From: John Conover <john@email.johncon.com>
Subject: Re: NASDAQ today vs DJIA of Great Depression
Date: 15 Feb 2001 04:42:35 -0000
Bjarte Haram writes:
> Have a look at the NASDAQ (1999-2001) vs DJIA (1928-1933) posted at:
>
> http://www.zealllc.com/
>
> It paints an interesting picture. Do you think we're heading the way the
> site's author thinks?
>
Ok, I'll take a shot at it.
If you overlay the DJIA on its self for modulus 4 years, there is a
similar graphical coincidence, 35% of the time, (8 out of 25 times in
the last century.) For modulus 4 minus 2 years, 56% of the time, (14
out of 25 times in the last century.)
No one knows why-those years are election years, or maybe its a
chaotic/NLDS thing, or cyclic phenomena, (but 2000 - 1929 = 71 which
is a prime number,) or when harvests come in moving the futures
markets; who knows?
Only once did one of these coincidences result in a prolonged
depression.
Its always easy to find statistical significance where there isn't
any.
The equity market crash of 29/30 probably didn't create the Great
Depression-it was a victim of it, (depending on who is telling the
story, of course.)
There are several significant differences between the current state of
economic affairs in the US and the Great Depression-by this time into
the Great Depression, the US equity market had lost 90% of it value,
asset values in the US had dropped by 60%, and the US GDP was down
45%.
Depressions like that are, indeed, a very rare event-using
Black-Scholes-Merton concepts to ponder the probabilities:
Between 7 September, 1929, and 6 June, 1932, the US equity markets
lost about 90% of their value, (DJIA values of 375.44 to 42.68.)
Most of that was the in the 400 trading days following October,
28'th and 29'th, 1929, (where the market dropped about 12% in each
of the two days, bounced back to being down only about 10%, and
then just constantly deteriorated for two years.)
The day-to-day fluctuations in the DJIA are about +/- 1%, rms,
(square root of the variance = root mean square, meaning that for
68% of the time, the fluctuations are less than +/- 1%,) so, since
the magnitude of bull and bear markets follows a square root
function in time, we would expect the DJIA to be about 0.01 * sqrt
(400), (meaning that if we look at all possible 400 day time
intervals of the DJIA, we would expect the increase, or decrease,
to be less than 20%, 68% of the time, at the end of 400 trading
days.)
So, 90% value deterioration would be 0.9 / 0.2 = 4.5 standard
deviations, or a probability of 0.00000339767, or once in 294,000
trading days, or about once every 1,200 years.
Call it a once a millennia probability.
Similarly for the NASDAQ for early this year:
The NASDAQ's went down, roughly, about 50% from mid March,
(5132.50 at its maximum, to 2642.49, about 170 trading days
later-and hasn't moved much since.) The deviation, (square root
of the variance = root mean square,) of the fluctuations is about
2% per day, (meaning that for 68.3% of the time, the day-to-day
fluctuations were less than 2%.)
The average magnitude of bull and bear markets follows a square
root function in time, so a standard deviation at the end of 170
trading days would be 0.02 * sqrt (170) = 26.1%, (meaning that for
68.3% of the time, the change in the index would be less than +/-
26% at the end of 170 trading days.)
Or, the current bear market is about a two sigma, (50% / 26%,)
affair-meaning that what we are seeing has about a 0.0228 = 2%
probability.
In other words, we would expect to see the NASDAQ down, at least
as much as its down now, (in a year,) twice in a century, or, on
average, about once every half-century.
Since the NASDAQ is a little over 30 years old, seeing it down this
far, (at least once in its history,) is well within the range of
expected probabilities.
So, comparing the NASDAQ's decline over the last year with the Great
Depression is probably jumping to conclusions-the probabilities just
aren't there to support the conjecture, (at least not yet.)
John
BTW, this doesn't mean that a Great Depression is not imminent-only
that its not probable-and it would be inappropriate to prognosticate
such an event based on the performance of the NASDAQ.
Assorted qualifications like the assumptions of ergodicity, no
leptokurtosis, a fractal dimension of 2, ya-de-da-da, are in order.
--
John Conover, john@email.johncon.com, http://www.johncon.com/