**Note from dshort**: The charts below have been updated based on the Federal Reserve Z.1 Flow of Funds Accounts release today, which includes data through the Q3. I have used the latest close of the Vanguard Total Market ETF to extrapolate the Q Ratio up to the present.

*The Fed routinely adjusts the data for earlier quarters without comment. Those adjustments — together with the new data for Q3 and extrapolations to reflect the Q4 rally to date — puts the Q Ratio at a level unprecedented prior to the Tech Bubble.*

* ***Background**

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 Accounts of 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 the end of Q3 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 0.30, 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 standardising 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 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 last two Z.1 releases have validated this approach. Based on the Flow of Funds data, at the end of the third quarter, the Q Ratio was 1.03. The extrapolated monthly ratios for October, November and December are 1.07, 1.08 and 1.12, respectively (the last calculated through today’s VTI).

**Bottom Line: The Message of Q**

The mean-adjusted charts above indicate that the market remains significantly overvalued by historical standards — by about 59% in the arithmetic-adjusted version and 72% in the geometric-adjusted version. Of course periods of over- and under-valuation can last for many years at a time.

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