Chapter 27: Arbitrage 441 
between 50 and 60 at expiration. In that case, the out-of-the-money, written options 
would expire worthless-the January 60 call and the January 50 put. This would leave 
a long, in-the-money combination consisting of a January 50 call and a January 60 
put. These two options must have a total value of 10 points at expiration with XYZ 
between 50 and 60. (For example, the arbitrageur could exercise his call to buy stock 
at 50 and exercise his put to sell stock at 60.) Finally, assume that XYZ is below 50 at 
expiration. The calls would expire worthless if that were true, but the remaining put 
spread- actually a bear spread in the puts -would be at its maximum potential of 10 
points. Again, the box spread could be liquidated for 10 points. 
The arbitrageur must pay a cost to carry the position, however. In the prior 
example, if interest rates were 6% and he had to hold the box for 3 months, it would 
cost him an additional 14 cents (.06 x 9½ x 3112). This still leaves room for a profit. 
In essence, a bull spread ( using calls) was purchased while a bear spread ( using 
puts) was bought. The box spread was described in these terms only to illustrate the 
fact that the arbitrageur is buying and selling equivalent positions. The arbitrageur 
who is utilizing the box spread should not think in terms of bull or bear spread, how­
ever. Rather, he should be concerned with "buying" the entire box spread at a cost of 
less than the differential between the two striking prices. By "buying" the box spread, 
it is meant that both the call spread portion and the put spread portion are debit 
spreads. Whenever the arbitrageur observes that a call spread and a put spread using 
the same strikes and that are both debit spreads can be bought for less than the dif­
ference in the strikes plus carrying costs, he should execute the arbitrage. 
Obviously, there is a companion strategy to the one just described. It might 
sometimes be possible for the arbitrageur to "sell" both spreads. That is, he would 
establish a credit call spread and a credit put spread, using the same strikes. If this 
credit were greater than the difference in the striking prices, a risk-free profit would 
be locked in. 
Example: Assume that a different set of prices exists: 
XYZ common, 75 
XYZ April 70 call, 8½ 
XYZ April 70 put, 1 
XYZ April 80 call, 3 
XYZ April 80 put, 6 
By executing the following transactions, the box spread could be "sold":