Definitions Deconstructed

Demonic Criteria

S. G. Lacey

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Deconstruction:
Even though this tale involves a pair of individuals named Shannon and Kelly, it doesn’t occur in an 18th century Irish pub near a cemetery, or on a Hollywood film set of a 90’s teenage horror spoof.  These are the surnames for a pair of colleagues at Bell Labs’ New York City offices during the 1950’s.  

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This iconic research organization, with the corporate namesake originating from the founding father of the telephone, Alexander Graham Bell, has a storied and complex history.  After the parent company’s establishment in the late 19th century, the renowned Bell Labs was independent from its 1925 creation until 1984, when the group merged will AT&T, then was spun back off for monopoly reasons just 12 years later.  In 2016, Finnish telecom player Nokia acquired Bell Labs, including the extensive intellectual property portfolio.     

 

Bell Labs has an impressively broad and technical resume of scientific contributions, from radio astronomy to the Unix operating system.  Just in the decade following World War II, during which Mr. Shannon and Mr. Kelly worked together, the collection of novel researchers employed there developed a multitude of technologies which continue to influence modern daily life: solar cells, transatlantic cables, basic lasers, and MOSFET transistors. 

 

In contrast to these various impressive physical inventions, some members of the elite scientific group at Bell Labs focused on analytical modeling pursuits like iterative codebreaking communications and algebraic digital circuitry.  Both Kelly and Shannon were forerunners in the field of information theory, an innovative school of thought pioneered at Bell Labs during the middle of the 20th century.  

 

The following pair of mathematical theorems developed by this dynamic duo of nerds are still relevant in the gambling and finance fields today.  Both offerings focus on the principle of compound yields, which is associated with exponential arithmetic.  The core concept underlying both algebraic formulas is the geometric drag on return, also known as the volatility premium.

 

Thus, it’s time for some precise definitions and mathematic proofs.

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Definitions:
Shannon’s Demon = Two uncorrelated assets with a zero expected return can produce positive results, if combined and managed in the right way.  [REF]

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Claude Elwood Shannon’s life arc is impressive.  Graduating from the University of Michigan, at just 20 years old, with dual bachelor’s degrees in mathematics and electrical engineering, just 4 years later, in 1940, he earned his doctorate in advanced math from MIT.  

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After college, Shannon quickly found his way to Bell Labs, starting out in the cryptography department during World War II, then expanding his research to a variety of seemingly disparate fields which, when combined, yielded numerous novel technological advances.  After two decades in industry, this savant transitioned back to a professorship role back at his Massachusetts alma mater.  

 

Mr. Shannon’s breadth of knowledge is highlighted by in the range of discoveries he facilitated, from Boolean algebra to arithmetic communication.  Dubbed “the father of information theory”, he essentially conceived the now-ubiquitous digital circuit while at Bell Labs. 

 

While diabolical in name, in this context, the term “demon” is simply technical jargon for a thought experiment.  This nomenclature finds its origin in the field of thermodynamics, specifically envisioning an actual devilish creature as a means of violating this field’s infallible 2nd law.  For Shannon’s postulation, as with the original fluid mechanics musing, unforeseen forces create unexpected outcomes.

 

In this case, “Shannon’s Demon” explains how counterintuitively combining a pair of investments which both have zero expected returns can yield a positive investment outcome.  Impressively, even selecting a couple assets which both have negative outcomes can result in a profitable portfolio in the long run, simply through using the frequent resizing principles espoused by Mr. Shannon.

 

This analytical approach is based on the “random walk” distribution of performance, otherwise known as “martingale” in probability parlance.  Most gambling activities, and many investment classes, exhibit such erratic behavior, with each subsequent result unknown, arbitrary, and unaffected by all prior activity.  

 

In this case, a simple example everyone can relate to, flipping a quarter, helps clarify the various terminology.  

 

A perfect coin, consistently alternating between heads and tails outcomes, with a 50% reward for guessing correctly, and a 33% loss when wrong, oscillates around the gambler’s starting outlay indefinitely.  However, with 50% rebalancing, represented by taking half the potential winnings off the table after each flip, the overall bankroll continues to grow in value steadily.  

 

Granted, an exact alternation of heads and tails isn’t feasible in real life, so care must be taken to size each bet accordingly.  That topic will be covered in the next section. 

 

As postulated, a pair of uncorrelated assets, each with a zero expected return, always yields a positive sum after a sufficient # of simulations, provided rebalancing occurs after each change in value.  The plot below demonstrates how the wide dispersion of returns from a few neutral assets can be combined to generate a reliably positive band of profits through consistent portfolio adjustment.