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

Subject: Re: Fractal "bubbles", Re: Business News from Wired News

Date: 30 Dec 1998 22:34:15 -0000

John Conover writes: > > Since bubbles started this diatribe, and since I had the daily NYSE, > NASDAQ, and AMEX historical data loaded, I made a PDF graph of the > bubble run lengths, for all stocks, in all indices, for the last 27 > years. The graph includes the run lengths of the three equity markets, > the run lengths of a simulated fractal with a 60% day-to-day > persistence, (made with the tsfBm program-I should have used 58%, but > 60% is close enough,) and the run lengths of a theoretical random walk > fractal, which would be erf (1 / sqrt (t)). > So, what does all this mean about equity value bubbles? It would appear that the empirical evidence supports the assumption that equity values can be modeled as a simple random walk fractal, at least reasonably well, ie., that the frequency distribution of the duration, or run length, of bubbles is erf (1 / sqrt (t)), which, for t > 1, is about 1 / sqrt (t). It would, also, appear that the empirical evidence supports another characteristic of simple random walk fractals, ie., that the range of a bubble, (ie., the magnitude of the bubble into the future,) is proportional to the sqrt (t). (The constant of proportionality is the root mean square of the marginal returns.) So, we have formulas for the probability of a bubble's duration, and its magnitude. If we attempt to exploit an equity value bubble, how much money would be made, on average? It would be the probability of a bubble lasting longer than some time, t, times the amount of money that would be made at time t, ie., the magnitude of the bubble at time t. (The value of t is that time where we would want to sell out of the bubble-if we can optimize that, we can all be rich.) But there is a problem; (1 / sqrt (t)) * sqrt (t) = 1 since the two sqrt (t)'s cancel, ie., t has dropped out of the equation, meaning that there is no one time that is any better to sell out, than any other time. So, how much money is made when trying to "time the market", or exploit bubbles? On the average, none. On the average, you end up with exactly what you started with. So, the conclusion is that exploiting bubbles, or attempting to time the market is not a viable strategy for making money. John BTW, this does not mean money can not be made on bubbles, or timing the market-its a fractal, and lot of money can be made ... for a while. But on the average, the money made will be equal to the money lost. For a net gain of zero. Peter Lynch was right, making money in the equity markets is easy ... keeping it is the hard part. -- John Conover, john@email.johncon.com, http://www.johncon.com/

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