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+Chapter 11: Ratio Call Spreads 219 
+of them are bought for 8 points, the spreader would not have to buy the remaining 3 
+until they were selling around 13. Thus, he could wait longer to the upside before 
+reducing the spread ratio to 1:1 (a bull spread). A formula can be applied to deter­
+mine the price one would have to pay for the additional long calls, to convert the ratio 
+spread into a bull spread. If the calls are bought, such a bull spread would break even 
+with the stock above the higher striking price at expiration: 
+Break-even cost of Number of short calls x Difference in strikes -Total debit to date 
+long calls - Number of naked calls 
+In the simple 2: 1 example, the number of short calls was 2, the difference in the 
+strikes was 5, the total debit was minus one (-1) (since it was actually a 1.:.point cred­
+it), and the number of naked calls is 1. Thus, the break-even cost of the additional 
+long call is [2 x 5- (-1)(1)]/l = 11. As another verification of the formula, consider 
+the 10:5 spread at the same prices. The initial credit of this spread would be 5 points, 
+and the break-even cost of the five additional long calls is 11 points each. Assume that 
+the spreader bought two additional April 40's for 8 points each (16 debit). This would 
+make the total debit to date of the spread equal to 11 points, and reduce the number 
+of naked calls to 3. The break-even cost of the remaining 3 long calls that would need 
+to be purchased if the stock continued to rally would be (10 x 5 - 11)/3 = 13. This 
+agrees with the observation made earlier. This formula can be used before actual fol­
+low-up action is implemented. For example, in the 10:5 spread, if the April 40's were 
+. selling for 8, the spreader might ask: "To what would I raise the purchase price of the 
+remaining long calls if I buy 2 April 40's for 8 right now?" By using the formula, he 
+could easily see that the answer would be 13. 
+ADJUSTING WITH THE DELTA 
+The theoretically-oriented spreader can use the delta-neutral ratio to monitor his 
+spreads as well as to establish them. If the underlying stock moves up in price too far 
+or down in price too far, the delta-neutral ratio of the spread will change. The spread­
+er can then readjust his spread to a neutral status by buying some additional long calls 
+on an upside movement by the stock, or by selling some additional short calls on a 
+downward movement by the stock Either action will serve to make the spread delta­
+neutral again. The public customer who is employing the delta-neutral adjustment 
+method of follow-up action should be careful not to overadjust, because the com­
+mission costs would become prohibitive. A more detailed description of the use of 
+deltas as a means of follow-up action is contained in Chapter 28 on mathematical 
+applications, under the heading "Facilitation or Institutional Block Positioning." The 
+general concept, however, is the same as that shown earlier for ratio writing.