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+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