868 Part VI: Measuring and Trading Volatility 
They are useful in establishing a new position, because one can see how much expo­
sure he is taking on. In addition, they are extremely useful for follow-up action, since 
one can see how his position's characteristics have developed in the current market­
place at the present time. In the following sections, the use of the risk measurement 
tools as aids in establishing a position or in following up on a position will be dis­
cussed in detail. 
DELTA NEUTRAL 
One popular type of neutral position is to be delta neutral - that is, to have the equiv­
alent stock position (ESP) or equivalent futures position (EFP) be zero. A delta neu­
tral position is one in which the sum of the projected price changes of the long options 
in the spread is essentially offset by the projected price changes of the short options 
in the same spread. 
Example: XYZ is trading at 50. The following three options are trading with the 
prices and deltas indicated. Furthermore, the "theoretical value" of each option is 
shown: 
XYZ:50 
"Theoretical 
Option Price Delta Value" 
January 50 call 3.00 0.55 3.50 
January 55 call 1.50 0.35 1.48 
February 50 put 3.50 -0.40 3.44 
Assuming that one can rely upon these "theoretical values" (a big assumption, 
by the way), it is obvious that the January 50 call is cheap with respect to the other 
options: They are close to their values, while the January 50 is 50 cents under. The 
neutral strategist would want to buy the January 50 call and hedge his purchase with 
one of the other two options presented. One choice would be to establish a spread 
wherein the January 50 calls are bought and a number of January 55's are sold. To 
determine how many are to be bought and sold, one merely has to divide the deltas 
of the two options: 
Delta neutral spread ratio = 0.55/0.35 = 11-to-7 
Thus, a delta neutral ratio spread would consist of buying 7 January 50's and sell­
ing 11 January 55's. To verify that this spread is neutral with respect to the change in 
price ofXYZ, notice that ifXYZ moves up in price 1 point, the January 50 will increase