If Wal-Mart moves lower, the delta gets more positive, racking up losses
at a higher rate. To add to Pete’s woes, theta becomes less of a benefit as the
stock drifts lower. At $47 a share, theta is about flat. With Wal-Mart trading
even lower than $47, the positive theta of the August call is overshadowed
by the negative theta of the September. Theta can become negative, causing
the position to lose value as time passes.
A big move to the upside doesn’t help either. If Wal-Mart rises just a bit,
the −0.323 gamma only lessens the benefit of the 0.563 delta. But above
$50, negative gamma begins to cause the delta to become increasingly
negative. Theta begins to wither away at higher stock prices as well.
The place to be is right at $50. The delta is flat and theta is highest. As
long as Wal-Mart finds its way up to this price by the third Friday of
August, life is good for Pete.