154 Part II: Call Option Strategies 
A more bullish write is constructed by buying 200 shares of the underlying stock 
and writing three calls. To quickly verify that this ratio (3:2) is more bullish, again use 
49 for the stock price and 6 for the call price, and now assume that two round lots 
were purchased. 
Maximum profit= (50-49) x 2 + 3 x 6 = 20 
Downside break-even = 50 - 20/2 = 40 
Upside break-even= 50 + 20/(3 - 2) = 70 
Thus, this ratio of 3 calls against 200 shares of stock has break-even points of 40 and 
70, reflecting a more bullish posture on the underlying stock. 
A 2: 1 ratio may not necessarily be neutral. There is, in fact, a mathematically 
correct way of determining exactly what a neutral ratio should be. The neutral ratio 
is determined by dividing the delta of the written call into 1. Assume that the delta of 
the XYZ October 50 call in the previous example is .60. Then the neutral ratio is 
1.0/.60, or 5 to 3. This means that one might buy 300 shares and sell 5 calls. Using 
the formulae above, the details of this position can be observed: 
Maximum profit= (50 -49) x 3 + 5 x 6 = 33 
Downside break-even = 50 - 33/3 = 39 
Upside break-even = 50 + 33/(5 --3) = 66½ 
According to the mathematics of the situation, then, this would be a neutral position 
initially. It is often the case that a 5:3 ratio is approximately neutral for an at-the­
money call. 
By now, the reader should have recognized a similarity between the ratio writ­
ing strategy and the reverse hedge (or simulated straddle) strategy presented in 
Chapter 4. The two strategies are the reverse of each other; in fact, this is how the 
reverse hedge strategy acquired its name. The ratio write has a profit graph that looks 
like a roof, while the reverse hedge has a profit graph that looks like a trough - the 
roof upside down. In one strategy the investor buys stock and sells calls, while the 
other strategy is just the opposite - the investor shorts stock and buys calls. Which 
one is better? The answer depends on whether the calls are "cheap" or "expensive." 
Even though ratio writing has limited profits and potentially large losses, the strate­
gy will result in a profit in a large majority of cases, if held to expiration. However, 
one may be forced to make adjustments to stock moves that occur prior to expiration. 
The reverse hedge strategy, with its limited losses and potentially large profits, pro­
vides profits only on large stock moves - a less frequent event. Thus, in stable mar­
kets, the ratio writing strategy is generally superior. However, in times of depressed 
option premiums, the reverse hedge strategy gains a distinct advantage. If calls are