Chapter 40: Advanced Concepts 865 
options. The following table of option prices may help to demonstrate these rela­
tionships: 
Example: With XYZ at 49, the following options have the rho indicated (January is 
the near-term expiration): 
Month/Strike Call Rho Put Rho 
January 35 0.05 -0.01 
January 50 0.03 -0.03 
January 60 0.00 -0.05 
July 35 0.18 -0.02 
July 50 0.14 -0.15 
July 60 0.07 -0.18 
Note that the in-the-money calls (35 strike) have larger rho than the out-of-the­
money 60's, in both January and July. Similarly, the in-the-money puts (the 60's) have 
larger rho on an absolute basis than the out-of-the-money 35's. Again, this is true for 
both January and July. 
Furthermore, note that the longer-term July rhos are all larger (again as 
absolute numbers) than their shorter-term January counterparts. 
Rho can also be calculated for an entire portfolio to obtain a "position rho," sim­
ilar to previous examples. Generally, one would not be overly concerned with his 
position rho unless his portfolio contained quite a few long-term options and/or 
deeply in-the-money ones. Thus, rho is more important as a consideration when one 
is trading LEAPS or warrants, both of which may be extremely long-term vehicles. 
Of the risk measures discussed so far, rho is the least used, since many traders tend 
to have relatively short-term options in their positions. 
THE GA,\1MA OF THE GAMMA 
Occasionally, one may hear reference to the "six measures of risk." This is the sixth 
one and it is the most arcane. At any point, one knows the delta and gamma of an 
option. As the stock moves, the delta changes (by the amount of the gamma), but so 
does the gamma. Some traders are interested in knowing how much the gamma will 
change when the stock moves. Hence, they will compute the gamma of the gamma, 
which is the arrwunt by which the gamma will change when the stock price changes. 
This concept will be discussed at the end of this chapter. It is most important for 
strategists involved in positions on highly volatile stocks, for if the stock moves far