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+Chapter 39: Volatility Trading Techniques 825 
+Speaking of neutrality, one can also use the deltas of the options in question to 
+alter the ratio of puts to calls, making the position initially as neutral as possible. This 
+is the suggested approach, since the volatility buyer does not care whether the stock 
+goes up or down. He is merely interested in stock movement and/or an increase in 
+implied volatility. 
+Example: XYZ is again trading at 39.60, and the trader wants a neutral position. He 
+should use the deltas of the options to construct a neutral position. Consider the 
+October 40 straddle, for example. Assume the volatility used for the probability cal­
+culations is 40%. Under those conditions (and the ones assumed in the previous 
+example), the October 40 call has a delta of 0.60 and the October 40 put has a delta 
+of -0.40. Thus a ratio of buying 2 calls and 3 puts is a neutral ratio. If the call is sell­
+ing for 6 and the put is selling for 5, then the break-even points for a 2-by-3 position 
+would be 53.5 on the upside and 31 on the downside. This information is summarized 
+as follows: 
+Delta of October 40 call: 
+Delta of October 40 put: 
++0.60 
+-0.40 
+Delta-neutral ratio: buy 2 calls and 3 puts 
+Price of October 40 coll: 
+Price of October 40 put: 
+Net cost of 2-by-3 position: 27 points 
+Break-even points: 
+6.00 
+5.00 
+Upside = 40 + 27 /2 = 53.50 
+Downside = 40 - 27 /3 = 31 .00 
+So, the probability calculations would endeavor to determine what the chances are of 
+the stock ever trading at either 53.50 or 31.00 at any time prior to expiration. In fact, 
+since there are straddles available in several expiration months, the strategist would 
+want to analyze each of them in a similar fashion. Table 39-1 shows how his choices 
+might look. If one were considering buying a strangle, similar calculations could be 
+made using the deltas of the put and the call, where the call strike is higher than the 
+put strike. 
+Another simple strategy that can be used when volatility is low is the calendar 
+spread, because it has a positive vega. That is, it can be expected to expand if implied 
+volatility increases. For most traders, though, the limited profit nature of the calen-