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

Subject: Re: forwarded message from John Conover

Date: Fri, 1 Nov 1996 15:25:52 -0800

John Conover writes: > > Yesterday, Garzarelli reiterated her prediction that the U.S. stock > market will crash right after the elections. Today, the UBS reiterated > their prediction that it won't: > > SINGAPORE - Contrary to popular belief, the U.S. stock > market is not on the verge of a crash or even major correction, > Union Bank of Switzerland (UBS) said. > Based on price earnings (PE) ratios, the U.S. equity markets > were only slightly overvalued at the moment, a group of UBS > economists told a briefing in Singapore. > > John > So, we have two very respected institutions, Garzarelli and UBS, with a very impressive set of credentials and historical track records, making conflicting predictions. There is also substantial evidence that there is a 58%, or so, chance that Garzarelli will be correct, and a 42% chance that the UBS will be correct. Of what use is that? Well it appears to present a bit of dilemma, since if you sell your portfolio, there is a 48% chance that the market will moved up, and you would not have participated in it, (ie., you would have lost money.) Likewise if you keep your portfolio, there is a 52% chance that you will loose money when the market moves down. Sounds like a probabilistic loose-loose scenario, huh? Not really. If you look at the probabilities, something like Garzarelli is predicting will happen every 741 business days, (ie., 3 sigma,) on average-a probabilistic number that has not changed since the U.S. Civil war. (We don't have records prior to that-but the same phenomena was observed in Holland in the 1600's when folks were investing heavily in tulip bulbs.) So, if you are an investor, you better have some prescription on how to address such issues. Modern economics theory does not look for underlying causes of these "surprises" in the equity markets. Here's why. Markets are considered to be something akin to pyramid games. For example, it is not P/E ratios that are important, per se, but the perceptions of the many agents participating in the market concerning the effect that P/E fluctuations has on their investment value, that determines the market dynamics. So, really, the market dynamics are caused by the agent's perceptions of the other agent's perceptions-which is self-referential. In modern economic theory, the perceptions of the agents are allowed to differ, as in the case of Garzarelli and the UBS. If we permit many agents to interact in the market, based on their perceptions of other's perceptions, it can be shown that[1]: 1) Since it is self-referential, the market investment process exhibits Godelian phenomena, ie., there is no "model" of the market that can be proposed that is consistent and complete[3 pp. 2]. (As a passing note, this indeterminacy is by no means an anomaly. On the contrary, it pervades all of economics and game theory[3 pp. 3].) 2) The market graph will be the same as a random walk, ie., a fractional Brownian fractal[1 pp. 29, 42][2 pp. 6][3 pp. 6]. This is a result of the dynamics of many agents operating on the market, each with different perceptions and expectations. It is the last statement that is the most important in our efforts to find a prescription on how to address "surprises" in the equity markets. Note that the last statement says that whatever we do, it will be done in a "noisy" environment, (fractional Brownian noise, to be exact.) Note, also, that this noise is caused by, or causes, (it is impossible to tell which-the first statement says that cause and effect are not distinguishable,) some agents to make decisions that other agents would consider inappropriate, based on their perceptions and experience. These two notes are very important concepts-and mean that the nature of the problem is information-theoretic. So, we now have multiple agents, each gaining information from a noisy environment, and making decisions on, (possibly incomplete,) information about the environment, and acting on those decisions, which in turn, affect the environment. Exactly the kind of thing that information theory was designed to handle[4]. And what does information theory tell us we should do? If we know the probability of making a correct decision in our noisy environment, we can calculate what the optimum fraction of our portfolio that should be invested in the equity markets. Obviously, we should not invest the entire portfolio, since if Garzarelli is correct, we would loose everything just after the election. Likewise, we should have some fraction of our portfolio invested, since if the UBS is correct, we could make money. Note that what we have to do is to SIMULTANEOUSLY maximize our gains and minimize our losses, (ie., exposure.) And how do we do that? If you measure the probability, p, of an agent making a correct decision, you will find it is 54% for the equities market. From information theory, (symmetric binary channel in a Brownian noise environment,) the optimum fraction of the portfolio to invest at any time, f, is: f = 2p - 1 or f = 8%. Note that it does not make any difference whether Garzarelli or the UBS is correct. (I didn't say the Garzarelli/UBS affair wasn't interesting, just that if you manage your portfolio right, it doesn't make any difference who i wins.) And, what else does information theory say about investing in multiple agent markets that create noise-ie., pyramid games? If we set up a simple model, where we have many alternatives of investment, and all investment markets are multiple agent markets with noise, and for simplicity, assume that p is the same for all markets, and equal to 54%, (not an unreasonable first order approximation in capitalist markets, by the way,) then: 1) Your investment portfolio should be made up of 12 categories, ie., currency, stocks, bonds, metals, etc. (Fancy that, just what CFO's know from experience.) So, how mutual funds compare with that when their diversity is only 2-stocks and bonds. (Hint, look at the pro forma of the top 50 mutual funds and compare them to the DJIA and S&P for the last fifteen years. You would have done much better by playing f = 2p - 1, and selecting your stocks with a dart thrown across the room at the WSJ.) 2) The stock category should consist of 12 stocks. (Fancy that, just what the brokers know from experience.) Naturally, you will find folks that made a killing in the last two years. (Which is not surprising, since it would have been difficult to loose money-not impossible, but difficult.) Ask them how they did in October of 1987. The folks doing f = 2p - 1 did very well, under the circumstances, and did extremely well the last two years, also. Note that p can be measured, dynamically, and your whole investment portfolio can be administered automatically using only the formula f = 2p - 1. At least in this simple case. Fancy that, we just invented programmed trading-note that it takes into account the aggregate perceptions and cognitions of the agents, and does not depend, per se, on anticipating what the market will do-in point of fact, that is impossible. Note, also, that the it does not depend on the market establishing an equilibrium for stock prices-for that, also, is impossible. Why impossible? It would not be a noisy environment if either were possible-and if you look at the graph of any stock's price, it just looks noisy. Now you have a prescription for handling the noise. (Whether it was created by Garzarelli/UBS, or any other source for that matter.) Of course now, if you have more that 8% of your investment portfolio invested in stocks, then maybe you should be worrying. John BTW, if you are running more than 8%, don't feel bad. You have a lot of company. Most of the PT's have been caving to greed the last two years-but when Garzarelli/UBS announced their "fantasies," everyone moved back to 8%-ASAP. [1] "Nonlinear Time Series, Complexity Theory, and Finance," William A. Brock and Pedro J. F. de Lima, To appear in "Handbook of Statistics Volume 14: Statistical Methods in Finance," edited by G. Maddala and C. Rao. New York: North Holland, forthcoming. Also available from http://www.santafe.edu/sfi/publications.", March, 1995. [2] "Competing Technologies, Increasing Returns, and Lock-In by Historical Events," W. Brian Arthur, Econ Jnl, 99, pp. 106-131, 1989. Also available from http://www.santa.fe.edu/arthur, June, 1988. [3] "Complexity in Economic and Financial Markets," W. Brian Arthur, Complexity, 1, pp. 20-25, 1995. Also available from http://www.santa.fe.edu/arthur, February, 1995. [4] "A New Interpretation of Information Rate," Bell System Tech. J., vol. 35, pp. 917-926, 1956. -- John Conover, john@email.johncon.com, http://www.johncon.com/

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