Seeking Alpha

Here's the latest update of my preferred market valuation method using the most recent Standard & Poor's "as reported" earnings and earnings estimates and the index monthly averages of daily closes for October 2010, which is 1171.58. The ratios in parentheses use the September monthly close of 1183.26. For the latest earnings, see the accompanying table from Standard & Poor's.

● TTM P/E ratio = 16.6 (16.8)

● P/E10 ratio = 21.4 (21.7)

The Valuation Thesis

A standard way to investigate market valuation is to study the historic Price-to-Earnings (P/E) ratio using reported earnings for the trailing twelve months (TTM). Proponents of this approach ignore forward estimates because they are often based on wishful thinking, erroneous assumptions, and analyst bias.

TTM P/E Ratio
The "price" part of the P/E calculation is available in real time on TV and the Internet. The "earnings" part, however, is more difficult to find. The authoritative source is the Standard & Poor's website, where the latest numbers are posted on the earnings page. Free registration is now required to access the data. Once you've downloaded the spreadsheet, see the data in column D.

The table here shows the TTM earnings based on "as reported" earnings and a combination of "as reported" earnings and Standard & Poor's estimates for "as reported" earnings for the next few quarters. The values for the months between are linear interpolations from the quarterly numbers.

The average P/E ratio since the 1870's has been about 15. But the disconnect between price and TTM earnings during much of 2009 was so extreme that the P/E ratio was in triple digits — as high as the 120s — in the Spring of 2009. In 1999, a few months before the top of the Tech Bubble, the conventional P/E ratio hit 34. It peaked around 47 two years after the market topped out.

As these examples illustrate, in times of critical importance, the conventional P/E ratio often lags the index to the point of being useless as a value indicator. "Why the lag?" you may wonder. "How can the P/E be at a record high after the price has fallen so far?" The explanation is simple. Earnings fell faster than price. In fact, the negative earnings of 2008 Q4 (-\$23.25) is something that has never happened before in the history of the S&P 500.

Let's look at a chart to illustrate the irrelevance of the TTM P/E for a consistent indicator of market valuation.

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The P/E10 Ratio
Legendary economist and value investor Benjamin Graham noticed the same bizarre P/E behavior during the Roaring Twenties and subsequent market crash. Graham collaborated with David Dodd to devise a more accurate way to calculate the market's value, which they discussed in their 1934 classic book, Security Analysis. They attributed the illogical P/E ratios to temporary and sometimes extreme fluctuations in the business cycle. Their solution was to divide the price by a multi-year average of earnings and suggested 5, 7 or 1-years. In recent years, Yale professor Robert Shiller, the author of Irrational Exuberance, has reintroduced the concept to a wider audience of investors and has selected 10 years as the earnings denominator. As the accompanying chart illustrates, this ratio closely tracks the real (inflation-adjusted) price of the S&P Composite. The historic average is 16.35. Shiller refers to this ratio as the Cyclically Adjusted Price Earnings Ratio, abbreviated as CAPE, or the more precise P/E10, which is my preferred abbreviation.

The Current P/E10
After dropping to 13.4 in March 2009, the P/E10 rebounded above 20. The chart below gives us a historical context for these numbers. The ratio in this chart is doubly smoothed (10-year average of earnings and monthly averages of daily closing prices). Thus the fluctuations during the month aren't especially relevant (e.g., the difference between the monthly average and monthly close P/E10).

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Of course, the historic P/E10 has never flat-lined on the average. On the contrary, over the long haul it swings dramatically between the over- and under-valued ranges. If we look at the major peaks and troughs in the P/E10, we see that the high during the Tech Bubble was the all-time high of 44 in December 1999. The 1929 high of 32 comes in at a distant second. The secular bottoms in 1921, 1932, 1942 and 1982 saw P/E10 ratios in the single digits.

Where does the current valuation put us?
For a more precise view of how today's P/E10 relates to the past, our chart includes horizontal bands to divide the monthly valuations into quintiles — five groups, each with 20% of the total. Ratios in the top 20% suggest a highly overvalued market, the bottom 20% a highly undervalued market. What can we learn from this analysis? The Financial Crisis of 2008 triggered an accelerated decline toward value territory, with the ratio dropping to the upper 4th quintile in March 2009. The price rebound since the 2009 low pushed the ratio back into the 1st quintile, and it is now positioned just below the lower boundary around 20. By this historic measure, the market is expensive.

A more cautionary observation is that every time the P/E10 has fallen from the first to the fourth quintile, it has ultimately declined to the fifth quintile and bottomed in single digits. Based on the latest 10-year earnings average, to reach a P/E10 in the high single digits would require an S&P 500 price decline below 540. Of course, a happier alternative would be for corporate earnings to make a strong and prolonged surge. When might we see the P/E10 bottom? These secular declines have ranged in length from over 19 years to as few as three. The current decline is now in its tenth year.

Or was March 2009 the beginning of a secular bull market? Perhaps, but the history of market valuations doesn't encourage optimism.

In response to the occasional request I receive for a real P/E10 based on the ShadowStats Alternate CPI for the inflation adjustment, see this chart, which suggests that the current market is fairly priced. On a personal note, I find the Alternate CPI version of the P/E10 interesting, but I think it is unreliable for estimating market valuation. Government policy, interest rates, and business decisions in general have been fundamentally driven by the official BLS inflation data, not the alternate CPI.

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Yet another approach, one which avoids the question of the "correct" inflation adjustment, is to use nominal values for calculating the P/E10. The is the method of analysis favored by by Bob Bronson, a market historian whose research is occasionally featured at dshort.com. For Bronson's rationale, see this post from May 5th. Thus I'm now including a monthly update of the nominal P/E10.

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The Q Ratio Indicates a Significantly Overvalued Market

The Q Ratio is a popular method of estimating the fair value of the stock market developed by Nobel Laureate James Tobin. It's a fairly simple concept, but laborious to calculate. The Q Ratio is the total price of the market divided by the replacement cost of all its companies. The data for making the calculation comes from the Federal Reserve Z.1 Flow of Funds Accounts of the United States, which is released quarterly for data that is already over two months old.

The first chart shows Q Ratio from 1900 through the first quarter of 2010. I've also extrapolated the ratio since June based on the price of VTI, the Vanguard Total Market ETF, to give a more up-to-date estimate.

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Interpreting the Ratio

The data since 1945 is a simple calculation using data from the Federal Reserve Z.1 Statistical Release, section B.102., Balance Sheet and Reconciliation Tables for Nonfinancial Corporate Business. Specifically it is the ratio of Line 35 (Market Value) divided by Line 32 (Replacement Cost). It might seem logical that fair value would be a 1:1 ratio. But that has not historically been the case. The explanation, according to Smithers & Co. (more about them later) is that "the replacement cost of company assets is overstated. This is because the long-term real return on corporate equity, according to the published data, is only 4.8%, while the long-term real return to investors is around 6.0%. Over the long-term and in equilibrium, the two must be the same."

The average (arithmetic mean) Q ratio is about 0.70. In the chart below I've adjusted the Q Ratio to an arithmetic mean of 1 (i.e., divided the ratio data points by the average). This gives a more intuitive sense to the numbers. For example, the all-time Q Ratio high at the peak of the Tech Bubble was 1.82 — which suggests that the market price was 158% above the historic average of replacement cost. The all-time lows in 1921, 1932 and 1982 were around 0.30, which is 57% below replacement cost. That's quite a range.

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Another Means to an End

Smithers & Co., an investment firm in London, incorporates the Q Ratio in their analysis. In fact, CEO Andrew Smithers and economist Stephen Wright of the University of London coauthored a book on the Q Ratio, Valuing Wall Street. They prefer the geometric mean for standardizing the ratio, which has the effect of weighting the numbers toward the mean. The chart below is adjusted to the geometric mean, which, based on the same data as the two charts above, is 0.65. This analysis makes the Tech Bubble an even more dramatic outlier at 179% above the (geometric) mean.

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The More Complicated Calculation of Tobin's Q

John Mihaljevic, who was Dr. Tobin's research assistant at Yale and collaborated with Tobin in revising the ratio formula, uses a more complex formula based on the Flow of Funds data for calculating Q. The formula is explained in detail at Mihaljevic's Manual of Ideas website. The chart below uses the Mihaljevic/Tobin formula for the Q calculation.

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I would make two points about the more intricate formula. First it produces results that are remarkably similar to the simple calculation (first chart above. Also, the chart here differs somewhat from the version posted at the Manual of Ideas website (reproduced here), even though my chart uses the Manual of Ideas calculation formula. I've corresponded with John about the differences, and he explained them as an artifact of undocumented revisions to the government's Flow of Funds data. The Manual of Ideas Q Ratio is updated quarterly when the latest Z.1 numbers are released, and no changes are made to the ratio for previous quarters. My charts were built from scratch with the historic Z.1 data with any undocumented revisions included.

Note: My calculations with the last two Z.1 releases confirm John's explanation of undocumented Fed tinkering with the older data. The changes are relatively minor, but they have resulted in over a dozen quarterly Q modifications ranging from -0.01 to +0.02, with the upward adjustments clustered toward the recent quarters.

Extrapolating Q

Unfortunately, the Q Ratio isn't a very timely metric. The Flow of Funds data is over two months old when it's released, and three months will pass before the next release. To address this problem, I've been making extrapolations for the more recent months based on changes in the market value of the VTI, the Vanguard Total Market ETF, which essentially becomes a surrogate for line 32 in the data. The last two Z.1 releases have validated this approach. The extrapolated ratios for July through October are 0.97, 0.92, 1.00 and 1.04.

Bottom Line: The Message of Q

The mean-adjusted charts above indicate that the market remains significantly overvalued by historical standards — by about 48% in the arithmetic-adjusted version and 60% in the geometric-adjusted version. Of course periods of over- and under-valuation can last for many years at a time.

Please see the companion article Three Market Valuation Indicators that features overlays of the Q Ratio, the P/E10 and the regression to trend in US Stocks since 1900. There we can see the extent to which these three indicators corroborate one another.

Disclosure: No positions