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9/25/2005
Polar Coordinates, by Victor Niederhoffer

A squall, a diversion, a relation, polar coordinates. The decline in stocks last week, the greatest in six months, led me to go beyond listening to the usual divertiment of the Schultz-Ebler transcription of the "Blue Danube Waltz" to the study of complex variables and polar coordinates. Polar coordinates are a way of representing a point in terms of its distance from the origin and the counterclockwise angle that the point makes with the x axis of the origin, an alternative to the usual graphing method. There are 2pi radians in a complete revolution. So 90 degree is 1/2 pi.

Radians are ideal for measuring the angles between two key variables such as bonds and stocks during big declines as well as other times. Some big down weeks in stocks, along with the change that week in bonds and the change in stocks the next week, follow.

With the kind assistance of Mr. Doc Castaldo, we have computed the angles measured in radians of all the concurrent moves in bonds and stocks, and tabled them along with the move in the S&P next week.

We studied all declines of 20 or more for stocks in a week.

Wk ending    SP move Bond move   Angle  Magnitude SP move next week
09/23/2005   -21.8    40.6       -0.50    46.1
04/15/2005   -40.0   221.9       -0.17   225.5     13.6
08/6/2004    -37.5   262.5       -0.14   265.2      2.6
04/30/2004   -33.4   -37.5       -2.30    50.2    -10.6
03/12/2004   -38.6    71.9       -0.50    81.6    -10.8
09/26/2003   -38.4   200.0       -0.19   203.7     34.0
03/28/2003   -30.3   203.1       -0.14   205.3     15.6
02/07/2003   -24.2    84.4       -0.28    87.8      6.5
01/24/2003   -42.8   131.3       -0.31   138.1    - 5.6
01/17/2003   -23.4   203.1       -0.12   204.4    -42.8
12/27/2002   -24.9   187.5       -0.14   189.1     38.1
12/13/2002   -26.5    81.3       -0.31    85.5     10.2
12/06/2002   -22.2   128.1       -0.17   130.0    -26.5
10/04/2002   -20.0    -9.4       -2.30    22.1     32.7
09/20/2002   -49.0    62.5       -0.67    79.4    -16.9
09/06/2002   -21.6    93.8       -0.22    96.3    - 3.4
08/30/2002   -24.9    93.8       -0.26    97.0    -21.6
07/19/2002   -73.3   - 9.4       -1.70    73.9      9.7
07/12/2002   -73.7   259.4       -0.28   269.7    -73.3
06/7/2002    -39.2   -34.4       -2.30    52.2    -19.4
05/24/2002   -22.8   134.4       -0.17   136.3    -14.9
04/26/2002   -54.7   165.6       -0.31   174.4      1.0
04/5/2002    -24.2   246.9       -0.10   248.1    -13.4
02/08/2002   -26.9    53.1       -0.47    59.5      8.3
01/11/2002   -27.5   325.0       -0.08   326.2    -18.7

Angles in radians, measured from bond axis (x-axis)

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