P/E Ratios: and their relation to the 10year Bond Rate
see also P/E Ratios

If Earnings/Price  that is,
1/{P/E} Ratio
 is related to Interest Rates, then one
might expect P/E Ratios to be higher when, say, the long term Bond Rates are lower.
(Remember! Bond Rates were HIGH twenty years ago!
If we take the current
P/E as 25 (roughly the current S&P 500 P/E, as I write this), and assume it varies inversely
with the 10year treasury, we get this historical (and fictitious) chart of
earlier P/E ratios:
Compare to the actual historical P/E Ratios:
So, based upon historical Bond Rates, is the market overpriced?
>You're assuming a current P/E of 25? Why don't you
determine what the P/E should be, today?
Okay, here's what we'll do:
 Plot E/P (data obtained
here)
vs 10year Tbond Rate.
 Determine the
best fit.
 Use that (based upon data for the last thirty years or so) to determine what the current P/E ratio should be.
Here are the charts:
The Best Fit to the E/P vs Tbond data is the straight line:
E/P = 0.9402 (Tbond)  0.0048
Hence, we can get our P/E Ratio estimate from the
Magic Formula:
P/E = 1/{0.9402 (Tbond)  0.48%}
Here, we put (Tbond) = 0.052 if the Tbond Rate is 5.2%.
If we plot this for thirty years (actually Jan, 1970 to Dec, 2000) we get the following chart:



>So?
So, the current P/E Ratio should be ... uh, let's see, the 10year Treasury Bond Yield
(obtained
is 5.25% as of July 10, 2001 (that's today) so, from our
Magic Formula,
P/E = 1/{ 0.9402(0.0525)  0.0048} = 22
>Exactly?
Uh ... the Magic Formula gives: 22.4413999
>Hey! That's pretty close, isn't it?
Pretty close.

>So, this was your idea, right? I mean, to consider historical
long term bond ...
Uh ... no. It was suggested by Don S.


It's been dubbed the Fed Stock Valuation Model by
Yardeni,
after Greenspan's consultation with some model and subsequent irrational exuberance comment.
>So,
Greenspan
uses historical
E/P ratios to see if the market is overpriced?
Actually, I think, according to Yardeni, he uses 12monthahead earnings
instead of our 12trailing and ...
>So, why didn't you?
Uh ... wait'll I find the data ...
However, one could use the Estimated Earnings found
here, but these
often win prizes for the best fiction of the year. Just remember:
There once was an Index: S&P
Whose ratios evoked much glee
Pick two numbers at random
Divide them in tandem
And generate your own PoverE
For example, we could do this
 If Fair Value P/E is 24, and
 Estimated Earnings are $35.47, then
 S&P 500 should be 24 * 35.47 = 851.28 by year's end, so
 a current S&P 500 of 917.93
 makes the current S&P overpriced by 917.93/851.28  1 = 0.78 or 7.8%
>I take it that this magic formula is valid back to the beginning of time ...
Well, actually ... uh ... it's pretty lousy prior to 1970. For example, from 1953 to 2000 the
E/P vs 10year Tbond looked like this:
The goodness of the fit ...
>The goodness of the fit? Are we talking shoes or ...?
... is measured by Rsquared (see
Rsquared bumpf) and you can
see it's pretty lousy for this entire period. But it's interesting, eh? Look at the crash of
1987 where ...
>Am I supposed to be able to follow that
blue line?
Why not?
>Anyway, what does this 19532000 goodness of fit predict for the current P/E?
Don't ask.
Here, you can play with the magic formula:
1/{0.9402 (Tbond)  0.0048}
based upon 19702000 S&P500 data:
Get Bond Yields here.

Here, you can play with the magic formula:
1/{0.4936 (Tbond) + 0.0356}
based upon 19532000 S&P500 data:

>That's quite a difference! I mean, what good is ...?
If you'd like to see whether looking at the past 10 years will say something about the
next 10 years, take a gander at these charts which show the monthly oscillations of
E/P versus the 10year Tbonds ... and the "Best Fit" line:
>I don't think I'd like to use the past ten years to predict ...
... the next ten? I'm with you.
>So, how do these formulas compare to the actual P/E?
>Wow! The late 1990s were really out of whack!
Yes, and that has a name.
>Irrational Exuberance?
You got it!
'course, y'all may like to
generate your own P?E ratio(s)
I was surprised to learn that some calculate not E/P values, but use the
Average Earnings over the previous 10 years. Starting in 1970, this would give the following charts, comparing
E/P and E10/P vs Tbonds:
Since the correlation is better (using E10 rather than just E), we get:
Using :
1/{0.6492 (Tbond) + 0.0018}
based upon 19702000 S&P500 data:
Get 10year Treasury Rate here.

Then again,
Shiller
uses the "real, CPIadjusted" S&P500 and Earnings, assuming that CPI = 100 in Jan, 2000.
That means that each S&P500 and Earnings value, for month M, is multiplied by CPI(Jan/00)/CPI(M).
This gives:
Using :
1/{0.8552 (Tbond) + 0.0055}
based upon 19702000 S&P500 data:


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