Daily Speculations

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Department of Connections

4/2/2004
Reflections on an Air Hockey Game, Victor Niederhoffer

The little daughter here and I discussing the best way to score the puck in air hockey. It led to discussions of angle of incidence, equals the angle if reflection. The angle of incidence being the angle below relative to the perpendicular and similarly for the reflection relative to that same perpendicular. The solution is to extend the line from the goal to the pocket, at an equal distance to the side, and then hitting the puck at the point on the side of the table that connects the extension of the line with the point you're hitting from.

A little Google research led to applications in pool, squash, the game of pong, mirrors,
rainbows, radar, sound, the theory of relativity, the form of trees, the Nigerian "I got $30 million for you " scam, and how nature organizes itself.

This led me to think of more direct specinvestment implications. The speed with which price swings back from one extreme to another would seem to correspond closely to the angles of incidence and reflection. Presumably some technical analyst has drawn a diagram of this without testing or quantifying it and presumably it relates to something called speed resistance or Gann angles, mystical concepts I've come across.

I propose a simple fruitful way of applying this quantitatively. Consider the consecutive 20 day maxima in stocks. Such occurring when today is the highest price that has occurred in the previous 20 days. but consider these when they are separated by a 20-day minimum. compare the move from minimum to maximum relative to time, i.e., compute a ratio, of the swing relative to time. then compare the consecutive values of this ratio to find out the predictivity of large and small value of this ratio. Then generalize the question for 5-day max and minima et al. and other markets. Someone's going to tell me that technician x already did it. And that Magee has it in the Technical Analysis of Stocks. But still, a rich way of looking at things that playing with and like a kid might inspire.

Jeremy Lyter replies:
The angle shot in air hockey is a good one. Another shot worth considering is down the middle with a high degree of force. This shot works well after faking an angle shot and then blasting it down the middle. I m sure you have used similar techniques while playing squash. Market implications concerning this post would be related to air hockey and physics. It might be interesting to measure the speed of a security from point A to B trying to predict (quantitatively) how far it will travel in that same direction to C. A security like a rolling ball would have other forces acting on it which you could quantify, compute, and adjust for. Once you have this number you could rework the problem and statistically compute the probability of this trend continuing for an X time period. After you have your number there is 100% probability for 1 second that this trend will continue, 2 seconds 99% so forth and so on. Someone may have a method such as this but I m not sure. Another interesting idea would be to study the re-growth of forests after a major fire. This could be used as a model for understanding the recovery of the stock market after a crash or correction. You could also look into if growth rate changes because of how the fire was started. If it was a man made or occurred naturally.