*Note: The charts below have been updated with estimates based on the July close of VTI.*

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 Accountsof 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 April based on the price of VTI, the Vanguard Total Market ETF, to give a more up-to-date estimate.

## 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 0.43, which is 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.

## 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.

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 latest Z.1 release confirm John's explanation of undocumented Fed tinkering with the older data. My comparison of the March release for Q4 and the June release for Q1 shows changes to the raw data as far back as 1996! The changes are relatively minor, but they have resulted in 14 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 collaborating with Jacob Wolinsky to make preliminary estimates for the Q Ratio for use in his monthly valuation update. We've been experimenting with 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 latest Z.1 release has validated our approach. The Extrapolations for January through May were 0.95, 0.98, 1.04, 1.06 and 0.98, respectively. The new data gives a March number of 1.04 — exactly our forecast. The high of 1.06 is thus an extrapolation that matches the April interim high. Extrapolated ratios for May, June and July are 0.98, 0.92 and 0.98 respectively.

## The Message of Q

The mean-adjusted charts above indicate that the market remains significantly overvalued by historical standards — by about 39% in the arithmetic-adjusted version and 51% in the geometric-adjusted version. Of course periods of over- and under-valuation can last for many years at a time.

Please see 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.

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