3. (3) Assume the following data. Further assume that lending and borrowing inte

Question

3. (3) Assume the following data. Further assume that lending and borrowing interest rates are the same.

US interest rate = 6% a year (1.5% for 3 months),

UK interest rate = 4% a year (1% for 3 months)

Spot exchange rate now = 1.5$/BP

90-day forward exchange rate now = 1.59$/BP

(a) Show numerically if there is an opportunity for a covered interest rate arbitrage?

(b) Where would you invest for 90 days, covering foreign exchange risk?

(c) Where would you borrow for 90 days, covering foreign exchange risk?

Explanation / Answer

a) The forward premium for 90 days for the BP in terms of $ = (1.59-1.50)/1.50 = 6.00% The annualized premium = 6*12/3 = 24.00% The difference in annual interest rate = 6%-4% = 2.00% As the interest rate differential is not equal to the forward premium, there is opportunity for covered interest arbitrage. b) As the interest rate differential is less than the forward premium the investment should be made in BP, which has the lower interest rate. c) For the above reason, the borrowing should be made in the currency having higher interest rate, ie: in $. STEPS-- ILLUSTRATION OF THE METHODOLOGY: i) Suppose that the borrowing is made for $1000 for 90 days. The maturity value of the loan after 90 days would be 1000*101.5% = $        1,015.00 ii) Convert the $1000 borrowed at spot to get 1000/1.5 = £            666.67 iii) Invest the BP 666.67 for 90 days to get 666.67*101% = £            673.33 iv) Sell forward BP673.33 at the rate of 1.59$. The above steps are to performed on day 1; that is today. After 90 days, the following setps will be made: i) Realize the deposit in BP to get BP673.33. II) Convert it to $ at the forward rate of 1.59$ to get = 673.33*1.59 = $        1,070.60 iii) Pay the borrowing made in $ together with interest of $        1,015.00 iv) Keep the balance, being the profit in the arbitrage process $              55.60

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