From: John Conover <john@email.johncon.com>

Subject: forwarded message from Kimberly Bodelson

Date: Wed, 22 Jan 1997 21:34:30 -0800

In case you are curious, Per Bak is a notable person in the field of computer mediated financial instrument trading, (ie., programmed trading.) Brownian motion, or random walk fractals (what most programmed trading methodologies are based on,) are but a simple subset of a mathematically sophisticated science. Random walk modeling provides modest gains over analytical methods of stock fundamentals. One of the issues is that random walk fractals assume that a Gaussian distribution of the normalized increments will adequately model equity prices-like, over a 40 year period, or so. As it turns out, this is an adequate model to somewhat beyond 3 sigma, or about 1 part in 1,000, (which is very good by engineering standards.) However, beyond 3 sigma, we have more drops, (October of 1927 and 1989 for example,) than can be accounted for, according to the statistics of a Gaussian distribution. These, traditionally, have followed "bubble" run ups in stock prices, (similar to where we are at the present-but the run down does not always happen; sometimes the market just stalls for exceeding long periods, for example, 1930-1955, and 1966-1984.) There have been a lot of theoretical proposals for the minute discrepancy; it is created by a chaotic strange attractor, (fractal systems are a subset of chaotic systems-which exhibit non-periodic cyclic phenomena, like attractors that jump back and forth, strangely and unpredictably, like the weather, for example); correlation phenomena, (from catastrophe theory, like social upheaval, for example); etc. Bak's proposal is interesting because it is simple and makes sense, both mathematically and economically. John BTW, the reason for the interest in the discrepancy is that by anyone's analysis, we are in a bubble, and folks want to be ready to measure it when, and if, it happens to understand the phenomena. BTW, there are an enormous number of noise traders. BTW, FYI, noise trading depends on the fact that a fractal with Gaussian distributed increments is mean reverting. People's heights are mean reverting, for example. Although the offspring of a tall person may be taller than average, his height will be less than the parents, on average, ie., offspring's height will revert to the mean. (A graph of such things has a bell curve distribution, of which a Gaussian distribution is one such-but not the only one. If you think about it, that is the way bell curves are made. Something can not be mean reverting, or ergotic in the technical vernacular, without having some kind of bell curve distribution.) Vice versa for small parents. So, what you do is measure the daily increments of the entire stock exchange, and sort by the stocks dropped the most in value, and invest in the 25-40 stocks that dropped the most. (If you think about it, and you were betting on the greater heights of offspring, you would bet on parents that are shorter than average, because their offspring, on the average will be taller, and you make money on folks who are taller than their parents-as an analogy.) Why 25-40 stocks? because you want your capital to grow with an average normalized increment that is the root mean square of the normalized increments, squared. If you do not do this, (its the old f = 2P - 1 Shannon probability stuff,) you will have great wealth, instantly, and then loose it all. (In this scheme, the volatility of your wealth is very high-you moderate it by the fact that volatilities, which you are playing, add root mean square, and that is how you lower the volatility of your wealth. A fact that is used in electronics extensively. Lower the band width of a system the signal is not effected, but the noise goes down with the square root of the bandwidth.) So, how well do noise traders do? Very well in a bubble run up, (they are probably creating it,) with a typical gain of 2-3X per year, or better. But suppose the bubble pops, and one day all 25-40 stock's prices get cut in half? And if you are playing the optimal, (f = 2P - 1, measured with an accurate statistical estimate)? You would have to settle for a more conservative 40% growth per year, (recent numbers,) and the big drop would effect your portfolio value by only about 10%. Which is better? Noise trading in the short run, but you are doomed to loose. The best that can be done in the long run is f = 2P - 1. So, I would imagine that there will be some unhappy noise traders, eventually. (Eventually is 15 years, plus, according to statistical estimation theory.) BTW, there is another way of doing it, and that is the theory of bold play, which can even be better than noise trading in up bubbles. But that is another story ... (I'll give you a hint. Set how much money you want, and if you reach it you quit playing, or you go broke, and quit playing-which ever comes first. The value you want is called K. If your capital is less than K / 2, you bet half your capital. Else, you bet K - your capital. You will probably loose, but you will maximize your chances of making K, before going broke. Your capital will assume a "devil's staircase" as a function of time. It is an interesting function-for example, if you want to increase your capital by a factor of 10, the expected number of plays is less than 25, but your chances of making your goal is about 1 in 10, in 50/50 odds games. Interestingly, it works with unfair games, too. It is the method of choice for professionals gaming in Las Vegas, or Reno, who are trying to break the bank. The devil's stair case is an interesting mathematical anomaly. Not well behaved at all. It is a fractal with a weird dimension, and is self-similar and self-affine, meaning it has no scale; its derivative vanishes almost everywhere except at values which form a Cantor set.) ------- start of forwarded message (RFC 934 encapsulation) ------- Received: (from john@localhost) by johncon.com (8.6.12/8.6.12) with UUCP id JAA25656 for john@email.johncon.com; Wed, 22 Jan 1997 09:45:16 -0800 Received: from sfi.santafe.edu by netcomsv.netcom.com with SMTP (8.6.12/SMI-4.1) id JAA05665; Wed, 22 Jan 1997 09:41:44 -0800 Received: by sfi.santafe.edu (4.1/SMI-4.1) id AA05769; Wed, 22 Jan 97 10:18:56 MST Message-Id: <9701221718.AA05764@sfi.santafe.edu> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-activities-announce@santafe.edu Precedence: bulk From: ksb@santafe.edu (Kimberly Bodelson) To: activities-announce@santafe.edu Subject: SFI Colloquium Series--Per Bak (Fri, 1/24, 4:00 PM) Date: Wed, 22 Jan 97 10:18:50 MST The Santa Fe Institute Colloquium Series is pleased to present A Talk by Per Bak presented by Per Bak Niels Bohr Institute. Friday, January 24, 4:00 p.m. SFI Main Conference Room ABSTRACT Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which fail to account for non-Gaussian statistics. A simple model is constructed, and it is argued that the the variations may be due to a crowd effect, where agents imitate each others behavior. The interplay between "rational" traders whose behavior is derived from an analysis of fundamental analysis of the stock, and "noise traders", whose behavior is governed solely by studying the market dynamics, is investigated. When the relative number of noise traders is large, "bubbles" often occur. When the number of rational traders is large, the market is generally locked within the price range they define. || 0======///===>>===========\\//============<<===\\\======0 \/ Kimberly S. Bodelson 505-984-8800 (phone) Santa Fe Institute 505-982-0565 (fax) 1399 Hyde Park Road ksb@santafe.edu Santa Fe, NM 87501 http://www.santafe.edu USA || 0======///===>>===========\\//============<<===\\\======0 \/ ------- end ------- -- John Conover, john@email.johncon.com, http://www.johncon.com/

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