440 Part IV: Additional Considerations 
manner, the conversion is merely the purchase of a (listed) put and the simultaneous 
sale of a (synthetic) put. Many equivalent strategies can be combined for arbitrage 
purposes. One of the more common ones is the box spread. 
Recall that it was shown that a bull spread or a bear spread could be construct­
ed with either puts or calls. Thus, if one were to simultaneously buy a (call) bull 
spread and buy a (put) bear spread, he could have an arbitrage. In essence, he is 
merely buying and selling equivalent spreads. If the price differentials work out cor­
rectly, a risk-free arbitrage may be possible. 
Example: The following prices exist: 
XYZ common, 55 
XYZ January 50 call, 7 
XYZ January 50 put, 1 
XYZ January 60 call, 2 
XYZ January 60 put, 5½ 
The arbitrageur could establish the box spread in this example by executing the 
following transactions: 
Buy a call bull spread: 
Buy XYZ January 50 call 
Sell XYZ January 60 call 
Net call cost 
Buy a put bear spread: 
Buy XYZ January 60 put 
Sell XYZ January 50 put 
Net put cost 
Total cost of position 
7 debit 
2 credit 
51/2 debit 
1 credit 
5 debit 
No matter where XYZ is at January expiration, this position will be worth 10 points. 
The arbitrageur has locked in a risk-free profit of½ point, since he "bought" the box 
spread for 9½ points and will be able to "sell" it for 10 points at expiration. To verify 
this, evaluate the position at expiration, first with XYZ above 60, then with XYZ 
between 50 and 60, and finally with XYZ below 50. If XYZ is above 60 at expiration, 
the puts will expire worthless and the call bull spread will be at its maximum poten­
tial of 10 points, the difference between the striking prices. Thus, the position can be 
liquidated for 10 points if XYZ is above 60 at expiration. Now assume that XYZ is