Chapter 40: Advanced Concepts 853 
if the stock moves far enough by expiration. Many market-makers and professional 
traders attempt to structure these types of positions, if possible, in order to take 
advantage of the sudden volatility that is inherent in today's markets. 
Position 
Position Delta Delta 
Short 4,500 XYZ 1.00 - 4,500 
Short 1 00 XYZ April 25 calls 0.89 - 8,900 
Long 50 XYZ April 30 calls 0.76 + 3,800 
Long 139 XYZ July 30 calls 0.74 + 10,286 
Total ESP: + 686 
This position, though complicated to the naked eye, reduces to being long only 
approximately 700 shares of XYZ. This is commonly referred to as being "delta long 
700 shares." Thus, the terms "delta," when referring to the sum of the deltas of a 
whole position, and "equivalent stock position" are synonymous. 
This position has some exposure to the market since it is delta long. If the posi­
tion delta were zero, it would be referred to as being delta neutral and would, theo­
retically, have no exposure to the market at that time. 
Note that one can derive some general characteristics of his delta by just exam­
ining his portfolio by eye: Short calls or long puts will introduce negative delta into 
the position; long calls or short puts will introduce positive delta. Furthermore, it is 
obvious that being long the underlying security adds to the long delta of the position, 
while being short the underlying security places more negative delta in the position. 
The use of this information to adjust the delta of one's position will be discussed in a 
later section of this chapter. 
Obviously, the delta of this entire position will change as the stock price moves 
up or down as time passes. The figure given is merely an instantaneous look at how 
the position is structured. It is the need to know how the position will change when 
other factors change that has led strategists to employ the following concepts. 
GAMMA 
Simply stated, the gamma is how fast the delta changes with respect to changes in the 
underlying stock price. It is known that the delta of a call increases as the call moves 
from out-of-the-money to in-the-money. The gamma is merely a precise measure­
ment of how fast the delta is increasing.