# Re: Rolling 10 or 5 year market performance question

From: John Conover <john@email.johncon.com>
Subject: Re: Rolling 10 or 5 year market performance question
Date: 1 Jan 2001 01:16:18 -0000

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Hi Taavo. A consequence of the EMH paradigm is that the dynamics of an
equity's price will exhibit Brownian motion fractal characteristics.

If that is assumed to be true, (and its probably a reasonable first
order approximation,) then from the derivation of the Law of Large
Numbers, (Abraham de Moivre/Jakob Bernoulli, circa the early 1700's,)
the fractal dynamics should should have bull, (or bear,) magnitudes
that are proportional to the sqrt (t), and run lengths, (i.e.,
durations,) that are proportional to erf (1 / sqrt (t)), which for t
>> 1, is approximately 1 / sqrt (t), (its the way the sample average
in iterated trials converges to the mean.)

Its the Black-Scholes assumptions and formulas-which, also, are based
on the paradigm of the EMH.

Further, such a fractal has a chance of returning to zero, (e.g.,
after a stock has been listed on an exchange, the chances of the
length of zero-free voids exceeding a given time-the presumption being
that a company of zero market capitalization would be
de-listed/liquidated/acquired,) that is proportional to the reciprocal
of the square root of time, (and then used the historical database of
the US markets for the 20'th century to see if the cumulative
distribution of the durations that companies were listed fit a 1 /
sqrt (t) function.)

I just used the EMH's fractal characteristics, but instead of
calculating options probabilities, calculated the probabilities of
zero-free run lengths.

John

traykoff@snet.net writes:
> In misc.invest.technical conover@rahul.net wrote:
>
> > BTW, empirically, the distribution of the duration that companies were
> > listed on the exchanges seems to be about a 1 / sqrt (t)
> > probability-half last less than 22 years, half more-a characteristic
> > that is consistent with the EMH.
>
> Can you explain how this is consistent with EMH?
>

--

John Conover, john@email.johncon.com, http://www.johncon.com/

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