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The Professor
Charles Pennington

8/30/2005
Rotational to Linear

Following up on the Chair's ideas about converting rotational to linear motion, as in Leonardo's inventions...

Using SPY data since 1993:

Define the magnitude of the "rotational" move as the following:

RotationalMove=absolute value(R0-R1+R2-R3+R4-R5+R6-R7+R8-R9)

where R0 is today's percent return, R1 is yesterday's percent return, etc.

The linear return LinearMove over the same period is the sum R0+R1+R2...+R9.

Notice that if the market makes 10 consecutive 1% moves, then the LinearMove would be 10%, but the RotationalMove would be zero.

Regressing LinearMove vs RotationalMove (this is NOT a predictive study), I find:

LinearMove=1.052-0.222*RotationalMove, correlation = -18% with about 3100 observations and about 310 independent observations.

So rotational churning seems to be accompanied by DOWN moves. Remember that the rotational and the linear moves can in principle be totally independent.

Next I try to find something predictive. I regress the LinearMove over the NEXT ten days vs the RotationalMove over the previous 10 days. Results:

LinearMove(Next 10 days)=0.46-0.003*RotationalMove(previous 10 days), correlation=0.2%.

So the RotationalMove as defined here doesn't have much predictive power.

Of course there are many possible ways to interpret and test the analogy, and this is just a start.

Charles Pennington trades stocks and stock index futures with Victor Niederhoffer's Manchester Trading in Weston, Connecticut. Before becoming a hedge fund trader Charles was a Full Professor of Physics at Ohio State University, where he taught for 13 years and served as advisor to eight successful doctoral candidates. He has published more than 40 scientific papers and won a Presidential Young Investigator grant (1993-1998). He earned his B.S. (1985) and Ph.D. degrees (1989) in Physics from the University of North Carolina at Chapel Hill and the University of Illinois at Urbana-Champaign, respectively.

Charles Pennington trades for Victor Niederhoffer's Matador Fund. He previously was a physics professor at Ohio State University. He holds a Ph.D. from the University of Illinois and did post-graduate work at the University of California at Berkeley. If anyone would like to chat about his fascinating paper, "Magnetic field independence of Cu(2) nuclear spin-lattice relaxation in the normal state of optimally doped YBa2Cu3O7," he would be happy to do so. Write to him c/o specs at mantrade.com.