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Romance, Bernanke and Discrete Mathematics, by Victor Niederhoffer

The wild fluctuations in the markets that accompanied the 3 pm announcement on CNBC that Fed Chairman Ben Bernanke had spoken to Maria Bartiromo about the reaction to his testimony at the Joint Economic Committee has unleashed a hornet's nest of questions about the context, purposes, and reactions. A thoughtful set comes in this reaction from reader Paolo Pezzuti:

My first reaction to this is that Dr. Bernanke suffers from a disease that old men are all too prone to -- the temptation to try to impress a pretty reporter. It's so easy to try to appear expansive and profound at an evening off the record session with an attractive reporter. "Why is it always romance?" Horace Rumpole asks at the end of one of his mysteries where he follows the pretty girl to catch an English Professor for a terrible crime? I believe that many of the most powerful people on Wall Street succumb to this character flaw and they should follow the motto that the prettier the reporter, the more careful they should be in their utterances.

However, for those that are subject to the vagaries of markets induced by such lapses, a good dose of counting is in order. If it were possible to quantify the influence of romance on markets it would be a good study. But in its absence, one might wish to do some counting on markets that are way up late in the day, but then end down on the day. A typical counting study shows that the 200 most similar stock market gyrations to yesterday showed a significant tendency for the gyrations at the end of the anomalous (romantic?) day to be reversed by approximately 1/3 during the next day.

The importance of counting to get a better foundation for reactions to romantic moves and other anomalies was underlined to me by the recent change in heart of Stephen Roach from pessimistic to optimistic. Along with Alan Abelson he has probably caused more people to stay out of the stock market and thus lose incalculable wealth than any other wealth destroyer in history. And yet, the former has changed without calculating how accurate his predictions have been, or what the errors in his reasoning were, and the latter has gone on leave without a single apology to his readers for his 40 years of bearishness during which the market has returned some 6400% during his constant bearishness.

The best antidote I have found to wishy-washy reasoning of this kind is to constantly read books on finite math. All such books start with a chapter on counting, showing how permutations and combinations should be enumerated, and extending basic principles of counting to every variety of problem. The two I am reading now are the highly recommended Kenneth Rosen's  Discrete Mathematics and its Applications  and the mind-blowing and path-breaking book,  A Logical Approach to Discrete Math by David Gries and Fred Schneider.

The Rosen book has chapters on counting, relations, graphs, trees, recurrence relations, Boolean Algebra, and computations. It's excellent on applications and models in all the physical and social sciences. The chapters are self contained and accessible to anyone who's willing to learn and has a pencil and paper handy. He summarizes what he wishes to accomplish as "Discrete structures are the abstract mathematical structures used to represent discrete objects and relationships between these objects. These discrete subjects include sets, permutations, relations, graphs, trees, and finite state machines."

The book by Gries and Schneider is revolutionary in that it teaches you how to work with the syntactical structure of language and how to manipulate it logically. It then takes these syntactical rules, mainly based on logical relations of the kind that we study in truth tables, and develops all the usual topics of finite mathematics such as those enumerated in the Rosen book as well as Propositional Calculus, Hilbert Style Proofs, Predicate Calculus, Programming, Mathematical induction, sequences, integer theory, and infinite sets. This book is a hard read, with many unusual special notations that require gaining good familiarity with before the book becomes readily accessible. It's the kind that's probably much easier to take in a class than as self study. However, because its applications are so deep, and extensive, it will change the way you look at math and life, and certainly will help to prevent you from getting whip lashed by Bernanke/Bartiromo type relations in the future.

The whole subject of discrete math is one that is particularly applicable to the study of markets. All information is disseminated between individuals. All markets have leads and lags with others. The prices themselves are discrete results of buying and selling decisions by different actors in the market panorama. The best way of understanding such activities is to build up the results of their decisions starting from what happens before all other decisions have been made, what G and S call "Starting with Zero".




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