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Great analysis. Could you do the analysis using the low of the S&P
instead of the close?
Regards
DanG '78
Gary Funck wrote:
>
> 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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>
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