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/

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