Jan

20

 I first learned about Thompson's On Growth and Form at a talk back in the late 80s by Benoit Mandelbrot, who referenced the book as an influence. I think Thompson's book has relevance to equity markets, philosophically as well as on more practical terms. Thompson simply observed nature and described relationships of form to function. He didn't attempt to infer an evolution process. In this sense the book is an early precursor of Bejan's Constructal Theory.

Examples: Thompson shows that the speed of a fish or ship is proportional to the square root of its length, and that the kinetic energy exerted by an organism is proportional to its mass to the fifth power. Thompson considered form as the product of the dynamic forces acting upon it. Logarithmic spirals reflect a constant proportional growth rate. The logarithmic spirals in pine cone scales or sunflower seeds result in a Fibonacci expansion in the number of scales or seeds. The Fibonacci sequence is just a discrete version of the continuous logarithmic curve.

It's not unrealistic to think that logarithmic spirals and Fib sequences crop up in equity prices. Daily returns are often assumed to be lognormally distributed. The relationships are probably not as simple as "stock x should drop to 38.1% Fib level and bounce".

One of the forces acting on the form in this case is human perception of emerging patterns. One of the more powerful conclusions drawn by Thompson is that many species share features that are invariant under simple linear transformations. So the shape of a gorillas skull and skeleton is the same as a human's through a "stretching" deformation.

If we make an analogy to stocks, this could imply self similarity in price patterns (fractal relationship) or the idea that we need to adjust for both price and time transformations when using historical analogs to predict future returns..


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  1. Bill Wolfe on January 22, 2016 1:58 pm

    For an example of how a Fibonacci spiral can contribute to identifying a turning point on SPY, and then how the move can be capitalized on with a SPY weekly option, please visit my website: http://www.wolfewave.com/ReferralRewards.htm

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