From: John Conover <john@email.johncon.com>
Subject: Re: forwarded message from William F. Hummel
Date: Sat, 15 Aug 1998 02:06:16 -0700
John Conover writes:
>
> A lot of folks are invested very heavily in the likes of Yahoo. They
> used to be invested very heavily in the likes of Netscape. You ask a
> while back how folks lost money in the market. We know that the
> Shannon probability of Netscape, Yahoo, whoever, is about 0.51. And,
> how much of their investment portfolio should have been invested in
> such a stock? f = 2P - 1 = 0.02, or about 2%. Many of these folks were
> invested in only one or two stocks, (which our model says 10,
> minimum.) And, that is how they lost money. They picked the stocks
> right, made a lot of money, but the didn't hedge their bets by
> investing in many, and promptly lost a lot of money. Investing in
> equities is gambling. It is a lottery. Its not the cards you are
> dealt, or the stocks you pick, its how you manage (eg, hedge,) your
> money that counts. Literally.
>
I kind of bounced around a lot of economics tonight. Note that we
determined that equity indices are determined by macroeconomic
monetary policy, (the constants in our model were based totally on the
7% average T-Bill rate,) and then concluded that a totally speculative
lottery construct was the way the markets worked, ie., a fractal. It
would intuitively seem that these are a logical contradiction.
I will present a heuristic argument that this is not the case by
reconciling the two through neoclassical economics, ie., game
theory. It turns out that all three say the same thing-its the
unfounded interpretations that are in conflict, and often the subject
of argument.
The following will plagiarize a tautology by the Stanford economist,
Brian Arthur.
Suppose there is a bar, and a hundred people frequent the
bar. Unfortunately, the bar can only, comfortably, accommodate 60
people, (note that the bar is the ecology, and has resource
limitations, so there are allocation issues-the classic problem in
economics.) Also, note that, obviously, on the average, there will be
60 people go to the bar every night-this is called the Nash
equilibrium from neoclassical economic game theory. It is, also, a
Keynesian equilibrium of supply and demand, (the bar could raise
prices so that only 60 people would come.) But there is a problem. It
involves logic. If everyone decides to go to the bar on a given night,
no one should. And, if everyone decides to stay home, everyone should
go to the bar. (We just solved the game-theoretic problem, by the
way-everyone should go to the bar, 6 nights out of 10, but mix it up
where no one knows whether you are going or not-ie., a random process
is the optimal game-theoretic solution to the problem.) Note that it
is a self-referential logical argument. But both are true,
however. (Anytime you hear two mutually exclusive truths, you should
expect that the outcome, iterated over time, will be a fractal.)
There is one remaining detail. If we are the proprietors of the bar,
how do we do the operations? I mean, although the average occupancy 60
people, it fluctuates from night to night. How much beer do we buy?
Its random-a lottery. Its exactly like the stock market problem, (and
has the same solution-note that what we are saying is that the very
nature of economics requires macroeconomic, neoclassical game theory,
and fractal sciences-they are all dependent on each other. An iterated
neoclassical game, like the bar problem, produces a fractal-which, in
the long run has an average that can be manipulated through
macroeconomic agenda, ie., policy-like raising prices.)
With that out of the way, we can proceed to the assorted
arguments. They are epistomological in nature. The crutch of the
matter is whether a fractal, like bar occupancy, is a deterministic
system. I mean, if it is a random process, it can't be deterministic,
can it? Quite the contrary. Concider rolling dice. Prediction of the
outcome of a roll is dependent on physical principles, (inertia,
forces, masses, etc.) But by everyone's standard, rolling dice is a
random process. (In point of fact, summing the outcomes of rolls of a
die produces a fractal.)
The key to understanding the epistemological issues is that it was
assumed for 4 centuries, (since the time of Newton,) that a
deterministic system was a predictable system. Such is not the case.
Deterministic systems can exhibit randomness. And the characteristics
of such systems are frequently fractals.
There is another epistemological issue worthy of argument-that of
manipulating an economic system (be it national policy, or picking
stocks,) through averages, or macroeconomic strategies. In the
previous simulation, 100,000 days were used to determine the
averages. Why? because at 100,000 days, there was a 70% confidence in
the metrics. The issue here is that implementation of a macroeconomic
agenda will not result in immediate effects-in the case of the equity
exchange model, altering interest rates, conceivably, could take
centuries to produce a desired outcome.
John
BTW, someone actually worked through the accuracies required for
prediction of the outcome of a rolling die. It is, technically, a
chaotic system. If during the bounce of a die, it lands on an edge,
then very minute perturbations will make the die go from one
trajectory to another. At the instant the die hits the table on an
edge or corner, it is like a pencil balanced on its point-it could go
in any direction. On the third bounce of a rolled die, the
gravitational effects of the Moon and Sun must be included in the
prediction. Disregarding that that's the notorious 3 body problem that
has no closed form solution for prediction, on the 5'th bounce of the
die, the local masses of the croupier and spectators must be taken
into effect. On the 9'th bounce, relativistic effects must be
considered. On the 18'th bounce, the forces exerted on the die by
distant galaxies must be considered. And, on the 22'nd bounce, one
trips over Heisenberg's uncertainty, which means that the very act of
making the measurements for the prediction, one altered the universe
in such a manner that the measurements are invalid. The last statement
means at this point, it is a self-referential system, like the
occupants face in the bar problem. Same drama-different cast of
characters.
--
John Conover, john@email.johncon.com, http://www.johncon.com/