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.