Chapter 24: Ratio Spreads Using Puts 363 
before near-term expiration, since the eventual large profits will be able to overcome 
a series of small losses, but could not overcome a preponderance oflarge losses. 
RATIO PUt CALENDARS 
Using the deltas of the puts in the spread, the strategist can construct a neutral posi­
tion. If the puts are initially out-of-the-money, then the neutral spread generally 
involves selling more puts than one buys. Another type of ratioed put calendar can 
be constructed with in-the-money puts. As with the companion in-the-money spread 
with calls, one would buy more puts than he sells in order to create a neutral ratio. 
In either case, the delta of the put to be purchased is divided by the delta of the 
put to be sold. The result is the neutral ratio, which is used to determine how many 
puts to sell for each one purchased. 
Example: Consider the out-of-the-money case. XYZ is trading at 59. The January 50 
put has a delta of 0.10 and the April 50 put has a delta of -0.17. If a calendar spread 
is to be established, one would be buying the April 50 and selling the January 50. 
Thus, the neutral ratio would be calculated as 1.7 to 1 (-0.17/-0.10). Seventeen puts 
would be sold for every 10 purchased. 
This spread has naked puts and therefore has large risk if the underlying stock 
declines too far. However, follow-up action could be taken if the stock dropped in an 
orderly manner. Such action would be designed to limit the downside risk. 
Conversely, the calendar spread using in-the-money puts would normally have 
one buying more options than he is selling. An example using deltas will demonstrate 
this fact: 
Example: XYZ is at 59. The January 60 put has a delta of -0.45 and the April 60 put 
has a delta of -0.40. It is normal for shorter-term, in-the-money options to have a 
delta that is larger (in absolute terms) than longer-term, in-the-money options. 
The neutral ratio for this spread would be 0.889 (-0.40/-0.45). That is, one 
would sell only 0.889 puts for each one he bought. Alternatively stated, he would sell 
8 and buy 9. 
A spread of this type has no naked puts and therefore does have large downside 
profit potential. If the stock should rise too far, the loss is limited to the initial debit 
of the spread. The optimum result would occur if the stock were at the strike at expi­
ration because, even though the excess long put would lose money in that case, the 
spreads involving the other puts would overcome that small loss. 
Another risk of the in-the-money put spread is that one might be assigned 
rather quickly if the stock should drop. In fact, one must be careful not to establish