From: John Conover <john@email.johncon.com>
Subject: Re: U.S. recovery: Recession is certain, economists say
Date: 21 Sep 2001 22:28:47 -0000
So, bottom line, I would suppose that the US equity market indices
will react to the recent tragic events with a decline in value of
about 25%, from the beginning of this week, through the end of next
week, or so-with around a 50/50 probability, (50% chance it will be
better, 50% chance worse.)
Note that prognosticating much worse, (like the tragedy will create a
Great Depression-which is being implied in the media,) is
unfounded. It might, and it might not-such things are unknowable.
However, such things as the Great Depression are vary rare events,
indeed-like once in centuries. See:
http://www.johncon.com/john/correspondence/010309164911.31439.html
for particulars.
John
BTW, how bad is a 25% decline?
On Friday, October 16, 1987, the DJIA closed at 2246.74. The next
trading day, on Monday, October 19, 1987, it closed at 1738.74-a
decline of 23% in a single day; the largest single day loss in the
history of the US equity markets.
A little over one year later, on January 24, 1989, it had gained it
all back, closing at 2258.43.
And, a little over a decade later, on Friday, January 14, 2000, it
closed at its all time high of 11723.00.
John Conover writes:
>
> The attached expresses a lot of concern about the number of
> consecutive "down days" in the US equity market indices.
>
> Bear in mind that the current tragic circumstances are a four sigma
> catastrophic event-it would be expected that the marginal increments
> of the market indices, assuming statistical independence, (a
> reasonable assumption,) have enough nearly consecutive negative
> movements to equal the probability of a four sigma event-about one
> in 50,000, or so, or about 16, since 2^16 = 65,536, (working with
> integer values, and round numbers.)
>
> So, we would give the markets a 50% chance a positive movement before
> mid-to-end of next week, and a 50% chance of no positive movements
> until after.
>
> So, the market's reaction to the recent tragic events is not
> to be unexpected.
>
> John
>
> BTW, all I'm doing here is working with the tails of the distributions.
> I counted how many catastrophic events, (of at least a certain
> significance,) there were in a large time interval. The probability
> of such a catastrophic event would be the number of events divided
> by the length of the time interval.
>
> I assumed that the equity markets react to events, which occur
> randomly, (as opposed to generating randomness their self,) meaning
> that the tails of the distributions of the increments of the market
> indices will have the same probability distribution, as the events
> that created them. I assumed statistical independence, meaning a
> normal distribution-since, historically, market indices can be
> expediently modeled in the short term, using such a distribution.
>
> The tails and standard deviation of the normal curve have to be
> related by sigma values, (otherwise, its not a normal curve's
> frequency distribution-by definition-and, empirically, we know
> that it is a reasonable assumption based on substantial
> theoretical foundations.)
>
> Knowing the historical value of the standard deviation of the
> indices, (via metrics,) and that the statistically independent
> increments are summed root mean square, the probabilities of
> expected values can be calculated over a short time interval.
>
> Note: Working with the tails of distributions is a very important
> concept. Extrapolating measured values of the standard deviation
> of the increments of a time series into the tails of the
> distribution is often a leap of faith producing misleading and
> erroneous probability values for catastrophic events. A good
> verification of standard deviation metrics is to count the number
> of 2 sigma, 3 sigma, 4 sigma, etc., events in the time series, and
> see if this frequency count can be justified with the empirical value
> of the standard deviation.
>
> Many applied mathematics folks prefer working with tail counts as
> opposed to standard deviation-they derive the standard deviation from
> the tail counts; not the other way around.
>
> > Certain is a big word. The US equity markets, with all the negative
> > sentiment in the media, are not doing that bad-at least considering
> > the difficult circumstances of the immediate past.
> >
> > More than 6,000 soles perished in the WTC attack. That would make
> > September 11, 2001, the bloodiest day in American history, (replacing
> > the battle of Antietam, September 15, 1862, in the US Civil War-in
> > which it is estimated that about 6,000 were killed, also.)
> >
> > Considering the US to be about 4 centuries old, or about 146,000
> > days, with two catastrophic instances of at least 6,000 soles perishing
> > in a single day, which would represent a probability of 2 / 146,000 =
> > 1.37E-5; i.e., the WTC attack was about a 4.2 sigma catastrophe.
> >
> > Since the standard deviation of the increments in an equity index is
> > about 2% per day, and if the increments are statistically independent,
> > (a reasonable assumption,) then in four days the standard deviation
> > of the value of the index would be 0.02 * sqrt (4) = 4%, (meaning that
> > in any 4 day interval, an indice would be within +/- 4% of its
> > starting value, 68% of the time.)
> >
> > The market's reaction, at the end of 4 days to a 4 sigma event, would
> > be about 4% * 4 = 16%, meaning that for 84% of the 4 sigma catastrophic
> > events, the market's reaction would be to drop less than a 16%, and for
> > 16%, they would drop more.
> >
> > Since the markets opened on Monday, the index values have dropped about
> > 12% in the last four days.
> >
> > So, the markets, although significantly down, are reacting a little
> > better than would be expected to the catastrophe of September 11,
> > 2001.
> >
> > John
> >
> > BTW, this does not mean that a recession is not imminent-it might be,
> > and might not. Such things are unknowable.
> >
> > http://www.infoworld.com/articles/hn/xml/01/09/20/010920hnrecession.xml
>
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--
John Conover, john@email.johncon.com, http://www.johncon.com/