Cl,apter 6: Ratio Call Writing 153 
one is more bearish on the underlying stock, he can write in-the-money calls in a 2:1 
ratio. 
There is another way to produce a slightly more bullish or bearish ratio write. 
This is to change the ratio of calls written to stock purchased. This method is also 
used to construct a neutral profit range when the stock is not close to a striking price. 
Example: An investor is slightly bearishly inclined in his outlook for the underlying 
stock, so he might write more than two calls for each 100 shares of stock purchased. 
His position might be to buy 100 XYZ at 49 and sell 3 XYZ October 50 calls at 6 points 
each. This position breaks even at 31 on the downside, because if the stock dropped 
by 18 points at expiration, the call profits would amount to 18 points and would pro­
duce a break-even situation. To the upside, the break-even point lies at 59½ for the 
stock at expiration. Each call would be worth 9½ at expiration with the stock at 59½, 
and each call would thus lose 3½ points, for a total loss of 10½ points on the three 
calls. However, XYZ would have risen from 49 to 59½ - a 10½-point gain - therefore 
producing a break-even situation. Again, a formula is available to aid in determining 
the break-even point for any ratio. 
Maximum profit= (Striking price - Stock price) x Round lots 
purchased+ Number of calls written x Call price 
D •d b ak Striking Maximum profit owns1 e re -even = - ------~~----price Number of round lots purchased 
U .d b ak Striking Maximum profit psi e re -even = + price ( Calls written - Round lots purchased) 
Note that in the case of a 2:1 ratio write, where the number of round lots purchased 
equals 1 and the number of calls written equals 2, these formulae reduce to the ones 
given earlier for the more common 2:1 ratio write. To verify that the formulae above 
are correct, insert the numbers from the most recent example. 
Example: Three XYZ October 50 calls at a price of 6 were sold against the purchase 
of 100 XYZ at 49. The number of round lots purchased is 1. 
Maximum profit = (50 - 49) x 1 + 3 x 6 = 19 
Downside break-even= 50-19/1 = 31 
Upside break-even= 50 + 19/(3 1) = 59½ 
In the 2:1 ratio writing example given earlier, the break-even points were 37 and 63. 
The 3:1 write has lower break-even points of 31 and 59½, reflecting the more bear­
ish posture on the underlying stock.