Chapter 12: Combining Calendar and Ratio Spreads 227 
itself is a rather high-probability event, because the stock is initially below the strik­
ing price. In addition, the spread can make large potential profits if the stock rallies 
after the near-term calls expire. Although this is a much less probable event, the prof­
its that can accrue add to the expected return of the spread. The only time the spread 
loses is when the stock rallies quickly, and the strategist should close out the spread 
in that case to limit losses. 
Although Table 12-2 is not mathematically definitive, it can be seen that this 
strategy has a positive expected return. Small profits occur more frequently than 
small losses do, and sometimes large profits can occur. These expected outcomes, 
when coupled with the fact that the strategist may utilize collateral such as stocks, 
bonds, or government securities to set up these spreads, demonstrate that this is a 
viable strategy for the advanced investor. 
TABLE 12-2. 
Profitability of ratio calendar spreading. 
Event 
Stock never rallies above 
strike 
Stock rallies above strike in a 
short time 
Stock rallies above strike after 
near-term call expires 
Outcome 
Small profit. 
Small loss if defensive 
action employed 
Large potential profit 
DELTA-NEUTRAL CALENDAR SPREADS 
Probability 
Large probability 
Small probability 
Small probability 
The preceding discussion dealt with a specific kind of ratio calendar spread, the out­
of-the-money call spread. A more accurate ratio can be constructed using the deltas 
of the calls involved, similar to the ratio spreads in Chapter 11. The spread can be 
created with either out-of-the-money calls or in-the-money calls. The former has 
naked calls, while the latter has extra long calls. Both types of ratio calendars are 
described. 
In either case, the number of calls to sell for each one purchased is determined 
by dividing the delta of the long call by the delta of the short call. This is the same 
for any ratio spread, not just calendars. 
Example: Suppose XYZ is trading at 45 and one is considering using the July 50 call 
and the April 50 call to establish a ratio calendar spread. This is the same situation