Investments, tenth edition

Action

Initial CF ($)

CF in 1 Year ($)

1.  

Borrow 1 U.K. pound in London. Convert to dollars.

     $E 

0

2

$E

1

(1 1 r

UK

)

2.  

Use proceeds of borrowing in London to lend in 

the U.S.

2

$E 

0

       $E 

0

(1 1 r

US

)

3.  

Enter (1 1 r

UK

) futures positions to purchase 

1 pound for F

0

 dollars.

0

(1 1 r

UK

)(E

1

 2 F

0

)

  

 TOTAL

0

E

0

(1 1 r

US

) 2 F

0

(1 1 r

UK

)

 Let us again review the stages of the arbitrage operation. The first step requires borrow-

ing one pound in the United Kingdom. With a current exchange rate of  E  

0

 , the one pound 

is converted into  E  

0

  dollars, which is a cash inflow. In 1 year the British loan must be paid 

off with interest, requiring a payment in pounds of (1  1   r  

UK

 ), or in dollars of  E  

1

 (1  1   r  

UK

 ). 

In the second step the proceeds of the British loan are invested in the United States. This 

involves an initial cash outflow of $ E  

0

 , and a cash inflow of $ E  

0

 (1  1   r  

US

 ) in 1 year. Finally, 

the exchange risk involved in the British borrowing is hedged in step 3. Here, the (1  1   r  

UK

 ) 

pounds necessary to satisfy the British loan are purchased ahead in the futures contract. 

 The net proceeds to the arbitrage portfolio are risk-free and given by  E  

0

 (1   1    r  

US

 )   2  

 F  

0

 (1   1    r  

UK

 ). If this value is positive, borrow in the United Kingdom, lend in the 

United States, and enter a long futures position to eliminate foreign exchange risk. If the 

value is negative, borrow in the United States, lend in the United Kingdom, and take a 

 What if the interest rate parity relationship were violated? For example, suppose the 

futures price is $1.97/£ instead of $1.981/£. You could adopt the following strategy. 

In this example let  E  

1

  denote the exchange rate ($/£) that will prevail in 1 year.  E  

1

  is, of 

course, a random variable from the perspective of today’s investors.