From: John Conover <john@email.johncon.com>
Subject: Decline in NASDAQ
Date: 12 Oct 2000 21:00:17 -0000
How bad is the decline? Since mid March, the NASDAQ has fallen about
40%. The variance of the returns for the NASDAQ typically runs a
little over 2% per day; so, using about 20 trading days per month,
from mid March to Mid October-about seven months, or about 140 trading
days-we would expect the index value to be +/- 24% per standard
deviation, (meaning that for 15.8% of the time we would expect it to
be above 24% gain, and 15.8% of the time, below 24% loss-the 24% came
from knowing that the magnitude of run lengths in a Brownian fractal,
which are self-similar, are equal to the square root of time, times
the daily variance, or sqrt (140) * 0.02 = 0.24.)
Or, 40% is about 40 / 24 = 1.67 standard deviations, or a probability
of one in 1 / 0.048 = 21; meaning that, on average, every 21 seven
month periods, (about 147 months, or 12.25 years,) we would expect to
see a decline, at least as bad as this one.
Not that bad when looked at in that way-depending on one's POV, and
who is telling the story, of course.
John
BTW, although the current decline is slightly faster than the
1930-1931 decline in the US equity markets, in the Great Depression
the market indices just continued to deteriorate for about a year and
a half-until the market capitalization had lost about 90% of its
value. Working through similar logic, (its Black-Scholes concepts,) it
turns out to be a once-a-millennia probability.
--
John Conover, john@email.johncon.com, http://www.johncon.com/