156 Part II: Call Option Strategies 
that if XYZ is anywhere between 60 and 70 at expiration, the stock will be called away 
at 60 against the sale of the October 60 call, and the October 70 call will expire worth­
less. It makes no difference whether the stock is at 61 or at 69; the same result will 
occur. Table 6-5 and Figure 6-3 depict the results from this variable hedge at expira­
tion. In the table, it is assumed that the option is bought back at parity to close the 
position, but if the stock were called away, the results would be the same. 
Note that the shape of Figure 6-3 is something like a trapezoid. This is the 
source of the name "trapezoidal hedge," although the strategy is more commonly 
known as a variable hedge or variable ratio write. The reader should observe that the 
maximum profit is indeed obtained if the stock is anywhere between the two strikes 
at eiqJiration. The maximum profit potential in this position, $600, is smaller than the 
maximum profit potential available from writing only the October 60's or only the 
October 70's. However, there is a vastly greater probability of realizing the maximum 
profit in a variable ratio write than there is of realizing the maximum profit in a nor­
mal ratio write. 
The break-even points for a variable ratio write can be computed most quickly 
by first computing the maximum profit potential, which is equal to the time value 
that the writer takes in. The break-even points are then computed directly by sub­
tracting the points of maximum profit from the lower striking price to get the down­
side break-even point and adding the points of maximum profit to the upper striking 
price to arrive at the upside break-even point. This is a similar procedure to that fol­
lowed for a normal ratio write: 
TABLE 6-5. 
Results at expiration of variable hedge. 
XYZ Price at XYZ October 60 October 70 Total 
Expiration Profit Profit Profit Profit 
45 -$2,000 +$ 800 +$ 300 -$900 
50 - 1,500 + 800 + 300 - 400 
54 - 1,100 + 800 + 300 0 
60 500 + 800 + 300 + 600 
65 0 + 300 + 300 + 600 
70 + 500 - 200 + 300 + 600 
76 + 1,100 - 800 300 0 
80 + 1,500 -$1,200 700 - 400 
85 + 2,000 -1,700 - 1,200 - 900