11 with the Index at 1159 (and note that this was meant to be a long-term tool not short-term)
26-Feb-11	1320	1165	-23.2% (8.8% actual loss annualized)	In the very early going, it appears we were correct, the market was over-valued
15-May-10	1136	944	1.6%	In the very early going, it appears we were correct that the market was over-valued. The return has been positive but too low.
5-Aug-09	1003	886	7.3%	It appears we were wrong to conclude that the market was over-valued.
20-Feb-09	770	896	17.7%	It appears we were correct, the index was under-valued on Feb 20, 2009
5-Oct-08	1099	991	1.9%	It appears we were correct, the market was over-valued and has delivered a poor return to buyers in October 2008
1-Jun-08	1400	1158	-5.7%	It appears that we were correct that the index was significantly over valued.
25-Mar-08	1358	1221	-4.5%	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 too high as well
10-Feb-08	1331	1388	-3.8%	It appears we were wrong to consider the market fairly valued. It has given a poor return
19-Aug-07	1446	1373	-5.4%	It appears we were directionally correct that the index was over valued, but it was more over-valued than we thought.
10-Feb-07	1438	1295	-4.6%	It appears we were directionally correct that the index was over valued, but it was more over-valued than we thought.
9-Sep-06	1299	1189	-2.3%	It appears we were directionally correct that the index was over valued, but it was more over-valued than we thought.
7-Apr-06	1295	1215	-2.0%	It appears we were directionally correct that the index was over valued, but it was more over-valued than we thought.
28-Feb-05	1191	925	-0.4%	It appears that we were correct that the index was  over valued.
4-Sep-04	1104	961	0.7%	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!