From: John Conover <firstname.lastname@example.org>
Subject: Re: Cycles or random shocks?
Date: 1 Nov 1999 00:36:46 -0000
j. tyler writes: > > Currently there is another thread on the likelihood of another 1929. Of > course, that is the $64,000 question - no one has any real informatiion. > The standard theory on the subject now is that "cycles" are due to > random shocks. That means now one really knows when another crisis may > strike. And it is doubtful that there is an economist in the country > who has a clear explanation why we are enjoying unusually good fortune > right now. > Ok, I'll give it a shot. 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 only about 10% down, and then just constantly deteriorated for two years.) The day-to-day fluctuations in the DJIA are about +/- 1%, rms, (meaning that for 68% of the time, the fluctuations are less than +/- 1%,) so assuming a first order approximation of equity prices as a Brownian motion fractal, (ie., no leptokurtosis,) at the end of a 400 trading day interval, we would expect the DJIA to be about 0.01 * sqrt (400) , or about 0.2, (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. So, 90% 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. John BTW, the "unusually good fortune right now", assuming the last bad year, (where the DJIA turned in negative numbers on the year,) was 1993, has a chance of continuing into its seventh year of about of 1 / sqrt (7), or about 37.8%-again assuming a first order approximation of a Brownian fractal as a mathematical expediency-ie., it was virtual certainty that at least one bull 8 year run would happen in the century, (likewise, for a bear market, too, as per 1930-1956, when the DJIA had recovered to its 7 September, 1929 value, in non-real index value, was a virtual certainty.) However, the *_depth_* of the 1930 recession was quite rare, (although its length would be considered rather common.) Assuming a first order approximation of a Browning fractal, the depth of things move on a 0.01 * sqrt (t), scenario, and the chances of something continuing move on erf (1 / sqrt (t)) which is about 1 / sqrt (t), for t >> 1. Which means that the average bear or bull market would last, on average, about 4.3 years, (but there would be a lot of variability since the 1/ sqrt (t) function has tails that initially fall off rapidly, then fall off very sluggishly.) There are empirical graphs of all possible bubble run lengths and magnitudes of the DJIA, S&P, and NYSE for the century, compared with the theoretical values of a Brownian fractal at: http://www.johncon.com/john/correspondence/981230002304.31518.html http://www.johncon.com/john/correspondence/990212211510.16959.html and it does seem to be a useful and reasonable first order approximation to the dynamics of the markets, (depending on who is telling the story, of course.) -- John Conover, email@example.com, http://www.johncon.com/