Question

why would traders enter a long box strategy? (options)

Answer 1

Traders would enter into a long box strategy because as long as the difference between strike prices is greater than the totl cost of executing the long box, the trader will always have a profit. Long box is constructed by buying an 'in-the-money' call and an 'in-the-money' put with different strike prices, selling an 'out-of-the-money' call and an 'out-of-the-money' put with same strike prices as the respective put and call.

This can be illustrated with an example: Suppose a stock is trading at $100. Trader buys a call option with strike of $95 for say $4 per share. He also buys a put option with strike of $105 for $4 per share. Then, he sells an 'out-of-the-money' call with a strike of $105 for $2 per share and also sells an 'out-of-the-money' put with a strike of $95 for $2 per share.

Total cost for the trader = -4 -4 +2 +2 = -4.

Suppose, the stock is trading at $100 at expiry so both in-the-money call and puts will be exercised and the out-of-money will not be exercised. Trader would make 100-95 = 5 from the long call and 105-100 = 5 from the long put. Net profit would be = 5 + 5 -4 = $6.

If the stock is trading at $115 at expiry then both calls will be in-the-money and will be exercised and both puts will expire without being exercised. The trader will gain 115-95 = 20 and have to give out 115-105 = 10. Net profit will be 20-10-4 = $6.

If the stock is trading at $85 at expiry then both puts will be in-the-money and will be exercised whereas both calls will expire without being exercised. Trader will gain 105-85 = 20 and will have to give out 95-85 = 10. Net profit will be 20-10-4 = $6.

In each scenario, the trader will have a profit.