Day One
The first day proves to be fairly volatile. The stock rallies from $40 to $42
early in the day. This creates a positive position delta of 5.60, or the
equivalent of being long about 560 shares. At $42, Harry covers the
position delta by selling 560 shares of the underlying stock to become delta
neutral again.
Later in the day, the market reverses, and the stock drops back down to
$40 a share. At this point, the position is short 5.60 deltas. Harry again
adjusts the position, buying 560 shares to get flat. The stock then closes
right at $40.
The net result of these two stock transactions is a gain of $1,070. How?
The gamma scalp minus the theta, as shown below.
The volatility of day one led to it being a profitable day. Harry scalped 560
shares for a $2 profit, resulting from volatility in the stock. If the stock
hadn’t moved as much, the delta would have been smaller, and the dollar
amount scalped would have been smaller, leading to an exponentially
smaller profit. If there had been more volatility, profits would have been
exponentially larger. It would have led to a bigger bite being taken out of
the market.