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+Cl,apter 6: Ratio Call Writing 161 
+Example: An investor initially sets up a neutral 5:3 ratio of XYZ October 50 calls to 
+XYZ stock, as was determined previously. The stock is at 49 and the delta is .60. 
+Furthermore, suppose the stock rises to 57 and the call now has a delta of .80. The 
+neutral ratio would currently be 1/.80 ( = 1.20) or 5:4. The ratio writer could thus buy 
+another 100 shares of the underlying stock. 
+Alternatively, he might buy in one of the short calls. In this particular example, 
+buying in one call would produce a 4:3 ratio, which is not absolutely correct. If he 
+had had a larger position initially, it would be easier to adjust to fractional ratios. 
+When the stock declines, it is necessary to increase the ratio. This can be accom­
+plished by either selling more calls or selling out some of the long stock. In theory, 
+these adjustments could be made constantly to keep the position neutral. In practice, 
+one would allow for a few points of movement by the underlying stock before adjust­
+ing. If the underlying stock rises too far, it may be logical for the neutral strategist to 
+adjust by rolling up. Similarly, he would roll down if the stock fell to or below the next 
+lower strike. The neutral ratio in that case is determined by using the delta of the 
+option into which he is rolling. 
+Example: With XYZ at 57, an investor is contemplating rolling up to the October 60's 
+from his present position of long 300 shares and short 5 XYZ October 50's. If the 
+October 60 has a delta of .40, the neutral ratio for the October 60's is 2.5:l (1 + .40). 
+Since he is already long 300 shares of stock, he should now be short 7.5 calls (3 x 2.5). 
+Obviously, he would sell 7 or 8, probably depending on his short-term outlook for the 
+stock. 
+If one prefers to adopt an even more sophisticated approach, he can make 
+adjustments between striking prices by altering his stock position, and can make 
+adjustments by rolling up or down if the stock reaches a new striking price. For those 
+who prefer formulae, the following ones summarize this information: 
+1. When establishing a new position or when rolling up or down, at the next strike: 
+N b f all t 11 Round lots held long um er o c s o se = 
+Delta of call to be sold 
+Note: When establishing a new position, one must first decide how many shares 
+of the underlying stock he can buy before utilizing the formula; 1,000 
+shares would be a workable amount. 
+2. When adjusting between strikes by buying or selling stock: