5. The spot market rate for the British pound is $1.6035/?. The 3-month futures

Question

5.  The spot market rate for the British pound is $1.6035/?.  The 3-month futures (forward) rate on the British pound is $1.6027/?.  The yield on a 3-month U.S. Treasury bill is 0.24 percent, annual percentage rate (APR).  The yield on a 3-month British government security is 0.48 percent, annual percentage rate (APR).  Show that interest rate parity (IRP) does not hold by solving for the forward rate that ensures IRP.  How would you take advantage of the arbitrage opportunity arising from the actual data (i.e., borrow 1,000,000 pounds, convert to dollars, invest in the U.S., sell the proceeds forward and repay your loan or borrow 1,000,000 dollars, convert to pounds, invest in the U.K., sell the proceeds forward and repay your loan)?

Explanation / Answer

Hi,

Please find the answer as follows:

Part A:

Spot Rate = 1.6035

Forward Rate = 1.6027

Three Month Yield (US) = .24%

Three Month Yield (Birtish) = .48%

Forward Rate Using Interest Rate Parity = Spot Rate*(1+ Three Month Yield(US)/4)(1+Three Month Yield(British)/4))

= 1.6035*(1+.24%/4)/(1+.48%/4) = 1.6025

Since, forward rate is coming to be 1.6025 as against 1.6027, there is a mismatch.

Part B:

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