# Re: What does the phrase "likelihood of an up movement" for a stock mean?

From: John Conover <john@email.johncon.com>
Subject: Re: What does the phrase "likelihood of an up movement" for a stock mean?
Date: 28 Aug 1999 19:32:58 -0000

```John Conover writes:
>
> John Conover writes:
> >
> > Someone ask the relationship between the Shannon Probability and the
> > likelihood of an up movement in the value of a stock. The Shannon
> > Probability, P, is calculated by finding the average, avg, and the
> > root mean square, rms, of the marginal increments in the value of a
> > stock:
> >
> >         avg
> >         --- + 1
> >         rms
> >     P = -------
> >            2
> >
> > where the t'th marginal increment at time t is:
> >
> >     V  - V
> >      t    t - 1
> >     -----------
> >       V
> >        t - 1
> >
> > ie., today's marginal increment in the value of a stock is today's
> > value, minus yesterday's, divided by yesterday's.
> >
>
> And that is the way the tsinvest program works, (well, it does a few
> more things, but that's the gist of it.) You can do it in Excel, or
> other spread sheet, too. You can get the daily closes of stocks from
> many sites on the Internet, like the investment section of Yahoo!, for
> example.
>
> The other formula needed is for the gain, G, in value of a stock:
>
>                  P            1 - P
>     G = (1 + rms)  * (1 - rms)
>
>

How well do these formulas work? At

http://www.johncon.com/john/correspondence/990204020123.28039.html

is a graph of the daily closes for the DJIA, from 2 January, 1900 to
14 June, 1993. The graph is overlayed with computer generated data
that has the exact same statistics, and the gain of both graphs.

Although there are discrepancies between the two graphs, the
similarities are remarkable-all the more remarkable since the computer
generated data was done with a random number generator.

Note the fractal characteristics of both graphs-how far, and how long
both graphs deviate from the gain, G, which is the long term growth in
value for both graphs. Although not trivial, there is a science for
these "bubbles."  See:

http://www.johncon.com/ntropix/FAQs.html#bubbles

John
--

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

``` 