Question

Currently, the spot exchange rate is $1.52/£ and the three-month forward exchange rate is $1.54/£. The three-month interest rate is 5.84% per annum in the U.S. and 5.84% per annum in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000. Your final answer should be in dollars.

If the IRP is not holding, determine the arbitrage profit. Otherwise input your answer as 0

PS: Please input your answer without any currency information.

Answer 1

Particulars	Amount
Spot Rate	$             1.5200
Hi	5.8400%
Fi	5.8400%
Home Country	US
Foreign Country	UK
Forward rate after ( in Years)	0.25
Actual Fwd Rate	$             1.5400
Fwd rate after ( In Months)	3
Amount Borrowed	$     100,000.00

According to Int Rate parity Theorm,
Fwd rate After 0.25 Years = Spot rate * [ ( 1 + Hi ) ^ n ] / [ ( 1 + Fi ) ^ n ]
= $ 1.52 * [ ( 1 + 0.0584) ^ 0 ] / [ ( 1 + 0.0584 ) ^ 0 ]
= $ 1.52 * [ ( 1.0584) ^ 0 ] / [ ( 1.0584 ) ^ 0 ]
= $ 1.52 * [ 1.0143 ] / [ 1.0143 ]
= $ 1.52 * [ 1 ]
= $ 1.52

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
= [ [ $ 1.54 - $ 1.52 ] / $ 1.52 ] * 100
= [ [ $ 0.02 / $ 1.52 ] * 100
= [ 0.0132 ] * 100
= 1.3158 %

Annualized % = Premium or Discounted / No. of Years
= 1.3158 % / 0.25
= 5.26 %

Effective Rate in Home Country
Effective Rate in Foreign Country

Effective Rate in Foreign currency = Int rate + Fwd Premium %
= 5.84 % + 5.26 %
= 11.1 %

Country which is cheap to Borrow is Home Country i.e US

If Home Country is Cheap:
Arbitrage 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
Step 2:
Amount in Foreign Currency
Step 3:
Invest in foreign currency for specified period
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
= 65789.47 * ( 1 + 0.0146)
= 65789.47 * ( 1.0146 )
= 66750
Step 5:
Convert foreign currency proceedings into Home Currency using Actual Fwd Rate
= 66750 * 1.54
= 102795

Step 6:
Maturity of Loan in Home country
= 100000 * ( 1 + 0.0146 )
= 100000 * ( 1.0146 )
= 101460.00

Step 7
Profit = Amount realized from Inv - maturity Value of Loan
= $ 102795 - $ 101460.00
= $ 1335

Book Profit of $ 1335
Pls comment, if any further assistance is required.