

Valuing US Equities and Ready Reckoner 
Introduction.
We have for many years been publishing every quarter an update on the valuation of the US stock market according to q and CAPE. We receive frequent questions as to how these are calculated and what are their current values.
On the lefthand menu we have not only published the regular quarterly update in word form but also made available to anyone who is interested an excel file which shows the Chart and the accompanying spreadsheets; we also provide an explanation showing how the data are compiled and how the calculations are made.
The spreadsheet (“q”) which can be found on Latest q & CAPE Data page, also has a ready reckoner which allows anyone to see how changes in the level of the stock market affect its current value between the updates which we post after the quarterly data are published by the Federal Reserve in their Financial Accounts of the United States (“Z1”), formerly known as the Flow of Funds Accounts.
We have encountered two, and only two, valid ways of measuring the value of the US stock market. A valid method must be testable and prove robust when tested. The tests that we have used, and we have so far been unable to think of any others, are set out in the two books listed below.
Valuing Wall Street: Protecting Wealth in Turbulent Markets by Andrew Smithers & Stephen Wright (published by McGrawHill in 2000).
Wall Street Revalued: Imperfect Markets and Inept Central Banker by Andrew Smithers (published by John Wiley & Sons in 2009).*
Other publications which are relevant to the valuation of markets are;
Irrational Exuberance by Robert Shiller (published by Princeton University Press in 2000).
Rational Pessimism: Predicting Equity Returns using Tobin’s q and Price/Earnings Ratios by Matthew Harney & Edward Tower (published in the Journal of Investing, Fall 2003).
The Basis of q and CAPE.
There are two possible approaches to valuing equities:
(i) The macroeconomic approach, which treats them as titles to the ownership of real assets and values them in line with their cost of production.
(ii) Valuing them as financial assets and therefore as the present value of all future cash flows to which the owner is entitled.
A truly satisfactory approach to value must encompass both and, allowing for the differences in the data sources, they need to agree. As you will see from the Chart, q and CAPE track each other closely and give very similar answers to the question as to how much the US stock market is over or undervalued at any time.
The Data Sources.
In order to calculate q we need to have an estimate of the current market value of nonfinancial companies (MV) and an estimate of their net worth (NW). The data sources for these are Stephen Wright’s work, Measures of Stock Market Value and Returns for the US Nonfinancial Corporate Sector, 1900 to 2002 (published in the Review of Income and Wealth 50 (4)) and that published by the Federal Reserve in Table B.102 of the Z1.
In combination we have data for q since the end of 1900. They are available on an annual basis since 1900 and quarterly since 1952.
In order to calculate CAPE we need to have estimates of the earnings per share (“EPS”) of quoted companies and of the consumer price index (“CPI”). These are regularly published by Robert Shiller on his website and, if we need to update them, we use the Standard & Poor’s website for EPS and BLS for the CPI.
EPS are published in nominal terms and, to avoid the distortions that might arise from fluctuations in the rate of inflation, they need to be adjusted to constant prices (EPS K).
CAPE is the ratio of EPS K measured by its average over a number of recent years (10 being the most usual) to EPS K measured since the data series start in 1987.
Calculating q.
On the attached excel file there is a spreadsheet labelled q. Column B gives the year ends for which the data are available, with the exception of the final entry, which is for the most recent quarterly data available. Column C gives the (unadjusted) value of q calculated from the data published by Stephen Wright. Column D is the (unadjusted) data published by the Federal Reserve in Table B.102 of Z1. It is the ratio of line 36 (Market value of equities outstanding) to line 33 (Net worth (market value) i.e. net worth adjusted for the impact of inflation; not the net worth at book value shown in B.102 line 46).
As the Federal Reserve makes from time to time adjustments to Z1, we link the most recent data published with the series published by Stephen Wright and this is shown in Column E. Column F shows the natural logarithms of Column E (i.e. logs to base e). The market values shown in B.102 line 36 include those of unquoted companies as well as quoted ones and the Federal Reserve statisticians value the former at a discount to the latter. The estimate of market value is therefore less than the equivalent value of quoted companies. The net worth data are estimated from the profits published by companies, which are habitually overstated (for an explanation of this see Chapter 9 of The Road to Recovery: How and Why Economic Policy Must Change by Andrew Smithers published by John Wiley & Sons Ltd. in 2013).
To allow for the undervaluation of market value and the overvaluation of net worth Cell F.124 shows the average (geometric mean) of q. Column G shows in logs the current value of q as a ratio to its own average and Column H shows this in natural numbers.
For those who like equations, the over or undervaluation of the US stock market is the extent to which q is greater or less than 1 when its value is calculated from:
q = (MVc/NWc) ÷ (MVa/NWa)
where
MVc is the current market value of US nonfinancial companies shown in Z1 Table B.102 line 36.
NWc is the current net worth of US nonfinancial companies shown in Z1 Table B.102 line 33.
MVa/NWa is the geometric mean of all previous year end values of MV/NW.
Calculating CAPE.
The spreadsheet labelled CAPE calc derives Columns B to F from Robert Shiller’s website (when appropriate we update this). Columns H and J adjust Column C (share price) and E (EPS) to constant prices. Column L is the geometric mean of EPS at constant prices over the previous 10 years. M is the Cyclically adjusted PE (measured by Column H divided by Column L). Column N shows the log values of Column N. Cell N 1729 is the average of the values in Column N and Cell O 1729 is the geometric mean of the values in Column O. (It is derived from the antilog of cell N 1729 (its exponential)).
Column O is the difference between the values in Column N and their own average shown in Cell N 1729 and thereby measures, in log numbers, the divergence from fair value shown by CAPE.
Column Q shows the year end values of Column N and these are the numbers shown in spreadsheet q. In this spreadsheet Column H shows, in natural numbers, the degree of misevaluation derived from q and Column K show these for CAPE.
Ready Reckoner for Changes in Stock Market.
As at the end of 2013 the S&P500 for q was 1848.357, Market Value from q was 1.734667, for CAPE was 1807.78 and the Market Value from CAPE was 1.757024
As at 9th April 2014 the S&P500 for q was 1872.179, Market Value from q was 1.757024, for CAPE was 1872.179 and the Market Value from CAPE was 1.828374
Columns F,G,H,I & J of lines 126, 127 and 128 of spread sheet q, have the above entries. Anyone wishing to update q and CAPE for changes in the S&P 500 can simply enter the new date in place of 9th April 2014 and the new S&P level; the values of q and CAPE should then change automatically to take account of the change in the stock market.
PS. Please let us know if you find any errors in the calculations. We try hard to avoid them but cannot guarantee success.
PPS. Please let us know if the explanations are unclear or if you have questions.
*Andrew Smithers and Stephen Wright teach students how to value the US stock market as part of the Didasko Course. Details can be found on www.didaskoeducation.org


