Re: [RT] 1929-1987 Spiral Calendar Analog update, RealTraders Email List Archive

Reversion to the mean is a math concept that can be explained in many ways. Suppose you had a population of 500 numbers ranging from 1 to 1000. You?ve already put all 1000 of them in a computer and you know, without any doubt whatsoever, the population?s mean is 500. Well, you decide to draw all 1000, one at a time and each time you average all the items you?ve sampled to date. Well, the first item drawn at random is a 10. Well, that?s a 490 away from the mean. The next time is a 590 so the sample average is (590 + 10) /2 = 300. Well, your sample mean is now a lot closer to the mean. The next you pull is 990 so the sample mean is (990 +590+10) /3 = 530. Well, not only have you ?reverted? to the mean, you?ve surpassed it. And that?s a concept implied by reversion to the mean. Observations exceed or go past the mean.

The 100 year Dow is a trend line reflection of a straight line which is upward sloping. The last 30 years has been a parabolic move up and the current level is likely 4000 points above the mean. Reversion to the mean would imply the Dow would want to return to its long term average. But it also means that when there is an overshoot of the mean. If Dow wants to get to the straight line regression ?mean? at 4000 (I don?t know what the number is but 4000 is in the ballpark), then it will likely exceed the regression line and go lower, 3000 or 2000.

What are the probabilities? Depends on your personal belief system. Mandelbrot and Taleb conclusively proved that the market is not a ?random walk? Gaussian coin toss. Mandelbrot believes there?s a hidden order to the market that exceeds human ?linear? thought to understand and allusion to it can only be gleaned by fractal geometry. In Taleb?s calculations, the possibility of the 1987 crash was a 1 in 5000 lifetimes (where a lifetime is the lifetime of the universe) possibility. In other words, it is infinitely impossible that 1987 occurred according to Gaussian gaming or bell curve probability.

So, if you believe in Gaussian randomness, the answer is the next coin toss is a 50/50 probability. If you believe there is order, the next toss is a head. If you believe in randomness, I believe the vast improbability that the first two dates COULD NOT HAVE occurred. Hence, I cautiously believe the next two dates will occur. It?s good enough for me to take a levered short position (I like QQQQs so I have 2400 contracts or 240K shares of November 38s and 5880 contracts of 37s).

My positions are based on entirely unlikely events and I lose most of the time. The time I won was this time last year and I won enough that it dwarfs all losses I?ve had in multiples of 10s. I call it my Black Swan Black Sholes strategy. Black Sholes was created by Merton, Black, and Sholes to project fair pricing for options. The Gaussian stochastic probability, as Mandelbrot proved rather conclusively in The Misbehavior of Markets, dramatically underprices the risk of ?long tailed events? in the bell curve; that far more of these long tailed events (renamed by Taleb as Black Swan events) occur than thought. And when they occur, out of the money options pay far too much given their Black Sholes pricing. So, at the most critical points of the crisis last year, there was question verbalized on CNBC by Joe Kernan as to whether the organized CBOE options market could survive. Of course it did, but that?s the defect in Black Sholes. And remember, the principals of Titanic LTCM quant fund were none other than the brilliant quants who developed Black Sholes (I hope I get this right), Fisher Black and Myron Sholes. The 1998 crisis that nearly melted the world economy was created by the greatest of all bell curve quants. So, I?ll take my losses and try to find the Black Swan that dwarfs the losses in leverage.

Jim

From: realtraders@yahoogroups.com [mailto:realtraders@yahoogroups.com] On Behalf Of Mark Simms
Sent: Sunday, October 25, 2009 9:13 PM
To: realtraders@yahoogroups.com
Subject: RE: [RT] 1929-1987 Spiral Calendar Analog update

What about "reversion to mean" theory ?

IOW, although 100 heads in-a-row is POSSIBLE, what are the probabilities of it occurring ?

So, in this case, what are the probabilities of 5 heads in-a-row occurring ?

Just a thought.....

From: realtraders@yahoogroups.com [mailto:realtraders@yahoogroups.com] On Behalf Of Jim Ross
Sent: Sunday, October 25, 2009 7:39 PM
To: realtraders@yahoogroups.com
Subject: RE: [RT] 1929-1987 Spiral Calendar Analog update

Nassim Taleb posed exactly that question in his book The Black Swan. The question was put to the MIT quant and Guido the street wise bookie as such:

This is a FAIR coin and FAIR coin toss and it has resulted in four heads in a row.

The quant said ?Of course not, the fifth trial is an entirely independent event and the probability is 50/50.?

Guido said. ?It?ll be a heads. Yas jest can?t flip four heads in a row. The game?s rigged. It?ll be a heads.?

The question is whether there?s a hidden order in time and space. Benoit Mandelbrot, the greatest mathematician of our lifetime IMO and the discoverer of the Mandelbrot set, would say there is a hidden order. But it isn?t a Gausian ?bellcurve? order; its not a gaming coin toss population of events . It is not linear and likely we will never discover it. Our only glimpse of it will be through fractal geometry.

Jim

From: realtraders@yahoogroups.com [mailto:realtraders@yahoogroups.com] On Behalf Of GerryB
Sent: Sunday, October 25, 2009 7:08 PM
To: realtraders@yahoogroups.com
Subject: Re: [RT] 1929-1987 Spiral Calendar Analog update

Now, consider that the model HAS SUCCESSFULLY predicted the first two
out of the four dates? Does that make the improbable less improbable?
I know it does, but by how much. About that I don?t have a clue. But,
again, it is interesting.

SAY YOU FLIP A COIN 4 TIMES IN A ROW AND IT COMES UP
HEADS...........DOES THAT INCRECREASE THE PROBABILITY THAT ON THE NEXT
FLIP IT WILL NOT BE HEADS?.................OR DOES IT REMAIN THE SAME:
50/50 AS IN THE FIRST 4 CASES?????

GERRYB