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+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.