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I ran a few experiments, using http://www.economagic.com and its "XY plot"
capability to try my hand at calculationg a current "fair value" for the S&P.
As an introduction, I focused on the period 1980-2002 period, which is
inclusive of the '82-'00 bull run. So, obviously any projection using this data
is going to be somewhat optimistic, and consistent with the assumption of a
continuation of an economic expansion that has been in place for some time. As
you'll see though, the projections still generally project fair values for the
S&P that are well below where the prices are at the moment.
I tried a number of regressions, looking at things like money supply, debt,
imports/exports, disposeable income, corporate after tax profits, GDP, GDP per
capita, real GDP, etc. as "drivers", or the independent variable in this simple
linear regression. I didn't try regressing *changes* against each other, simply
because that took more computational steps. You'll also note that there is no
compensation for dividend payout rates, or stock dilution here. As they say,
that is beyond the scope of this study. The following discussion looks at the
results of two of those regression studies: one using after tax coporate
profits, and the other using nominal GDP as drivers.
First, using the after tax corporate profits series, for the 1980-2002 time
period, we end up with the following regression results (see first attached
chart):
Y = S&P 500 Close
X = Corporate profits with inventory valuation and capital; GDP; Billions of
dollars SAAR
Y = -313.38212576326625842696629213 + 1.66846363325952*X
Std Err = .071687041060042
t value = 23.2742711735317
r = .928233476583702
R2 = .861617387050666
Standard deviation of errors = 152.307095246021
Number of observations = 89
An R-squared of .86 tells us that about 86% of the observations were consistent
with changes in after tax profits. Not a bad fit, but not a great fit either.
By this reckoning, the Q1-2002 after tax profits were 827.8B, and the fair
value of ths S&P is 1069 approximately, which is about 16% higher than the
current S&P reading of 921.
But, if we take a look at the regression chart, we see a rather linear looking
arrangement with the early data, but a lot of dispersion at the end. If we
narrow the focus of our regression to the 1980 to 1993 (second chart) era,
things come into better focus:
Y = S&P 500 Close
X = Corporate profits with inventory valuation and capital; GDP; Billions of
dollars SAAR
Y = -110.62928256932046428571428571 + 1.07865014658344*X
Std Err = 5.32068925800605E-02
t value = 20.2727521619572
r = .94014205932136
R2 = .883867091705008
Standard deviation of errors = 38.3818414558014
Number of observations = 56
A somewhat better fit. By this reckoning the S&P should trade at 781, or
about -16% below current levels.
Using the GDP series instead of after tax profits, for the period '80-'02, we
get a better overall fit than given by the after tax proftis:
Y = S&P 500 Close
X = Gross domestic product; Billions of dollars SAAR
Y = -524.97684896888425842696629213 + .169128595516886*X
Std Err = 6.5628017020173E-03
t value = 25.7707916825977
r = .940305844689056
R2 = .884175081556398
Standard deviation of errors = 139.341465438545
Number of observations = 89
But again, we see a lot of dispersion in the later data samples. By this
reckoning given the Q1-2002 GDP reading of 10449.8 billion, we arrive at a fair
value for the S&P of 1242, which is a whopping 35% above where we are now.
If we narrow our regression to the "old valuation" period of 1980 to 1993, we
get a much better fit on the data:
Y = S&P 500 Close
X = Gross domestic product; Billions of dollars SAAR
Y = -161.40023800868446428571428571 + 8.93034898893421E-02*X
Std Err = 2.57217271443495E-03
t value = 34.719087636757
r = .978326607794308
R2 = .957122951518318
Standard deviation of errors = 23.3217210909821
Number of observations = 56
Here, we can observe that for whatever reasons during the period 1980 through
1993, that the S&P price increased apace with increases in the GDP. Plugging in
the current GDP figures, we arrive at a fair value for the S&P of 771, which is
in good agreement with the value calculated using after tax profits for the
same time period, and -17% below current levels.
Note that I didn't have access to the current GDP or after tax profit figures,
and these were likely a percent or two higher that the Q1-2002 results.
By excluding dividend yields, real returns and other factors, we're probably
over-simplyfing and reducing the usefulness of these forecasts. Also, the
forecasts depend a lot upon our choice of data sample. I'm personally
comfortable using the 1980 to 1993 period, because it seemed to me that
conventional valuation metrics were more applicable to that time period, than
the exubrant 1995-2000 time frame. As a working number, I'd look at about 770
on the S&P to be "fair value" in the current economic environment, keeping in
mind that this is still a bullish projection.
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