Aug

14

If you have ever lost your keys or your wallet you will understand this problem. What is the best way to find things?Every student of Computer Science is required to learn a technique called a binary search. The primary requirement of a binary search is that the list of items to be searched must be sorted in order from smallest to largest or A to Z. Given that fact, the search examines the item in the middle of the list and is able to rule out all of the items before or all of the items after the examined one. Half are eliminated in one look. For the half which remain we again look at the middle element and further reduce the remaining possibilities by half. Using this technique one can search a list of up to 1,024 items by examining only 10 elements.

Sometimes we do not have the luxury of a perfectly sorted list of items. Occasionally the list may have increasing values up to a certain point and then declining values thereafter. Such an arrangement is known as an unimodal distribution — it has only one peak somewhere in the middle. For example a list of the probability values of the normal distribution would have one peak in the middle and a decline thereafter. In optimization problems such a pattern arises quite naturally, with the values to be optimized rising up to a certain point, after which they will fall. That point is the optimum (maximum).

To search a unimodal list the search of choice is called a Fibonacci Search which relies on the spacing between the Fibonacci numbers to calculate its next step size. As such it is more adaptable than the binary search. Under certain circumstances it can be shown that the Fibonacci search is an optimal search algorithm for such problems.

The Chair has frequently noted that the financial ecosystem requires much upkeep; a massive numbers of people and huge capital investment are required to keep the markets functioning all cost money. The source of revenue to fund these operations comes from three main sources, commissions, market spreads and professional advice and the key driver of all of these revenue sources is volume. The relationship between volume and commissions and market making profits are obvious. Order flow is everything to a commission broker or market maker. However those who sell advice also thrive on volume which is a proxy for interest in the market. When the public is interested in the market more money flows in and a certain portion of that money needs advice. The entire ecosystem of the financial industry thrives on volume, when volume is maximized the health of the financial system is maximized.

In this context it may be that the objective of the markets is not to maximize the price discovery process but rather to maximize the volume of trading, after all the health of the markets is integrally bound to the health of the financial system itself. If volume optimization is the real goal of the market is it not likely that the market uses an efficient search technique to discover the optimum. In this context the Fibonacci search is the best known algorithm for such a search in a unimodal volume environment.

One hastens to note that this is quite different from the mystical application of Fibonacci numbers which some traders try to apply in the price domain.


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