**Quick take:** Based on data extrapolations through the end of July, the Q Ratio is 72% above its arithmetic mean and 85% above its geometric mean. If we use the calculation method of Nobel Laureate James Tobin, the ratio is 90% above its arithmetic mean and 108% above its geometric mean.

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 Financial Accounts of the United States, which is released quarterly.

The first chart shows Q Ratio from 1900 to the present. I've calculated the ratio since the latest Fed data (through 2014 Q1) based on a subjective process of extrapolating the Z.1 data itself and factoring in the monthly averages of daily closes for the Vanguard Total Market ETF (NYSEARCA:VTI).

## 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 36 (Market Value) divided by Line 33 (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 0.68. 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 1.64 - which suggests that the market price was 141% above the historic average of replacement cost. The all-time lows in 1921, 1932 and 1982 were around 0.30, which is approximately 55% below replacement cost. That's quite a range.

Note that the latest Q-Ratio is now higher than any of the peaks preceding the Tech Bubble.

## 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 76%. This analysis makes the Tech Bubble an even more dramatic outlier at 160% above the (geometric) mean.

## Extrapolating Q

Unfortunately, the Q Ratio isn't a very timely metric. The Z.1 data is over two months old when it's released, and three additional months will pass before the next release. To address this problem, I've been experimenting with estimates for the more recent months based on a combination of changes in the VTI (the Vanguard Total Market ETF) price (a surrogate for line 36) and an extrapolation of the Z.1 data itself (a surrogate for line 33).

## The Message of Q: Overvaluation

Based on the latest Z.1 data, the Q Ratio at the end of the first quarter of 2014 was 1.11. Four months later, at the end of July, the broad market was up about 5.1%. My latest estimate would put the ratio about 72% above its arithmetic mean and 85% above its geometric mean. Of course, 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 is close to the vicinity of market tops, with Tech Bubble peak as an extreme outlier.

For a quick look at the two components of the Q Ratio calculation, market value and replacement cost, here is an overlay of the two since the inception of quarterly Z.1 updates in 1952. There is an obvious similarity between market value and a broad market index, such as the S&P 500 or VTI. Price is the more volatile of the two, but this component can be easily extrapolated for the months following the latest Fed data. Unfortunately, the less volatile replacement cost is not readily estimated from coincident indicators.

I added the regressions through the two data series to help illustrate the secular trend toward higher valuations.

**Footnote on Z.1 Revisions:** The Fed's Z.1 Financial Accounts of the United States is subject to revisions with each release. Of the two metrics used in calculating the Q-Ratio, line 33 ("corporate equities; liability" aka "Replacement Cost") is subject to significant revisions. In Q2 2013, the data for this metric was substantially revised in light of the addition of the catch-all for intangible assets "Intellectual Property Products" to the equation. Here is the Fed's note on the change:

Data for investment and depreciation flows and capital stocks of all sectors have been revised to reflect BEAs new concept of fixed assets as part of the comprehensive revision. Under the new concept, fixed investment now includes expenditures for research and development and entertainment, literary, and artistic originals. Reflecting this change, a new category called intellectual property products is now shown on tables B.100, B.102, B.103, R.100, R.102, R.103 and in the Integrated Macroeconomic Accounts. The new category includes the two new items plus expenditures on software.

The effect has been a systemic lowering of the Q-Ratio.

Without the intellectual property adjustment, the Q-Ratio at the end of the first quarter of 2014 would have been 1.24 and would be 1.30 at the end of July. That would put it 82% above its arithmetic mean and 98% above its geometric mean

The chart below shows the Q-Ratio using a calculation method shared with me a few years ago by John Mihaljevic, formerly Dr. James Tobin's research associate at Yale. It is based on several values from the Z.1 data and does not factor in intellectual property. The Q Ratio using this method of calculation is 90% above its arithmetic mean and 108% above its geometric mean.

Does it make sense to exclude intellectual property from the Q-Ratio? An email I received from a professional in the industry makes a cogent case for excluding intangible property:

One firm's competitive advantage (or intangible capital) is another's competitive disadvantage (or negative intangible capital). It is a zero sum.