From: John Conover <john@email.johncon.com>
Subject: Re: (no subject)
Date: 3 Aug 2001 17:06:04 -0000
Why do industrial markets and stock prices work the way they do?
As with other sciences, the empirical answers were discovered before
the questions were formalized.
There are URL links on the tsinvest home page,
http://www.johncon.com/ntropix/, for those that made significant
contributions to the science of entropic economics.
The reason that industrial markets work the way they do was formalized
in 1965 by the economist Paul Samuelson in "Proof that Properly
Anticipated Prices Fluctuate Randomly". It was a monumental
achievement in abstract applied mathematics. Basically, in a nut
shell, it says that if a system is complex enough, (in our case,
enough customers and enough competitors in a market place,) the
marginal increments of the industrial market, (or stock price, or
GDP,) will have a normal, (or Gaussian,) bell shaped distribution.
The randomness comes from the self-referential properties of everyone
attempting to determine what everyone else is going to do in the
future.
Samuelson established the isomorphism between arbitrage systems, (the
formal name for things like stock and industrial markets, GDPs, etc.,)
and the stochastic calculus. It was not a new idea-Louis Bachelier had
proposed it in 1899 based on empirical evidence.
In 1956, J. L. Kelly, Jr., in "A New Interpretation of Information
Rate," established the isomorphism between Claude Shannon's
information-theoretic concept of a symmetric binary communication
channel and the characteristics of arbitrage systems. It was a stroke
of genius-it defined how the variables derived by stochastic calculus
could be used for optimization of business and financial
operations. Without Kelly's contribution, the variables would have
been just intellectual curiosities-Kelly defined how to pragmatically
use them to solve operational problems.
Thus, the two most important concepts of twentieth century mathematics
were drug in to formalize the concepts of modern entropic economics.
But the mathematicians had beat everyone to the punch-in 1713 Jakob
Bernoulli, in "Ars Conjectandi,", with contributions a little later by
Abraham de Moivre in "The Doctrine of Chances," had formalized the
mathematics used to this very day in entropic economics.
John
BTW, there is an enormous wealth of information about entropic
economics on the Internet-its accessible through your favorite search
engine-http://www.google.com, if you don't have one. You will usually
find the stochastic calculus most often associated with modern
physics-its the mathematical "engine" of the quantum
mechanics. Information theory is most often associated with the fields
of electronics and communications. As a starter, search for the words
"Black Merton Scholes", and "stock bubble". Also, search for the words
"financial engineering", which is another name for entropic
economics. Searching for the terms "financial derivative" is
worthwhile, too. Or, as a start:
http://www.johncon.com/ntropix/links.html
http://www.johncon.com/ndustrix/links.html
will probably suffice as a general survey.
The web page, http://www.johncon.com/ndustrix/utilities.html, has the
source code to sixty some programs used for analysis in entropic
economics. The document, http://www.johncon.com/ndustrix/archive/fractal.pdf,
was published using these programs on data from the US Department of
Commerce.
John Conover writes:
> So, how much confidence should one put in market forecasting models
> that use regression methodologies?
>
> For a typical industrial market, the average daily marginal increment
> is about 0.0004, and the deviation is about 0.02, (note that if those
> two numbers are equal, there is no risk, and the market is perfectly
> predictable-what these numbers say is that managing risk is the name
> of the game in industrial markets; not managing market growth.) Those
> numbers have been constant for the ten millenia of civilization.
>
> We know from the previously mentioned graphs, that the deviation adds
> root-mean-square, so at the end of a calendar quarter of 60 business
> days, the deviation for the quarter will be 0.02 * sqrt (60) = 0.15,
> or about 15%. The average adds linearly, so the quarterly average
> would be 0.0004 * 60 = 0.024, or a little over 2%.
>
> The probability, from information theory, that the future quarter
> would be about like last quarter would be ((0.024 / 0.15) + 1) / 2, or
> about 0.58, or just under 60%.
>
> So, when we set around in staff meetings, pondering the future based
> on the last quarter's pro forma, (or investing in a stock, based on a
> company's quarterly results,) only 6 times out of 10, on the average,
> will the conjectures materialize.
>
> Its sobering thought-that is only 10% better than using a tossed coin
> as a decision mechanism.
>
> John
>
> BTW, what fraction of the value of the company should be placed at
--
John Conover, john@email.johncon.com, http://www.johncon.com/