*by Doug Short and John Lounsbury*

Here is an combined perspective on three market valuation indicators routinely followed at dshort.com:

- The relationship of the S&P Composite to a regression trendline (more)
- The cyclical P/E ratio using the trailing 10-year earnings as the divisor (more)
- The Q Ratio — the total price of the market divided by its replacement cost (more)

This article first presents an overview and summary by way of chart overlays of the three and then looks at more individual details, as well as another long term measurement technique useful for making projections.

To facilitate comparisons, the Q Ratio and P/E10 have each been adjusted to their arithmetic mean, which is represented as zero. Thus the percentages on the vertical axis show the over/undervaluation as a percent above mean value, which I’m using as a surrogate for fair value. Based on the latest S&P 500 monthly data, the index is overvalued by 41%, 46% or 67% depending on which of the three metrics you choose.

The S&P regression data has been plotted as an area chart type rather than a line to make the comparisons a bit easier to read. It also reinforces the difference between the two line charts — both being simple ratios — and the regression series, which measures the distance from an exponential regression on a log chart.

The chart below differs from the one above in that the two valuation ratios (P/E and Q) are adjusted to their geometric mean rather than their arithmetic mean (which is what most people think of as the “average”). The geometric mean weights the central tendency of a series of numbers, thus calling attention to outliers. In my view, the first chart does a satisfactory job of illustrating these three approaches to market valuation, but the geometric variant has been included as an interesting alternative view for P/E and Q.

As frequently pointed out at dshort.com, these indicators aren’t useful as short-term signals of market direction. Periods of over- and under-valuation can last for years. But they can play a role in framing longer-term expectations of investment returns. At present they suggest a cautious long-term outlook and guarded expections. , these indicators aren’t useful as short-term signals of market direction. Periods of over- and under-valuation can last for years. But they can play a role in framing longer-term expectations of investment returns. At present they suggest a cautious long-term outlook and guarded expections.

**Taking a Closer Look at the Tobin Q Ratio**

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. Fortunately, the government does the work of accumulating the data for the calculation. The numbers are supplied in the Federal Reserve **Z.1 Flow of Funds Accounts** of the United States, which is released quarterly.

The first chart shows Q Ratio from 1900 to the present. I’ve estimated the ratio since the latest Fed data (through 2010 Q4) based on a combination of the price of VTI, the Vanguard Total Market ETF, and an extrapolation of the Z.1 data itself.

**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 0.71. In the chart below the Q Ratio has been adjusted 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 about 57% below replacement cost. That’s quite a range.

**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.

**Extrapolating Q**

Unfortunately, as mentioned earlier, 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, dshort.com has been making estimates for the more recent months based on changes in the market value of the VTI, the Vanguard Total Market ETF. In an effort to improve the estimates, it now uses a combination of the VTI price change and an extrapolation of the Flow of Funds data itself.

**Bottom Line: The Message of Q**

The mean-adjusted charts above indicate that the market remains significantly overvalued by historical standards — by about 67% in the arithmetic-adjusted version and 81% in the geometric-adjusted version. Of course, as we said previously, periods of over- and under-valuation can last for many years at a time, so the Q Ratio is not a useful indicator for short-term investment timelines. This metric is more appropriate for formulating expectations for long-term market performance. As we can see in the next chart, the current level of Q is close to several market tops in history — the Tech Bubble being the most notable exception.

Note: In addition to the Tech Bubble, the Q-value remained above the current level for much of the from 1900 to 1912 (there were two significant bear markets during that time span), 1928-1930 (before the horrific bear market that bottomed in 1932) and for most of 1963 to 1970 (followed by the mega bear 1973-74). However, the long lead times to get to the bear markets simply emphasize the deficiency of using the Q-ratio as a short-term timing tool (even short term as in 1-2 years in some cases).

**Adding the Shiller PE/10 to the Mix**

A preferred market valuation method at dshort.com uses the most recent Standard & Poor’s “as reported” earnings and earnings estimates and the index monthly averages of daily closes for March 2011, which is 1,363.61. The ratios in parentheses use the March monthly close of 1331.51. For the latest earnings, see the adjacent table from Standard & Poor’s.

● TTM P/E ratio = **15.9** (16.3)

● P/E10 ratio = **23.1** (23.6)

**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 say such estimates are often based on wishful thinking, erroneous assumptions, and analyst bias. Others find forward earnings estimates very useful. An excellent discussion of methods using one year forward earnings estimates has recently been presented by Jeff Miller, here and here.

**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. Follow these steps:

- Click the S&P 500 link in the second column.
- Click the plus symbol to the left of the “Download Index Data” title.
- Click the Index Earnings link to download the Excel file. 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 close to 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 unsuitability of the TTM P/E as a consistent indicator of market valuation.

**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 10-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 16.39. 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 13.3 in March 2009, the P/E10 has rebounded above 23. 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).

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 second quintile in March 2009. The price rebound since the 2009 low pushed the ratio back into the top quintile. By this historic measure, the market is expensive.

We can also use a percentile analysis to put today’s market valuation in the historical context. As the chart below illustrates, latest P/E10 ratio is approximately at the 88th percentile. If we leave out the Tech Bubble, the current P/E10 would be at 90.2%.

A more cautionary observation is that every time the P/E10 has fallen from the top to the second quintile, it has ultimately declined to the first 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? Previous secular declines have ranged in length from over 19 years to as few as three. The current decline is now in its eleventh year.

Or was March 2009 the beginning of a secular bull market? Perhaps, but the history of market valuations suggests a cautious perspective.

** Note 1:** For a fascinating look as several additional indicators of market valuation, see this monthly update by Jacob Wolinsky, whose ValueWalk.com website in included in my favorites.

** Note 2**: For readers unfamiliar with the S&P Composite index, see this article for some background information.

**What About Reversion to the Mean?**

About the only certainty in the stock market is that, over the long haul, over performance turns into under performance and vice versa. Is there a pattern to this movement? Let’s apply some simple regression analysis (see footnote) to the question.

Here’s a chart of the S&P Composite stretching back to 1871.

The chart shows the real (inflation-adjusted) monthly average of daily closes. We’re using a semi-log scale to equalize vertical distances for the same percentage change regardless of the index price range. The regression trendline drawn through the data clarifies the secular pattern of variance from the trend — those multi-year periods when the market trades above and below trend. That regression slope, incidentally, represents an annualized growth rate of 1.71%.

The peak in 2000 marked an unprecedented 157% overshooting of the trend — nearly double the overshoot in 1929. The index had been above trend for nearly 18 years. It dipped about 9% below trend briefly in March of 2009, but at the beginning of April 2011 it is 45% above trend. In sharp contrast, the major troughs of the past saw declines in excess of 50% below the trend. If the current S&P 500 were sitting squarely on the regression, it would be hovering just above 900. If the index should decline over the next few years to a level comparable to previous major bottoms, it would fall to the low 400s.

Another way to look at the cyclical behavior of stock markets is to plot moving averages. In the following discussion we’ll look at 10-year and 20-year moving averages for the DJIA (Dow Jones Industrial Average) using annual returns on the index (not including dividends) since 1896. This technique was last posted by one of the authors in the summer of 2008 using the annual returns for the years 1896 through 2007. At that time the conclusion was that the most probable outlook for the next several years (starting with 2008) was that U.S. stocks would see very limited accumulated gains and possibly losses. What is the conclusion three years later?

First, lets look at the moving average graph through the end of 2010:

The important observations from the graph include:

- There are 3 periods varying in length from 7 to 21 years where the 10-year moving average has exceeded the long term average annual return.
- The first two such periods of outperformance were both followed by long periods of under performance (16 and 20 years).
- The period from 1906 to 1923 (17 years) was also a period of under performance.
- The most recent period of outperformance ended in 2007.
- The previous periods of under performance have seen both the 10-year and the 20-year moving averages fall below 5%.
- The current 10-year moving average has also fallen below (well below) the 5% line.
- The 20-year moving average has not yet come close to 5%.

If we make the assumption that this period of underperformance will repeat the pattern of the previous cycles, what will it take over the next several years to get the 20-year moving average to get to or below the 5% line?

A clue is given when we look at the years that will be replaced in the 20-year moving average. When 2011 is added, 1991 will be dropped. In 1991 the DJIA index (without dividends) rose more than 20%, so when 2011 goes into the average a big number will come out. In fact the next nine years will see big gains drop from the 20-year average most years. The average return to be dropped over the next 5 years is 14.5% (dropping 1991-95); and for the following four years 22.5%. For the entire nine years 1991-99, the average gain per year was 18.2%.

The above observations mean that there might actually be positive returns for many of the next nine years and the 20-year moving average could still drop below the 5% line. To examine this possibility we have projected the intitial forward to 2020 with two assumptions:

- The long term average for DJIA (7.4%) will be achieved each year; and
- A gain in the DJIA Index will br 5% each year.

The following graph results:

While it is clear that the 20-year moving average would fall below the 5% well before 2020, the graph is extremely cluttered and so a shorter time line (2011 to 2020) has been plotted below:

So, while the current precautions regarding valuation using the two PE techniques and the Tobin-Q analysis are valid and should not be ignored, in the longer run (5-10 years) there are valid historical comparisons that would argue that an average return of 5% or more per year could well produce a pattern compatible with the three under performance cycles of the twentieth century. And, of course, dividends will only add to the index gains.

While not shown on the graphs, returns that average between 9% and 9.5% a year (before dividends) could produce a 20-year moving average that would just reach the 5% line but not go significantly below it.

Not all analysts are as optimistic. Many are expecting another decade of below average results. Ed Easterling has presented an excellent analysis which explains why the coming decade may have stock market performance that falls short of the 5% to 9% suggested here.

The outlook for the historical moving average analysis in 2011 is producing a more optimistic outlook than it did in 2008.

Bottom line: Remain watchful in the near term, but there are reasons for a good outlook over a longer time frame.

**Related Articles**

Regression to Trend: A Perspective on Long-Term Market Performance by Doug Short (at *dshort.com*)

Is the Stock Market Cheap? by Doug Short (at *dshort.com*)

Market Valuation: The Message from the Q Ratio by Doug Short (at *dshort.com*)

Using Forward Earnings Estimates by Jeff Miller

Profiting from Forward Earnings Estimates by Jeff Miller

Bull or Bear? Let History Be the Guide by John Lounsbury (at *Seeking Alpha*)

Consensus: A Groundhog Decade for Stocks by Ed Easterling