Chapter 40: Advanced Concepts 881 
Hence, it is always a simple matter to create a position that is both gamma and delta 
neutral. In fact, it is just as simple to create a position that is neutral with respect to 
delta and any other risk measure, because all that is necessary is to create a neutral 
ratio of the other risk measure (gamma, vega, theta, etc.) and then eliminate the 
resulting position delta by using the underlying. 
In theory, one could construct a position that was neutral with respect to all five 
risk measures (or six, if you really want to go overboard and include "gamma of the 
gamma" as well). Of course, there wouldn't be much profit potential in such a posi­
tion, either. But such constructions are actually employed, or at least attempted, by 
traders such as market-makers who try to make their profits from the difference 
between the bid and off er of an option quote, and not from assuming market risk 
Still, the concept of being neutral with respect to more than one risk factor is a 
valid one. In fact, if a strategist can determine what he is really attempting to accom­
plish, he can often negate other factors and construct a position designed to accom­
plish exactly what he wants. Suppose that one thought the implied volatility of a cer­
tain set of options was too high. He could just sell straddles and attempt to capture 
that volatility. However, he is then exposed to movements by the underlying stock He 
would be better served to construct a position with negative vega to reflect his expec­
tation on volatility, but then also have the position be delta neutral and gamma 
neutral, so that there would be little risk to the position from market movements. This 
can normally be done quite easily. An example will demonstrate how. 
Example: XYZ is 48. There are three months to expiration, and the volatility of XYZ 
and its options is 35%. The following information is also known: 
XYZ:48 
Option Price Delta Gamma Vega 
April 50 call 2.50 0.47 0.045 0.08 
April 60 call l.00 0.17 0.026 0.06 
For whatever reasons - perhaps the historical volatility is much lower - the 
strategist decides that he wants to sell volatility. That is, he wants to have a negative 
position vega so that when the volatility decreases, he will make money. This can 
probably be accomplished by buying some April 50 calls and selling more April 60 
calls. However, he does not want any risk of price movement, so some analysis must 
be done. 
First, he should determine a gamma neutral spread. This is done in much the 
same manner as determining a delta neutral spread, except that gamma is used.