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Here is one way to adjust an existing options position so that any
zigzag portion of the original P/L expiration graph will, in the
modified position, be a line parallel to the axis representing the
expiration values of the underlying. I will use examples from MC's GS
trade, currently being discussed in this forum.
The following matrix respresents the number of puts in the first row
and calls in the second row at strikes 130, 135, 140, 145, 150 of the
GS trade on 5/17. To the right of the first row is the number of puts
at strikes higher than 150. At the left of the second row is the
number of calls at strikes lower than 130. The *'s indicate don't
care values for flattening the expirataion graph between 130 and 150.
|* -1 0 0 0 | -1
0 |0 0 -3 0 * |
The first step is to choose a matrix corresponding to the flat section
of the new expiration graph. It should have the property that the two
entries in each of the middle columns sum to zero and the sum of the
left two call entries (including the one outside the matrix) equal the
sum of all the put entries excepting the don't care position. For
example:
|* 3 -2 0 0| -1 or |* 0 1 0 0| -1 or
0 |0 -3 2 0 *| 0 |0 0 -1 0 *|
| * 0 0 0 0| -1 or |* 1 0 0 0| -1
0 |-1 0 0 0 *| 0 |0 -1 0 0 *| .
Next, one subtracts the original matrix from the new one in order to
get the adjustment matrix. For the 4 examples above, this gives
respectively:
| 0 4 -2 0 0| |0 1 1 0 0|
| 0 -3 5 0 0| |0 0 2 0 0|
| 0 1 0 0 0| |0 2 0 0 0|
|-1 0 3 0 0| |0 -1 3 0 0|.
The first adjustment was given by MC, the second by JP. The third
adjustment in equation form is: 135p -130c + 3*140c. The sum of the
entries in the put row impacts the portion of the position that lies
at lower expiration values than the section to be flattened, in
particular gamma. The sum of the entries in the call row, likewise,
impacts the portion of the graph at higher values. Thus not all
adjustments are equal. The slope of the expiration graph below 130 is
only -1 with the third adjustment, not -2 like the others. How does
one pick the best one? HaHa.
A second example comes from the 4/30 adjustment. The goal was to
create a 140/145/165/170 condor from a complicated position. Thus the
segment covering the strikes 145, 150, 155, 160, 165 is to be flat but
there are no don't cares because the condor goal requires those
entries be specified. The starting matrix was:
| 2 -1 -2 1 0| 0
0 | 0 1 -2 0 0|
A guts condor was the goal so the target matrix was of the form:
| 0 0 0 0 -1| 0
0 |-1 0 0 0 0| . The adjustment matrix is then:
|-2 1 2 -1 -1|
|-1 -1 2 0 0| which corresponds to the adjustments Michael made
at those strikes. An iron condor would correspond to a target
|-1 0 0 0 0| 0
0 | 0 0 0 0 -1| and the adjustment is then:
|-3 1 2 -1 0|
| 0 -1 2 0 -1|
I hope this helps clear away some of the mystery about the GS trades.
Writing it certainly did that for me.
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