Question

Use the following information to answer the question. The Canadian annual interest rate is 2 percent. The interest rate in the U.K. is 4 percent. The spot rate is CAD$1.60/£. The forward rate is CAD$1.58/£ and has a one-year maturity. An arbitrager can borrow a maximum of CAD$1,000,000 or £625,000. What is the net cash flow in one year?

	A.	CAD$238.65
	B.	CAD$14,000
	C.	CAD$46,207
	D.	CAD$11,300
	E.	CAD$7,000

Answer 1

Assuming Canada is home country & UK is forein country.

Particulars	Amount
Spot Rate	1.6000
Hi	2.0000%
Fi	4.0000%
Home Country	Canada
Foreign Country	UK
Forward rate after ( in Years)	1
Actual Fwd Rate	CAD 1.5800
Fwd rate after ( In Months)	12
Amount Borrowed	CAD 1,000,000.00

According to Int Rate parity Theorm,
Fwd rate After 1 Years = Spot rate * [ ( 1 + Hi ) ^ n ] / [ ( 1 + Fi ) ^ n ]
= $ 1.6 * [ ( 1 + 0.02) ^ 1 ] / [ ( 1 + 0.04 ) ^ 1 ]
= $ 1.6 * [ ( 1.02) ^ 1 ] / [ ( 1.04 ) ^ 1 ]
= $ 1.6 * [ 1.02 ] / [ 1.04 ]
= $ 1.6 * [ 0.9808 ]
= $ 1.5692

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
= [ [ $ 1.58 - $ 1.6 ] / $ 1.6 ] * 100
= [ [ $ -0.02 / $ 1.6 ] * 100
= [ -0.0125 ] * 100
= -1.25 %

Annualized % = Premium or Discounted / No. of Years
= -1.25 % / 1
= -1.25 %

Effective Rate in Home Country	2.00%
Effective Rate in Foreign Country	2.75%

Effective Rate in Foreign currency = Int rate + Fwd Premium %
= 4 % + -1.25 %
= 2.75 %
Country which is cheap to Borrow is Home Country i.e Canada

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   CAD 10,00,000.00
Step 2:  
Amount in Foreign Currency   GBP 6,25,000.00
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
= 625000 * ( 1 + 0.04 ) ^ 1
= 625000 * ( 1.04 ) ^ 1
= 625000 * ( 1.04 )
= 650000

Step 5:
Convert foreign currency proceedings into Home Currency using Actual Fwd Rate
= 650000 * 1.58
= 1027000

Step 6:
Maturity of Loan in Home country
= 1000000 * ( 1 + 0.02 ) ^ 1
= 1000000 * ( 1.02 ) ^ 1
= 1000000 * ( 1.02 )
= 1020000

Step 7
Profit = Amount realized from Inv - maturity Value of Loan
= 1027000 - 1020000
= 7000

Book Profit of 7000

Profit realized is CAD 7000.

OPtion E is correct.