From: John Conover <john@email.johncon.com>
Subject: Re: U.S. recovery: Recession is certain, economists say
Date: 21 Sep 2001 23:14:24 -0000
BTW, suppose it is assumed that the recession is certain, (which is
certainly a prognosticating leap of faith-but it sells well in the
media,) how long will it last?
It started on Monday, January 17, 2000, (I'm using the market index
metrics-the GDP numbers are too sparse, and their construction, too
ambiguous; but the GDP was in certain decline later in 2000, too.)
From:
http://www.johncon.com/john/correspondence/981230002304.31518.html
http://www.johncon.com/john/correspondence/990215192020.29398.html
the probability that a recession will last at least 4 years is about
50%. Half of the recessions are shorter-half longer. The typical
scenario would be a decline of about two years, and an accelerated
growth of about two years, such that at the end of four years, the
market's values would be the same as if the recession never happened.
So, there is a 50% chance that the declines will give way to growth by
about early-to-mid next year, (and a 50% chance that they won't,)
being back on track by about mid 2004.
John
BTW, why do half of the recessions last less than four years, and half
more? Because half is 50%, and 1 / sqrt (4) = 0.5. This is an
approximation to the theoretical value which is erf (1 / sqrt (n)),
where erf is the error function. If n >> 1, then it is an accurate
approximation. The actual 50/50 value is 4.3 years.
John Conover writes:
>
> 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
> >
> > http://www.idg.net/ec?content_source_id=25&idgnet_page=1&page_id=1793&channel_id=1-1681&remote_addr=192%2E160%2E13%2E9&doc_id=697713&site_id=366&referer=http%3A%2F%2Fwww%2Eidg%2Enet%2F
--
John Conover, john@email.johncon.com, http://www.johncon.com/