From: John Conover <john@email.johncon.com>
Subject: ZDNet: eWEEK: Why faux Linux companies won't fly
Date: Mon, 19 Jun 2000 23:17:54 -0700
It is not exactly true that Linux stocks are *_significantly_* down,
(down, maybe, but not *_significantly_*, depending on how one looks at
it, of course.)
Here's why. Assuming a simple model, (actually, Black-Scholes, so we
can do it in our heads,) the chances that Linux stocks would be down
at least as low as they are, (down about 80%, on average,) is about
10%, in any three calendar month period.
The square root of the variance of the daily returns of LNUX and RHAT
runs a little over 8%, (about 3 times the average for all stocks on
the NASDAQ-about 1% of the stocks on the NASDAQ fall in the same
range.)
So, according to B-S, since the standard deviation of the drop would
be expected to be about 0.08 * sqrt (60) for about 60 trading days
since mid March, or about 62%, (i.e., 86% of the time, the drop would
be less than 62%.) Or, it would be a 1.29 sigma chance, for 80%, or
just under a 10% chance.
So, since the linux stocks have been on the market for about nine
months, what is the chances that we would would have seen at least an
80% drop that lasted for at least three months in those nine months?
How about 1 - (1 - 0.1)^6 = 47%, (because there are 9 - 3 = 6 ways of
doing something with a 90% chance of it not happening.)
Quite a significant probability.
Or, in rough numbers, according to Black-Scholes, (which is adequate
for these short term things,) what we are seeing had about a 50/50
chance of happening, sometime in the last nine months.
Note that the issue is the high variance of marginal returns, 8%. A
90% drop in a few months is very uncommon-about once in many centuries
for a single stock with a variance of 2% per day, but relatively
common for those running 8%.
(You can work through similar logic for a "typical" stock on the
NASDAQ with a variance of marginal returns of 2%, and you will find
that, on the average, in a year, a stock's maximum divided by its
minimum is about a factor of two-which is easy to verify, empirically;
it is one of the cornerstones to the Black-Scholes concepts.)
John
BTW, before you run out and invest in cheap Linux stocks, it is
disturbing that the Shannon Entropy, (i.e., the likelihood that a
stock's price will move up on any day,) over the entire nine months is
less than 50%, which means, that risk mitigation through
diversification in Linux stocks would have been a disaster-a
portfolio's value would have gone down *_more_* than *_any_* of the
stocks in the portfolio. (For this reason, there is no reason to
invest unless the Shannon Entropy is greater than 50%-but the day
traders look for other things besides investment quality-they are the
folks that make the variance of the marginal returns for Linux stocks
three times what they should be.)
http://www.zdnet.com/eweek/stories/general/0,11011,2587948,00.html
--
John Conover, john@email.johncon.com, http://www.johncon.com/