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Suppose the following conditions exist between the U.S. and Canada. U.S. interest rate = 4.5%. Canadian...

Suppose the following conditions exist between the U.S. and Canada. U.S. interest rate = 4.5%. Canadian interest rate = 3.4%. Spot rate: 1 CAD = .9537 USD. 6 month forward rate: 1 CAD = .9612 USD. Are the conditions of interest rate parity violated? If so, what would be our profit if we engaged in covered interest arbitrage with $2M?

	A.	Interest rate parity is not violated- no opportunity
	B.	Yes, interest rate parity is violated. We can make a profit of $4,995.60 with our $2M.
	C.	Yes, interest rate parity is violated. We can make a profit of $5,655.90 with our $2M.
	D.	Yes, interest rate parity is violated. We can make a profit of $2,887.32 with our $2M.

Expert Solution

As per Interest Rate Parity,

Theoretical Forward Rate $/CAD = Spot $/CAD*(1+Interest Rate on $)/(1+Interest Rate on Candian $)

= 0.9537*[1+(0.045/2)]/[1+(0.034/2)]

= 0.9589

Actual Forward Rate < Theoretical Forward Rate

As the Rates are different, Interest Rate Parity(IRP) DOES NOT exist i.e. Conditions ARE VIOLATED

Actual Forward Rate of CAD is Overvalued

To make an Arbitrage Gain, Buy CAD in Spot and Sell in Forward

Steps to make an Arbitrage Gain:

Now,

(1) Borrow $2000000 for 6 months

(2) Buy CAD at Spot Rate using $2000000 and receive 2000000/0.9537 = CAD 2097095.5227

(3) Invest CAD 2097095.5227 for 6 months

(4) Enter into Forward Contract to Sell 2097095.5227*(1+0.017) = CAD 2132746.146

After 6 months,

(5) Realize Investments and receive 2097095.5227*(1+0.017) = CAD 2132746.146

(6) Sell CAD 2132746.146 under Forward Contract and receive 2132746.146*0.9612 = $2049995.596

(7) Repay the borrowings along with interest and pay 2000000*(1+0.0225) = $2045000

(8) Arbitrage Gain = Difference = $2049995.596 - $2045000 = $4995.6

jeff jeffy answered 2 years ago

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