882 Part VI: Measuring and Trading Volatmty 
Merely divide the two gammas to determine the neutral ratio to be used. In this case, 
assume that the April 50 call and the April 60 call are to be used: 
Gamma neutral ratio: 0.045/0.026 = 1.73-to-l 
Thus, a gamma neutral position would be created by buying 100 April 50's and sell­
ing 173 April 60's. Alternatively, buying 10 and selling 17 would be close to gamma 
neutral as well. The larger position will be used for the remainder of this example. 
Now that this ratio has been chosen, what is the effect on delta and vega? 
Option Position Option Position Option Position 
Position Delta Delta Gamma Gamma Vega Vega 
Long 1 00 April 50 0.47 +4,700 0.045 +450 0.08 + $800 
Short 173 April 60 0.17 -2,941 0.026 -450 0.06 -1,038 
Total: + 1,759 0 - $238 
The position delta is long 1,759 shares of XYZ. This can easily be "cured" by 
shorting 1,700 or 1,800 shares ofXYZ to neutralize the delta. Consequently, the com­
plete position, including the short 1,700 shares, would be neutral with respect to both 
delta and gamma, and would have the desired negative vega. 
The actual profit picture at expiration is shown in Figure 40-11. Bear in mind, 
however, that the strategist would normally not intend to hold a position like this until 
expiration. He would close it out if his expectations on volatility decline were fulfilled 
( or proved false). 
FIGURE 40-11. 
Spread with negative vega; gamma and delta neutral. 
40000...., .... 
10000 
50 55 60 
XVZ :Stock Price