Chapter 40: Advanced Concepts 869 
in price by 0.55; so seven of them will increase by 7 x 0.55, or 3.85 points total. 
Similarly, the January 55 will increase in price by 0.35, so eleven of them would 
increase in price by 11 x 0.35, or 3.85 points total. Hence, the long side of the spread 
would profit by 3.85 points, while the short side loses 3.85 points - a neutral situation. 
The resulting position is a ratio spread. The profitability of the spread occurs 
between about 51 and 62 at expiration as shown in Figure 40-8, but that is not the 
major point. The real attractiveness of the spread to the neutral trader is that if the 
underpriced nature of the January 50 call (vis-a-vis the January 55 call) should dis­
appear, the spread should produce a profit, regardless of the short-term market 
movement of XYZ. The spread could then be closed if this should occur. 
To illustrate this fact, suppose that XYZ actually falls to 49, but the January 50 
call returns to "fair value": 
XYZ: 49 
"Theoretical 
Option Price Delta Value" 
January 50 call 3.00 0.52 3.00 
January 55 call 1.10 0.34 1.13 
February 50 put 3.90 -0.42 3.84 
Notice that the theoretical values in this table are equal to the theoretical val­
ues from the previous table, less the amount of the delta. Since the XYZ January 50 
call is no longer underpriced, the position would be removed, and the strategist 
would make nothing on his January 50's, but would make .40 on each of the eleven 
short January 55's, for a profit of $440 less commissions. 
This example leans heavily on the assumption that one is able to accurately esti­
mate the theoretical value and delta of the options. In real life, this chore can be 
quite difficult, since the estimate requires one to define the future volatility of the 
common stock. This is not easy. However, for the purposes of a spread, the ratio of 
the two deltas is used. Moreover, the example didn't require that one know the exact 
theoretical value of each option; rather, the only knowledge that was required was 
that one of the options was cheap with respect to the other options. 
As an alternative to a ratio spread, another type of delta neutral position could 
be established from the previous data: Buy the January 50 call (this is the basis of the 
position since it is supposedly the cheap option) and buy the February 50 put - the 
only other choice from the data given. This position is a long straddle of sorts. Recall 
that the delta of a put is negative; so again, the delta neutral ratio can be calculated 
by dividing the absolute value of two deltas: 
Delta neutral straddle ratio= 0.55/1-0.401 = 11-to-8