Nov

2

Dan Rockmore’s book Stalking the Riemann Hypothesis, written for the recreational mathematician, brought forth in me the profound emotions. Reading it seemed quite similar to my enlightenment in reading my first Calculus book. The book completely avoided the messy math and stuck to the core concepts behind the math. And what a mathematical journey is was. Starting with the early history of pure math, with the Greeks, to modern day theories. It seems that search to prove Riemann’s hypothesis has lead to many the leading edge of science. Chaos theory, Fractals, the edge of probability theory, Random infinite matrices and more.

Besides the beautiful ideas it goes introduces you to many of the great minds that have worked on this problem, and are working on this problems. Two quotes that just floored me:

Eugene Wigner: “The unreasonable effectiveness of mathematics” (sounds like a counter to me)

And for those convinced they can’t ever get through the math. Polya in his book “How to Solve It”

“If you cannot solve a problem then there is an easier problem that you can solve. Find it.”

These alone make it worth the read. You find all sorts, much like you would in our field. The magician turned mathematician. The hungry kid getting a break. Each story is inspiring. Some you probably are familiar with but, Dan writes very interesting facts on each.

But beyond this, it has a profound impact due to the underlying philosophical impact. The hope that we are beginning to understand the meaning to randomness, and through this perhaps a light showing hidden secrets of our universe, in the infinite and infinitesimal.

For those of you not familiar with the Riemann Hypothesis, it is one of the most studied areas in pure math, due to its relevance to the prime numbers. Before Riemann expanded it through analytic continuation to the complex plane, Euler expressed it as for any S > 1 as = 1/(1^s)+ 1/(2^s) + 1/(3^s) + 1/(4^s)+ 1/(5^s)…. The relationship to the primes can be seen by its equivalence to Product of 1/(1-p^-s). Though not in the book, this proof is quite beautiful and can be seen sieving out the primes.  The hypothesis is that the Reimann zeta function, the expansion to the complex plane, only has non-trivial zeros on the real line 1/2. (The trivial zeros are multiples of -2). With a little imagination and idea of what the Fourier transform does, the Fourier waves turn at the prime to give a estimate for any number how many prime their are before it. The math is beautiful, the writing is great, and the spirit is uplifting.

Vincent Andres responds:

Concerning didactic books and Fourier waves, a very didactic and commendable book is The World According to Wavelets, by Barbara Burke Hubbard.  The title of the book is about wavelets, but in fact half of the book is about Fourier, in a very didactic way.

Oct

24

It is sometimes helpful to understand the infrastructure of Wall Street and LaSalle Street. Consider what must go through the minds of margin clerks and risk managers and heads of firms when the market can spike up by 20+ S&P points in one minute on light volume. That’s a $5000 per contract move in the big S&P, and any margin account that couldn’t stand that and be in good shape at the time, would cause great trepidation. Consider also, the others hanging onto their shorts. “Dear, don’t give me that ‘d#mned broker’ stuff any more. If it had stayed up there for one more minute, you could have gotten a call and we would have had to cancel the vacation and send Joe to State College. Promise me that you won’t put us in that position again.” You can try also to put yourself in the minds of those who were short and saw themselves on their knees or backs, and were repreived when Clever Hanses knocked the price back from 1398 to 1376. “My goodness, tell me again how close to death I was before they defilibrated me? I promise I’ll give up smoking now.”

Jason Goepfert replies:

While difficult, I would suggest that everyone try to find a way to observe the inner workings of a brokerage firm margin department.

I managed such in the late 90s for the discount side of a large bank. When traders are heavily margined and facing a call, the vast majority do not use objective analysis, or even limited intelligence, in making their decisions. They use raw emotion.

And what most don’t realize is that those on the other end of the phone are subject to the same. There is an extraordinary amount of pressure on the margin clerks and managers, and when faced with settlement deadlines, their pulse quickens as well - it is not all about rules and procedure.

One nasty day in particular a large client dipped below his equity requirement and was up for a forced sell out. None of my margin clerks could reach him - it turns out he was in the championship of the World Series of Poker at the time.

At the 11th hour, he called frantically insisting that he had the funds available in a bank safe, denominated in poker chips. Given the amount and the client, the decision of whether to sell him out went all the way up to just under the CEO. He said sell, so we did, adding not a little pressure to the current market decline.

The client promptly sued us. And won. A lot.

While I believe the impact of margin selling on overall market performance is greatly exaggerated most of the time, in times of duress it is not as wave after wave of sell orders emanate from these shops, often in close proximity as the guidelines from firm to firm are fairly close.

Dr. Kim Zussman adds:

Adaptive Optics is a technology used by astronomers to counteract atmospheric blurring effects which degrade images for earth-based telescopes.

One method uses a laser to project to the upper atmosphere, creating an “artificial star”. Images of this star, which contain information about how light waveforms are distorted as they fall through the local atmosphere, is used to modulate a flexible mirror which corrects the wavefront and greatly sharpens actual star images.

Might “fat finger” events or other strange/large trades represent a form of artificial star designed to perturb markets for the purpose of sharpening the real picture? If so, who are these astronomers and can we benefit with our own specs?

Vincent Andres responds:

Another image which comes to my mind is that such events may be a voluntary stress applied to the market in order to visualize where may be germs of possible fracture lines.

Not obvious to exploit when seeing only the input signal’s echo and without precise dating.

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