2.16. On July 1, 2013, a Japanese company enters into a forward contract to buy $1 million with yen on January 1, 2014. On September 1, 2013, it enters into a forward contract to sell $1 million on January 1, 2014. Describe the profit or loss the company will make in dollars as a function of the forward exchange rates on July 1, 2013, and September 1, 2013.

The total payoff is given as [tex]F_2-F_1[/tex] million yen where [tex]F_1[/tex] and [tex]F_2[/tex] are the forward exchange rates of contract made on July 1, 2013 and September 1, 2013 respectively.

Explanation:

Suppose the forward exchange rates for the contrat are given as

[tex]F_1[/tex] is the forward exchange rate entered in contract on July 1, 2013 in yen per dollar.

[tex]F_2[/tex] is the forward exchange rate entered in contract on September 1, 2013 in yen per dollar.

Now the spot exchange rate on January 1, 2014 is given as [tex]S[/tex] in yen per dollar.

So the net payoff from the first contract is given as

[tex]PO_1=S-F_1[/tex] million yen

So the net payoff from the second contract is given as

[tex]PO_2=F_2-S[/tex] million yen

So the total payoff is given as

[tex]PO=PO_1+PO_2\\PO=S-F_1+F_2-S\\PO=F_2-F_1[/tex]

So the total payoff is given as [tex]F_2-F_1[/tex] million yen where [tex]F_1[/tex] and [tex]F_2[/tex] are the forward exchange rates of contract made on July 1, 2013 and September 1, 2013 respectively.