**Note from dshort**: I've revised this update with data from latest Flow of Funds report released on today.

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 calculated the ratio since the latest Fed data (through 2012 Q3) 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 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 1.78 — which suggests that the market price was 153% 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 173% above the (geometric) mean.

## 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 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 35) and an extrapolation of the Flow of Funds data itself (a surrogate for line 32).

## The Message of Q: Overvaluation

Based on the latest Flow of Funds data, the Q Ratio at the end of the fourth quarter was 0.90. Two months later, at the end of February, the broad market was up about 6.6%. My latest estimate would put the ratio about 40% above its arithmetic mean and 51% 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 still 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 Flow of Funds 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 intangibles:** I frequently receive emails asking about the absence of a line item for intangibles in my Q Ratio analysis. On this topic I defer to Andrew Smithers, who touches on the topic in the FAQs on his website:

Does the Existence of Intangible Assets Invalidateq?

No, the evidence is that that the aggregate value of intangibles, if any, does not change over time relative to the replacement value of tangible assets. This is shown by the mean reversion ofqrelative to its average. For an academic analysis see "What DoesqPredict?" by Donald Robertson and Stephen Wright, available on http://www.econ.bbk.ac.uk/faculty/wright.

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