Re: forwarded message from William F. Hummel

From: John Conover <>
Subject: Re: forwarded message from William F. Hummel
Date: Fri, 14 Aug 1998 23:47:30 -0700

John Conover writes:
> or about an 11% growth per year, which is reasonable in comparison
> with the 14% predicted, above, (depending on one's point of view, of
> course.)

So, could we improve our model? Maybe. If you look at the model, there
are too many stocks. Why? Because, for the NYSE:

    avg = 0.00437

    rms = 0.00874

We can compute what rms' is by:

    rms = 0.00874 = rms' / sqrt (n)

or, n = 5.720824, which is about 6. But how can we justify that when
there are over 3,000 stocks in the NYSE composite. Easy, a little work
on the SEC corporate database at,
looking at the form 10Q's for the NYSE, we find that the NYSE is
dominated by about a half a dozen companies. (Look at GM's market
valuation which is directly reflected in the NYSE Composite index.)

So, the average stock would be:

    avg = 0.00437

    rms = 0.02090454


    P = 0.5104523

And, recalculating the characteristics of the exchange:

    P' = ((sqrt (6) * (0.000437 / 0.02090454)) + 1) / 2 = 0.5256027

    avg' = 0.000437

    rms' = 0.02090454 / sqrt (6) = 0.008534243

    G' = 1.000401

The simulation with these values gives:

    avg = 0.000452

    rms = 0.008590

    P = 0.5263097

    G = 1.000415

which is in very close agreement with the metrics of the NYSE. What
these numbers mean is that, for an average stock on the NYSE, there is
a 2% volatility, (ie., for 68.3% of the time, the daily movements of
the stock will be less than +/- 2% of its value,) and that over the
course of a calendar year, the average stock's maximum value divided
by its minimum value will be a factor of 2. Some will be less for a
short time, some more, but on the average, these numbers will
represent the stock's movement. Also, any portfolio's volatility will
be greater than the volatility of the index, and its growth will be
less than the growth of the index-at least in the long run.

So, bottom line, you can flee to quality and buy T-Bills, but, on
average, your portfolio will only grow half as fast, in the long run,
as if you bought equities. But if you buy a few equities, your
portfolio value will vary by +/- 50% over a year, in getting a long
term growth that is somewhat less than twice what T-Bills give
you. The magic solution, (actually, optimal,) would be to have 10
stocks, (but not many more,) comprising 40% of your portfolio value,
the remainder of your portfolio being T-Bills-at least in our simple
equity exchange model. That would make your portfolio grow the maximum
possible, with the minimum volatility and risk. This optimal solution
maximizes your gain, while, simultaneously, minimizing your risk
exposure. You get the best of both worlds.


BTW, if you talk to an institutional fund manager, or a really good
broker, he knows these numbers. There were known, intuitively, for
many decades. One of the triumphs of applying information-theoretic
means to the equity markets were formal proofs of such things. The
proofs were offered between 1956 and 1989. See the tsinvest(1) manual
page for particulars and bibliography.


John Conover,,

Copyright © 1998 John Conover, All Rights Reserved.
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