Will The Real S&P 500 Fair Value Please Stand Up?

Have you ever tried to explain something difficult? A precursor to explaining the idea is first understanding the idea. Sometimes when we do not understand an issue, we take someone's opinion as "fact." Luckily, there are those that say "prove it." So let's walk through a difficult idea which should provide a better understanding and offer clarity for where the S&P 500 rests in "fair value" terms.

There are many "fair value" metrics that exist, but one of the most popular -- and the subject of this article --  is Professor Robert Shiller's Cyclically Adjusted Price to Earnings ratio; straight from his site, shown below:

The blue line indicates the current level of (get ready) 10 years' worth of trailing price-to-earnings ratio for the S&P 500. Got that? Professor Shiller takes an average of daily closes on a monthly basis for the S&P 500, then divides that number by 10 years' worth of earnings. The red line is self-explanatory -- the history of the 10-year.

What isn't so obvious - what does 21.17 actually mean? Simply, Shiller uses the long-term average of 16.37 and determines that the S&P 500 is roughly 22% overvalued from the average of monthly closes (in this example, Shiller uses 1122.08 for September). The result? About 860 on the S&P.

But wait, Cyclically Adjusted implies something, doesn't it? Very astute observation. Professor Shiller goes further into the nominal data and adjusts both price and earnings by the CPI from BLS. OK, once you stop laughing -- the only reason I gather that he does it -- is simply because that's what an economist would do.  Check out the difference from the nominal numbers (actual if you prefer) and Shiller's CPI adjusted to make your own decision on the validity of the adjustment:

Looks the same to me, but then again, I am not an economist. Back in the REAL world (couldn't resist), whether the S&P traded nominally at 1480 in Oct. 2000 or on a real (CPI adjustment) basis of 1880 doesn't really matter. I can easily glean that the silly market was "overvalued" back then, similar to now.

Since I like to present information and let others decide how to decipher it, I created a table that answered many of the questions I possessed. Why 10 years (didn't we have record earnings, mortgage securitizations, and explosive derivative growth)? Why average 10 years' worth of trailing earnings -- why not use a Monthly Price to Earnings? What about historical long-term earnings growth? To answer these questions, I turbocharged his data and generated the following chart:

With this table, one can see plainly where the valuation rests with the S&P 500 predicated on many variables. Pick your time frame, use CPI data, or combine everything. Using this table should help investors determine whether they should be trusting "What day is it - then buy" Bob Doll, or listening to Jeremy Grantham (he stated 900 as fair value on CNBC).

Before you load up on long puts or outright start shorting, please take heed of the improved Shiller and the nominal chart for comparison. Shown below is the example of simply placing data on a chart that is automatically calculated. Another improvement is simply using a logarithmic scale to show the differences over such a long time. Note that the market can stay overvalued for many years! But, it ALWAYS goes back to fair value at some point!

The chart simply shows that back in March '09, the S&P reached "fair value." And it also points out that we have rapidly reached overvalued again (anyone say "trillion").

When comparing Shiller's data and the nominal below, note that both are very close. Whether one chooses 903 or 892, both agree we are about 20% overvalued at this point.

Perhaps these charts  supports the Hussmans, Rosenbergs, and Shillers of the econ world, but what really matters is what you do with the information. We will reach a fair value at some point either through earnings growth or by price decline.

Lastly, I created many combinations to capture a faster moving and more realistic value metric. I took pieces of data and combined them into a Combined Fair Market Value shown in the chart below.

The Combined Fair Market Value uses some sentiment (current index price), mixed with a little long term earnings growth, a pinch of averages and topped with some monthly PE data.   Feel free to use whatever valuation metric suits your thought process.

The entire 15-page report is available for the low low price of -- free. Just a click away! The full report explains the mathematics, gives charts, links to source data, and provides methodology of calculations.
Hopefully this article helped explain something difficult. Now, when you read about Professor Shiller's CAPE chart, you will understand the "magic" behind the numbers, or should I say behind the "CAPE."

Post at DShort

S&P 500 Combined Fair Market Value - 3rd QTR 2010

Attached below is the comparison of Professor Robert Shiller's Cyclically Adjusted Price to Earnings Ratio (CAPE 10) vs Nominal for differing time periods.

Apparently - Jeremy Grantham agrees with fair value around 900 - about 17:00 minutes into interview!

And cash has a— a virtue that people don't appreciate fully. And that is its— its optionality. In other words, if anything crashes and burns in value— say the U.S. stock market, if you have no resources, it doesn't help you. If the bond market crashes, and you have no resources, it doesn't help you. And what cash is is an available resource. It buys you the right to buy the U.S. market if the S&P drops from 1,220 today to 900, which is what we think is fair value.





Full report below:
CFMV-Q3-10

S&P 500 Combined Fair Market Value - 2nd QTR 2010

Attached below is the Combined Fair Market Value for the 2nd Quarter for the S&P 500.  This compares the Cyclically Adjusted Price to Earnings ratio created by Professor Robert Shiller to simple nominal terms.

Full report is located here:

CFMV-Q2-10-Final

Cyclically Adjusted Price to Earnings Research

http://dshort.com/articles/guest/Chris-Turner-CAPE-1006.html

Statistical Norm?

How far off can GAAP and Operating earnings be you might ask? I think the nearby charts speak for themselves. These charts summarize the difference between the actual GAAP earnings and "operating" earnings from 1988 to present. Anomaly perhaps?



Hmmm - Looks like the books are cooked a bit - don'tcha think?

WSJ Publishes Comics

All right - apparently - the WSJ Money and Investing section now prints Comics. You haven't seen it? Look no farther than the chart for the S&P (usually around C-4) and the "trailing earnings" and you will have a laugh. Yeah Yeah Yeah - you don't get it, how about this - the WSJ printed 13.09 yesterday and it should be 18.43... A one-off event? Sorry - not only do they know about the error - they continue to print it.

Hey WSJ and Birinyi - I used my 10 year old son to calculate this for me:

Previous 4 quarters (operating) = $45.16
Current Price (as of yesterday) = 832.39
Trailing P/E (832.39/45.16) = 18.43

Need some background? I sent the following to a well known blogger to spark some interest in the erroneous data being published by the WSJ.

I have been tracking the S&P trailing P/E for years via the WSJ. At the beginning of 09 I realized my math and the math of the WSJ seemed to be different. The WSJ publishes the chart of the S&P on Tues/Thu/Sat from Birinyi Associates that shows the trailing p/e. The chart is normally on page C4 during the week and B4 in the Saturday edition.

Prior to calling the WSJ in early April, the most current chart is Thursday - April 2 and shows a trailing p/e of 12.43 with a price of 811.08. Those of us with a little brain power actually go to the S&P website and use Mr. Silverblatts weekly update during earning season to see how earnings are progressing. What was clearly listed on the S&P website during that week was the following "operating earnings" for the previous 4 quarters:

> Q4-08 $-0.09 (1st negative in history btw)
> Q3-08 $15.96
> Q2-08 $17.02
> Q1-08 $16.62
>
Now - we all know the definition of trailing p/e - meaning "previous 4 quarters." But here is the dilemma - those 4 quarters add to $49.49. So, a smart man might have used the price of 811.08 (from their chart) and divide that by 49.49 to achieve a trailing P/E of 16.39 which just so happens, matched what S&P puts out for free on the internet. This isn't "exactly" correct since we were three months in the future, but, the most current.
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What isn't so clear - and why I called the WSJ - is how in the world they are arriving at 12.43 trailing p/e that was posted that day. Well, after spending nearly 2 weeks with phone tags and leaving messages, I reach a New Jersey office that does the Money and Investing section for the WSJ. This is the part that I am not making up - I spoke with a person and after multiple lengthy conversations trying to show them that the number was incorrect, they essentially said that they stick by Birinyi's numbers and those are the most current numbers Birinyi has available.
>
A day later, I had an epiphany - and figured out how on earth the calculation could be so off. It was worse than I thought, simply by adding the 4 quarters ending in September (adding Q4-07 $15.22) and not the most current quarter of $-.09, suddenly nets $64.82 in operating earnings. Now the calculation makes sense, price 811.08 divided by 64.82 is $12.51 - strikingly close to Birinyi's calculation of 12.43...

This is simply egregious and reprehensible - using current price and comparing latest earnings from 6 mos ago to arrive at a "cheap" valuation for the S&P.
>
After learning of this - I again spoke with the same person for about an hour explaining in detail how the WSJ was publishing not only incorrect data, but data that was 6 mos old! Not only did they agree and understand the calculation - they also had the audacity to simply repeat ad nauseum that they stick by Birinyi and their calculations. After a thorough tongue lashing, I educated this person that there is only one moment in time where P/E can be "accurately" reported - and that is after the quarter ends and use that price of the index in the calculations. Which, for Q4-08 is 18.25 - not anywhere close to 12.43...
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I repeatedly told this person that yahoos like me having been reading their paper for years and watching this number. I told them that the average trailing earnings since 1936 has been $15.80 (for Actual BTW - not operating) and that if we were indeed at 12.43 - I would consider that cheap and begin to employ money back into equities. I let this person know that I moved to bonds back in 2006 and am still there, but as soon as I see trailing earnings (by my calculations) get close to 10, I will move back into equities.
>
The travesty in all this - is that they recognize the data is in error, admit the calculation is wrong, yet standby and do nothing. In fact, they use Birinyi's methods for the Russell and Nasdaq, to which I told this person, "good, now I know those indexes are wrong as well."
>
Below is the S&P reference - free to all - from Mr Silverblatt and S&P.
>
> http://www2.standardandpoors.com/spf/xls/index/SP500EPSEST.XLS
>
My only desire is to educate the populace - that the WSJ not only publishes incorrect data, but stands by it. And, in doing so, seems content to literally make us all dumber for reading their paper.

So, on a whim - I send off the following to Birinyi Associates -

Hello,

I am not sure who to discuss this with at Birinyi - but I have a concern about the trailing earnings that is reported in the Wall Street Journal from Birinyi Associates on page C-4 for the Sat/Tue/Thu editions. I have been following this trailing earnings number for years and recently noticed the severe dislocation between my calculations and yours.

The data seems to not only be inaccurate, it seems to be extremely outdated.

The footnote simply states "trailing earnings" without providing a disclaimer of operating vs actual. Additionally - the only way I can make the most current calculation come close is by dividing current price by the summation of the 4 quarters ending Sept 08.

The correct calculation can only be "official" once the data comes in and the price is used at the end of the quarter. For Q408, the trailing "operating earnings" would have been $18.25 based on earnings of $49.49. Your calculations appear to be way off at 12.77 unless one uses the current price as of Sat @ 842.5 and divide by earnings for the 4 quarters ending Q308 of $64.82. Only then can the calculation of 12.77 be somewhat plausible mathematically.

But, since this does not meet the definition of "trailing earnings," I can only surmise that your data is off somewhere.

Please forward to who needs to address this as I think this might be somewhat of an embarrassment for Birinyi Associates.

If I have performed the calculations in error - please advise.

Thanks for your time in addressing this issue.

To which they replied:

Thank you for your message. I certainly understand your confusion. Long ago when WSJ asked us to provide this data we had a conversation about exactly what to provide (as reported or operational). WSJ asked us to provide P/E figures based on operating earnings. Specifically provide P/E data based on trailing 12 month diluted EPS from continuing operations.

However, we have been in recent conversation with WSJ about converting to ‘as reported data’, as we feel this is a more appropriate figure to use. Just recently we started sending them both sets of figures each week (operating and as reported). Obviously today they are still using operational data, but that may change soon.

Thank you for your message.

Draw your own conclusions to why the WSJ continues to print this data in error. Since this whole thing started, the final numbers are out and the actual trailing earnings for the S&P during Q4-08 is operating 18.24 and GAAP of 60.70. The previous 4 quarters earnings are Operating $49.51 and GAAP $14.88.

The real news is that since 1936 - the highest GAAP, or actual trailing earnings was 46.50 back in 2001. We all know where the market went after that! Now, Q4-08 just printed 60.70 and Q1-09 may print 119, Q2 @ 127. and Q3 at 1936...

The last print I saw from the WSJ was... roll the drums... 13.09... Crazy!