Chapter 40: Advanced Concepts 903 
Recall that this is the sixth risk measurement of an option position. The gamma 
of the gamma is the anwunt by which the gamma will change when the stock price 
changes. 
Recall that in the earlier discussion of gamma, it was noted that gamma 
changes. This example is based on the same example used earlier. 
Example: With XYZ at 49, assume the January 50 call has a delta of 0.50 and a 
gamma of 0.05. If XYZ moves up 1 point to 50, the delta of the call will increase by 
the amount of the gamma: It will increase from 0.50 to 0.55. Simplistically, if XYZ 
moves up another point to 51, the delta will increase by another 0.05, to 0.60. 
Obviously, the delta cannot keep increasing by 0.05 each time XYZ gains anoth­
er point in price, for it will eventually exceed 1.00 by that calculation, and it is known 
that the delta has a maximum of 1.00. Thus, it is obvious that the gamma changes. 
In reality, the gamma decreases as the stock moves away from the strike. Thus, 
with XYZ at 51, the gamma might only be 0.04. Therefore, if XYZ moved up to 52, 
the call's delta would only increase by 0.04, to 0.64. Hence, the gamma of the gamma 
is -0.01, since the gamma decreased from .05 to .04 when the stock rose by one 
point. 
As XYZ moves higher and higher, the gamma will get smaller and smaller. 
Eventually, with XYZ in the low 60's, the delta will be nearly 1.00 and the gamma 
nearly 0.00. 
This change in the gamma as the stock moves is called the gamma of the 
gamma. It is probably referred to by other names, but since its use is limited to only 
the most sophisticated traders, there is no standard name. Generally, one would use 
this measure on his entire portfolio to gauge how quickly the portfolio would be 
responding to the position gamma. 
Example: With XYZ at 31. 75 as in some of the previous examples, the following risk 
measures exist: 
Option Option Option Position 
Position Delta Gamma Gamma/Gamma Gamma/Gamma 
Short 4,500 XYZ 1.00 0.00 0.0000 0 
Short 100 XYZ April 25 calls 0.89 0.01 -0.0015 -15 
Long 50 XYZ April 30 calls 0.76 0.03 -0.0006 - 3 
Long 139 XYZ July 30 calls 0.74 0.02 -0.0003 - 4 
Total Gamma of Gamma: -22