From: John Conover <john@email.johncon.com>
Subject: Re: script that does the same thing as tsinvest?
Date: 14 Dec 2000 19:25:40 -0000
As kind of an aside, it is fairly easy to show that most stocks on the
American exchanges have optimal growth in value, and have optimal
risk for investors.
The rms, (root mean square of a stock's price fluctuations,) is the
volatility, which is, also, the risk of investing in the stock.
The avg, (average of the stock's price fluctuations,) is the gain in
value of a stock, which is what one gets for taking the risk and
investing in the stock.
It can be shown, (using information-theoretic methodologies,) that
optimal, (meaning maximum,) growth in the price of a stock occurs when
avg = rms^2. If rms > sqrt (avg), the growth will be less, and if avg
< rms^2 it will be less, too.
And where do stocks run on the American exchanges?
Using the -r option to tsinvest, the "typical" stock's avg is
0.000949, (I just averaged them up, for all stocks.) The average rms
for all stocks, (again, just averaging them all up,) is 0.027238.
What is the optimal rms for an avg of 0.000949? Taking the square root
of the avg, the optimal rms = 0.0308058436, which is within 10% of
perfection.
What does this mean?
It means, that on the average, the typical American company's
executive suites are mitigating the risk of doing business almost
perfectly, and growing the company's market capitalization almost
perfectly, (it is best to err for avg to be ever so slightly greater
than the square root of rms-there is never any reason for rms > sqrt
(avg), which is the hallmark signature of a naive executive suite-it
is the signature of throwing caution to the wind.)
John
BTW, throwing caution to the wind can be a valid strategy in the short
run, sometimes with huge run ups in market capitalization-for a
while. Unfortunately, an executive suite can not remain a fugitive
from the laws of probability forever, and the inevitable eventually
happens when the humbling experience of a stock price crash occurs.
The dot-com companies are a notable example.
John Conover writes:
>
> Note that the model used is very close to compound interest in a
> savings account, with variable rates-you just don't know what the
> interest rate, (which can be negative,) will be tomorrow, or the next
> day.
>
> If there are no fluctuations, (i.e., avg = rms,) then:
>
> P = ((avg / rms) + 1) / 2 = 1
>
> (i.e., the likelihood of an up movement is 100%, or a certainty,) and:
>
> G = ((1 + rms)^P) * ((1 - rms)^(1 - P)) = 1 + avg
>
> which is the formula for compound interest, i.e., after n many days,
> the value of the investment would be (1 + avg)^n.
>
> John
>
> BTW, note that the interpretation of the root mean square of the
> fluctuations, rms, is slightly different than that of Black-Scholes.
>
> The Black-Scholes model uses the rms to be the square root of the sum
> of the square of the fluctuations minus the average, avg, (i.e., the
> variance.) This is the risk of investing, and if it is zero, (i.e.,
> avg = rms,) there is zero risk. This method of computing rms is the
> "standard" from probability theory, and larger rms means more risk.
>
> The method of computing rms in tsinvest is not to subtract the avg
> from the square of each fluctuation since tsinvest is based on finding
> the probability of an up movement, i.e., the Shannon Entropy. The
> value avg is the offset of the median of the fluctuations, which are
> assumed to have a normal distribution, with a standard deviation of
> rms.
>
> Although different methods, in reality, they are very close to being
> the same since rms >> avg by several orders of magnitude for equity
> prices.
>
> John Conover writes:
> >
> > The numerical methods used in tsinvest are quite straight forward, and
> > most can be done in a spread sheet.
> >
> > There is, also, a set of 60 some programs that can be used for general
> > fractal analysis at http://www.johncon.com/ndustrix/utilities.html, or
> > they can be downloaded as a tape archive from
> > http://www.johncon.com/ndustrix/archive/fractal.tar.gz.
> >
> > The tsinvest sources were, largely, cut-and-stick from the sources to
> > these programs.
> >
> > A possible scenario to automatically pick stocks might be:
> >
> > To find the marginal increments, (i.e., the fluctuations,) of a
> > stock's price, use the tsfraction program.
> >
> > To find the average increase in value, use the tsavg program.
> >
> > To find the risk of the investing in a stock, (i.e., the root mean
> > square of the fluctuations,) use the tsrms program.
> >
> > which is the two values used by tsinvest.
> >
> > So, if sprice is the name of a file containing the price of a stock
> > over time:
> >
> > tsfraction sprice | tsavg -p
> >
> > would print the average increase in value of the stock, avg, and:
> >
> > tsfraction sprice | tsrms -p
> >
> > would print the risk of investing in the stock, rms.
> >
> > Then, the Shannon Entropy, (or Shannon Probability, i.e., the
> > likelihood of an up movement,) P, would be:
> >
> > P = ((avg / rms) + 1) / 2
> >
> .
> .
> .
> > To calculate the gain, G, in value of a stock, use the tsgain program:
> >
> > tsgain -a avg -r rms
> >
> > which, as a stock picker, bigger values are better. All it does is
> > solve the equation:
> >
> > G = ((1 + rms)^P) * ((1 - rms)^(1 - P))
--
John Conover, john@email.johncon.com, http://www.johncon.com/