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/

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