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/