Question

Suppose that the one-year interest rate is 4.58 percent in the United States and 2.66 percent in Germany, and that the spot exchange rate is $1.1321/€ and the one-year forward exchange rate, is $1.2449/€. Assume that an arbitrageur can borrow up to $1,000,000. Calculate his arbitrage profit. If there is no arbitrage opportunities enter zero as your answer.

Answer 1

Particulars	Amount
Spot Rate	$             1.1321
Hi	4.5800%
Fi	2.6600%
Home Country	US
Foreign Country	Germany
Forward rate after ( in Years)	1
Actual Fwd Rate	$             1.2449
Fwd rate after ( In Months)	12
Amount Borrowed	$ 1,000,000.00

According to Int Rate parity Theorm,
Fwd rate After 1 Years = Spot rate * [ ( 1 + Hi ) ^ n ] / [ ( 1 + Fi ) ^ n ]
= $ 1.1321 * [ ( 1 + 0.0458) ^ 1 ] / [ ( 1 + 0.0266 ) ^ 1 ]
= $ 1.1321 * [ ( 1.0458) ^ 1 ] / [ ( 1.0266 ) ^ 1 ]
= $ 1.1321 * [ 1.0458 ] / [ 1.0266 ]
= $ 1.1321 * [ 1.0187 ]
= $ 1.1533

As Actual Fwd rate is not equal to IRPT Fwd rate, Covered Interest arbitrage exists.

Foreign Currency Premium or Discount:
= [ [ Fwd rate - Spot Rate ] / Spot Rate ] * 100
= [ [ $ 1.2449 - $ 1.1321 ] / $ 1.1321 ] * 100
= [ [ $ 0.1128 / $ 1.1321 ] * 100
= [ 0.0996 ] * 100
= 9.9638 %

Annualized % = Premium or Discounted / No. of Years
= 9.9638 % / 1
= 9.96 %

Effective Rate in Home Country
Effective Rate in Foreign Country

Effective Rate in Foreign currency = Int rate + Fwd Premium %
= 2.66 % + 9.96 %
= 12.62 %

Strategy:

Step	Activity
1	Borrow in Home Country
2	Convert Into Foreign currency using spot rate
3	Invest in foreign currency for specified period
4	Realize the Maturity Value in Foreign Currency
5	Convert foreign currency proceedings into Home Currency using Actual Fwd Rate
6	Maturity of Loan in Home country
7	Repay the loan along with Int and book profit

Step 1:  
Amount Borrowed   $1,000,000.00
Step 2:  
Amount in Foreign Currency   883,314.19
Step 3:  
Invest in foreign currency for specified period   1 Years
Step 4:  
Realize the Maturity Value in Foreign Currency  
Maturity Value = Amount Deposited * ( 1 +r ) ^ n   
r = Int Rate per anum  
n - Time period in Years  
= 883314.19 * ( 1 + 0.0266 ) ^ 1  
= 883314.19 * ( 1.0266 ) ^ 1  
= 883314.19 * ( 1.0266 )   
= 906810.35  
  
Step 5:  
Convert foreign currency proceedings into Home Currency using Actual Fwd Rate  
= 906810.35 * 1.2449  
= 1128888.20
  
Step 6:  
Maturity of Loan in Home country  
= 1000000 * ( 1 + 0.0458 ) ^ 1  
= 1000000 * ( 1.0458 ) ^ 1  
= 1000000 * ( 1.0458 )  
= 1045800  
  
Step 7  
Profit = Amount realized from Inv - maturity Value of Loan  
= 1128888.20 - 1045800
= 83088.20   
Book Profit of 83088.20 after 1 year.