Question

1. Suppose the annual interest rate is 3.5% in U.S. and 4.5% in
U.K., and that the spot exchange rate is S($/£) = 1.3918 and the
forward exchange rate with 12-month maturity is F_{12}($/£)
= 1.3526. Assume you are a U.S. trader and can borrow up to
$1,000,000 (or £1,000,000). Answer the following questions.

a. Is there an arbitrage opportunity according to the Interest Rate Parity based on the above information? (show your work!)

b. Show the strategy to capture the arbitrage profit by setting up a transaction table. Listing the required transactions and cash flows. Your arbitrage profit should be in U.S. dollar.

Answer #1

**Part A:**

IRPT FWD Rate = Spot Rate * (1+Hi )/ (1 +Fi)

where HI is int rate in US & Fi is Int rate in London

= 1.3918 * (1.035) / 1.045

= 1.3785

Actual Fwd rate is not equal to IRPT forward rate, Hence arbitrage is possible.

**Part B:**

Fwd Discount = Fwd rate - Spot rate / Spot rate

= 1.3526 - 1.3918 / 1.3918

= -0.0392 / 1.3918

= -2.8%

Adjusted Fi = 4.5% -2.8%

= 1.7%

Thus Borrow in Pounds

Borrow Pounds 1,000,000

COnvert it into USD using Spot rate

AMount in USD = 1,000,000 * 1.3918

= 1,391,800

Dposit this amount in USD

Maturity Value = 1391800 * 1.035

= USD 1,440,513

COnvert it into Pounds using Fwd rate

Amount in Pound s = 1,440,513 / 1.3526

= 1,064,995.56

Settle the loan along with Int

= 1,000,000 * 1.045

= Pound 1,045,000

Book Profit = 1,064,995.56 - 1,045,000

= 19,995.56

Arbitrage Profit in USD = 19,995.56 * 1.3526

= USD 27,046

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