Suppose that three month interest rates (annualised) in Japan and Australia are

Question

Suppose that three month interest rates (annualised) in Japan and Australia are 1% and 6% respectively. Further HSBC Bank quotes a spot rate of ¥82.64 and 90-day forward rate of ¥81.30. using the Derivation of Interest Rate Parityp(forward premium)={(1+interest rate home)/(1+foreign interest rate)}-1

a. Does interest rate parity hold?

b. Where would you invest?

c. Where would you borrow?

d. Do the foreign exchange quotes and interest rates present any arbitrage opportunity? If so, what arbitrage opportunity exists? Show your profits for A$5 million investment, assuming zero transaction costs.

e. If transaction costs were 0.25% per transaction, would your answer to d) above change?

Explanation / Answer

a) If the IRPT holds good, the 3 month forward rate would be 82.64*1.0025/1.015 = 81.62 As the forward rate is different, the IRPT does not hold. b) & c) The forward premium/(discount) = 81.30/82.64-1 = -1.62% The annualized discount = -1.62*4 = -6.49% As against this, the interest rate differential is 6%-1% = 5.00% As the interest rate differential is less than the forward discount, it would be beneficial to borrow the currrency having higher interest rate and invest in the currency having lower interest rate. d) Yes, the quotes present arbitrage opportunity. It would be beneficial to borrow money in the currrency having higher interest rate and invest in the currency having lower interest rate. So borrowing is to be made in A$ and investment is to be made in Yen. The following steps can be taken. On day 1: Millions a) Borrow A$5 million at 1.5% interest; the maturity value of the loan being 5*1.015 = 5.075 A$ b) Convert the A$5 million into Yen at spot to get 5*82.64 = 413.200 Yen c) Invest the Yen received to get 413.200*1.0025 = 414.233 Yen after 3 months. d) Enter into a forward contract for selling Yen at 81.30. On the due date (after 90 days): Sell the Yen and get = 414.233/81.30 = 5.095 A$ Pay the loan of A$ 5.075 million and profit 5.095-5.075 = 0.020 A$ e) Transaction cost would change the profit to loss = 0.020-5*0.25%+5.095*0.25% = -0.005 A$

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