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