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 > > 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/

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