# Long Box Spread-Outcomes at Expiration

A long box position has five possible outcomes at expiration. As summarized in Table 6-20, the stock price can be below the lower strike price, exactly at the lower strike price, between the two strike prices, exactly at the higher strike price, or above the higher strike price.If the stock price closes below the lower strike price at expiration, outcome 1 in Table 6-20, then both calls are out of the money and expire worthless.

The long 100 Put is exercised, creating a stock sale transaction at 100, and the short 90 Put is assigned, creating a stock purchase transaction at 90. The simultaneous purchase and sale of stock incurs two commission costs but does not result in a stock position. However, a net amount equal to the difference between the strike prices, or 10 in this example, is received.

This amount pays back the borrowed funds, the transaction costs, the borrowing costs, and the net profit, if any. If the amount received is less than the loan plus costs, however, then the result is a loss.If the stock price closes between the strike prices, outcome 3, then the short call and short put are out of the money and expire worthless.The long call and long put, however, are in the money and are exercised.

Exercising the 90 Call creates a stock purchase transaction at 90, and exercising the 100 Put creates a stock sale transaction at 100. As in the preceding outcome, simultaneously buying and selling stock creates a net result equal to the difference between the strike prices, or 10.If the stock price rises above the higher strike price, outcome 5, then both puts are out of the money and expire worthless. Both calls, however, are in the money.

The long 90 Call is exercised, creating a stock purchase transaction at 90, and the short 100 Call is assigned, creating a stock sale transaction at 100. Again, the trader would receive an amount equal to the difference between the strike prices of 10.Therefore, if the stock price is below the lower strike price, between the strike prices, or above the higher strike price at expiration, then the long box position will be closed.

As a result, a trader will not be left with an open stock position and the attendant risk that could reduce the profit or create a loss.Long Box—Double Pin Risk A stock price closing exactly at one of the strike prices at expiration, outcomes 2 and 4, creates a pin-risk situation. The out-of-the-money option will expire worthless, and in theory, both the at-the-money call and the at-the-money put will expire worthless.

The in-the-money option from the other strike price, however, will create a stock position with pin risk.If the stock price closes exactly at the lower strike price of 90, outcome 2 in Table 6-20, then exercise of the in-the-money 100 Put will create a short stock position. If the stock price closes exactly at the higher strike price of 100, outcome 4, then exercise of the in-themoney 100 Call will create a long stock position.

As with pin risk in conversion and reverse conversion positions, it is impossible to predict how many of the short at-the-money options will be assigned.Consequently,market makers typically respond by exercising half the long at-the-money options, hoping that only half the short options will  be assigned. Undoubtedly, more or less than half the short options will be assigned, and a trader will need to close a stock position on Monday.

As with conversions and reversals, all a trader can do is hope that the experience will not be too costly.Pricing a Long Box Spread:Given the high probability that a box spread will result in a cash payment equal to the difference between the strike prices at expiration,the value of a long box spread is equal to the DPV of the difference between the strike prices less costs and a profit margin.

The next example discusses a box spread involving 100 and 110 strike prices, not 90 and 100 strike prices, as in the preceding example.Tables 6-21 through 6-23 show, in three parts, how a 100–110 box spread might be priced. Table 6-21 states the assumptions. The price of the 100 Call (1) is 9.10. The price of the 100 Put (2) is 2.30. The price of the 110 Call (3) is unknown. The price of the 110 Put (4) is 6.70.

The borrowing rate (5) of 5 percent and the days to expiration (6) of 60 lead to the DPV of the difference between the strike prices (7) of 9.92. There are also trading costs (8 and 9) of 1 cent per share to trade an option and for option exercise or assignment. The total costs therefore are 6 cents, 4 cents for opening the four-part position plus 2 cents for exercise or assignment of the in-the-money options at expiration that close the position.Finally, the target profit (10) is 5 cents per share in this example.