3/23/07 (Fri.) at weekly close:

IBM at 95.03 K=90 option: 15.30/15.60; use 15.45, gain 1.25 x -100 = -125.00 (loss)
K=130 option: 1.60/1.80; use 1.70; gain +0.175 x +100 = +17.50
shares: 95.03; gain +2.08 x 58 = +120.64
TOTAL: gain of +13.14 (all gains cumulative from original transaction)

3/21/07 (Wed. at close) IBM at 95.36 K=90 option: 15.40/15.80; use 15.60, gain 1.40 x -100 = -140.00 (loss)
K=130 option: 1.65/1.85; use 1.75; gain +0.225 x +100 = +22.50
shares: 95.36; gain +02.41 x 58 = +139.78
TOTAL: gain of +22.28 (all gains cumulative from original transaction)

3/20/07 (10:40am Tue.) IBM at 93.62 K=90 option: 14.40/14.70; use 14.55, gain 0.35 x -100 = -35.00 (loss)
K=130 option: 1.60/1.75; use 1.675; gain +0.15 x +100 = +15.00
shares: 93.62; gain +0.67 x 58 = +38.86
TOTAL: gain of +18.86 (all gains cumulative from original transaction)

3/16/07 (Fri.) at weekly close:

IBM down 0.17 at 93.28
K=90 option: 14.30/14.60; use 14.45, gain 0.25 x -100 = -25.00 (loss)
K=130 option: still 1.55/1.70; use 1.625; gain +0.10 x +100 = +10.00
shares: 93.28; gain +0.33 x 58 = +19.14
TOTAL: gain of +4.14 (all gains cumulative from original transaction)

3/15/07 (Thur.) at close:

IBM at 93.45
K=90 option: 14.50/14.70; use 14.60, gain 0.40 x -100 = -40.00 (loss)
K=130 option: still 1.60/1.75; use 1.675; gain +0.15 x +100 = +15.00
shares: 93.45; gain +0.50 x 58 = +29.00
TOTAL: gain of +4.00 (all gains cumulative from original transaction)

3/13/07 (Tue.) at close:

IBM down 1.40 to 92.71
K=90 option: 13.90/14.10; use 14.00, gain -0.20 x -100 = +20.00 (gain)
K=130 option: still 1.45/1.55; use 1.50; gain -0.025 x +100 = +2.50
shares: 92.71; gain -0.24 x 58 = -13.92
TOTAL: gain of +3.58 (all gains cumulative from original transaction)

We have had two big swings (up Monday, down Tuesday) but our beta- and vega-neutrality seems to be working. Yahoo shows a large gain in IBM after hours on Tuesday (up $1+ between 4pm and 5pm, apparently not reflected in options trading) so we may see another big swing on Wednesday.

3/12/07 (Mon.) at close:

IBM at 94.11
K=90 option: 14.80/15.00; use 14.90, gain 0.70 x -100 = -70.00 (loss)
K=130 option: still 1.55/1.70; use 1.625; gain 0.10 x +100 = +10.00
shares: 94.11; gain 1.16 x 58 = +67.28 (gain)
TOTAL: gain of +7.28

3/12/07: How should we understand those transactions from Friday?

1. We bought 58 shares of IBM for $92.95/share, for a total of $5391.10. It is easy enough to track the share price --- we'll just use the price of the most recent trade. That's what people usually mean by "current price" or "closing price."

2. It's harder to track the option prices. We shouldn't use the last trade, because it might be old, and therefore inconsistent with the share price. So, let's use the midpoint between Yahoo's posted bid and asked prices. By that standard, the prices at the time of purchase were these:

Jan09 calls, K=130: bid 1.45, asked 1.60, midpoint 1.525
Jan09 calls, K=90: bid 14.10, asked 14.30, midpoint 14.20.

But in each case, we traded "at the market" and gave up the spread. That is, we bought 100 K=130 calls for 160.00, which by our standard were immediately worth 152.50, and we sold 100 K=90 calls for 1410.00, which by our standard were immediately worth 1420.00 (well, for us, really -1420.00).

3. Let's regard the immediate $17.50 loss as a transaction cost. We would count the commission as a transaction cost, too, but there was no commission. (Question for economists: should we count using up one of my 25 free trades as an opportunity cost? If so, how much is that worth? A typical commission for any of these trades would be $7.95 or a little more.)

4. So, let's take the starting point for the combined position as

Shares: 58 @ 92.95 = + 5391.10
K=90 options: 100 @ 1.525 = + 152.50
K=130 options: -100 @ 14.20 = - 1420.00
TOTAL market value of position: + $ 4123.60.

Effectively, we paid 4123.60 to get into this position, and also paid 17.50 in transaction costs.

5. Our theory is that the "deltas" for the K=90 and K=130 calls, respectively, were about 0.169 and 0.749 respectively. This means that an increase of $1 in the IBM share price should result in changes of...

+58 in our share position
+16.90 in our K=90 position
-74.90 in our K=130 position,

for a net change of zero in the overall market price. Actual observations might jump around in the +-20.00 range; we'll see. (Note: those deltas are from before class Friday; we had slightly different values in class.)

6. We also got rough "vega" neutrality by balancing the two option trades. If the prices change because of the market's view of volatility, we would expect the option prices to vary from the predictions in the last paragraph, but in opposite directions and in roughly offsetting amounts.

7. Here are the market prices at about 11:45 am Monday:

K=90 option: 14.20/14.50; use 14.35, gain 0.15 x -100 = -15.00 (loss)
K=130 option: still 1.45/1.60; use 1.525; no change
shares: 93.25; gain 0.30 x 58 = +17.40 (gain)
TOTAL: gain of +2.40

which is just noise. We'll have to wait for a larger price movement to test the theory.