Suppose that the current spot exchange rate is 1.50/and the one-year forward exc

Question

Suppose that the current spot exchange rate is 1.50/and the one-year forward exchange rate is 1.45/. The one-year interest rate is 5.6% in euros and 4.9% in pounds. You can borrow at most 1,500,000 or the equivalent pound amount, i.e., 1,000,000 at the current spot exchange rate. a. Show how you can realize a guaranteed profit from covered interest arbitrage. Also determine the size of the arbitrage profit. Assume that you are a euro-based investor, i.e., you can borrow whichever currency you like, but your final profit must be in euros. b. Discuss how the interest rate parity may be restored as a result of the above transactions. c. Suppose you are a pound-based investor now (i.e., you can borrow whichever currency you like, but your final profit must be in pounds). Show the covered interest arbitrage process and determine the pound profit amount.

Explanation / Answer

Spot Rate (SR) = 1 £ = € 1.50

1 year Forword Rate (FR) = 1 £ = € 1.45

1 year interest rate :   £ = 4.9 % and € = 5.6%

Calculation of Parity Check,

Exchange rate quoted in € / £

As per Interest rate parity theory (IRPT),

( 1 + PIF(€) )^n = FR (€ / £) / SR (€ / £) * ( 1 + PIF(£) )

( 1 + 0.056 )^1 = 1.45 / 1.50 * ( 1 + 0.049)^1

1.056 = 1.014

LHS > RHS

€ = Depositing Country

£ = Borrowing Country

Thus Arbitrage Profit by Borrowing in £ and depositing in €.

Calculation of arbitrage profit :

1. Borrow £ 10,00,000 at 4.9% for 1 year.

2. Convert at SR :

(SR) = 1 £ = € 1.50

= 10,00,000 £ = € 15,00,000

3. Deposit € 15,00,000 at 5.6% for 1 year:

Withdrawl Amount = 15,00,000 * ( 1 + .056)^1

= € 15,84,000

4. Convert at FR :

(FR) = 1 £ = € 1.45

= € 15,84,000 / 1.45 = £ 10,92,414

5. Repay Borrowing :

= £ 10,00,000 * ( 1 + 0.049)^1

= £ 10,49,000

Arbitrage Profit :

Withdrwal Amount - Repayment Amount

= £ 10,92,414 - £ 10,49,000

= £ 43,414

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