Developed by Nobel Laureate James Tobin, the Q Ratio is a popular method of estimating the fair value of the stock market. 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 2011 Q2) 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).

*Click to enlarge*

## 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 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 157% 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 its 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, 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 estimates for the more recent months based on a combination of changes in the VTI (the Vanguard Total Market ETF) price changes 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 42% in the arithmetic-adjusted version and 54% in the geometric-adjusted version. 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 of Q has been associated with several market tops in history — the Tech Bubble being the notable exception.

Please see the companion article 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.