Chapter 40: Advanced Concepts 885 
Note: All the equations cannot be set equal to zero, or the solution will be all 
zeros. This is easily handled by setting at least one equation equal to a small, nonzero 
quantity, such as 0.1. As long as at least one of the risk factors is nonzero, one can 
determine the neutral ratio for all other factors merely by solving these simultaneous 
equations. There are plenty of low-cost computer programs that can solve simultane­
ous equations such as these. 
This concept can be carried to greater lengths in order to determine the best 
spread to create in order to achieve the desired results. One might even try to use 
three different options, using the third option to neutralize delta, so that he wouldn't 
have to neutralize with stock. The third equation would use deltas as constants and 
would be set to equal zero, representing delta neutral. Solving this would require 
solving three equations in three unknowns, a simple matter for a computer. 
As long as at least one of the risk factors is nonzero, one can determine the neu­
tral ratio for all other factors merely by solving these simultaneous equations. Even 
more importantly, the computer can scan many combinations of options that produce 
a position that is both gamma and delta neutral and has a specific position vega 
(-$238, for example). One would then choose the "best" spread of the available pos­
sibilities by logical methods including, if possible, choosing one with positive theta, 
so time is working in his favor. 
To summarize, one can neutralize all variables, or he can specify the risk that he 
wants to accept in any of them. Merely write the equations and solve them. It is best 
to use a computer to do this, but the fact that it can be done adds an entirely new, 
broad dimension to option spreading and risk-reducing strategies. 
EVALUATING A POSITION USING THE RISK MEASURES 
The previous sections have dealt with establishing a new position and determining its 
neutrality or lack thereof. However, the most important use of these risk measures is 
to predict how a position will perform into the future. At a minimum, a serious strate­
gist should use a computer to print out a projection of the profits and losses and posi­
tion risk at future expected prices. Moreover, this type of analysis should be done for 
several future times in order to give the strategist an idea of how the passage of time 
and the resultant larger movements by the underlying security would affect the posi­
tion. 
First, one would choose an appropriate time period - say, 7 days hence - for the 
first analysis. Then he should use the statistical projection of stock prices (see Chapter 
28 on mathematical applications) to determine probable prices for the underlying 
security at that time. Obviously, this stock price projection needs to use volatility, and