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Optional chapter 6 1 Suppose that the treasurer of IBM has an extra cash reserve of $100,000,000 to invest for six months The six month interest rate is 8 percent per annum in the United States and 7[.]
Optional chapter Suppose that the treasurer of IBM has an extra cash reserve of $100,000,000 to invest for six months The six-month interest rate is percent per annum in the United States and percent per annum in Germany Currently, the spot exchange rate is €1.01 per dollar and the six-month forward exchange rate is €0.99 per dollar The treasurer of IBM does not wish to bear any exchange risk Where should he or she invest to maximize the return? To maximize the return without bearing any exchange risk, the treasurer of IBM should use the covered interest rate parity (CIRP) formula to determine the expected return on investment in each currency and choose the currency with the higher expected return According to CIRP, the expected return on investment in the US dollars is: (1 + 0.08/2) x (1.01/0.99) - = 6.1% On the other hand, the expected return on investment in euros is: (1 + 0.07/2) - = 3.5% Where (1 + 0.07/2) is the six-month compounding interest rate for euros Therefore, investing in US dollars would provide a higher expected return of 6.1% compared to 3.5% for euros Therefore, the treasurer of IBM should invest the extra cash reserve of $100,000,000 in US dollars to maximize the return without bearing any exchange risk While you were visiting London, you purchased a Jaguar for £35,000, payable in three months You have enough cash at your bank in New York City, which pays 0.35 percent interest per month, compounding monthly, to pay for the car Currently, the spot exchange rate is $1.45/£ and the three-month forward exchange rate is $1.40/£ In London, the money market interest rate is 2.0 percent for a three-month investment There are two alternative ways of paying for your Jaguar a Keep the funds at your bank in the United States and buy a £35,000 forward b Buy a certain pound amount spot today and invest the amount in the U.K for three months so that the maturity value becomes equal to £35,000 Evaluate each payment method Which method would you prefer? Why? a Keep the funds at your bank in the United States and buy a £35,000 forward: £35,000 / 1.40 = $49,000 $100,000 x (1 + 0.0035)^3 = $101,053.68 The cost of the car in dollars after earning interest would be: $49,000 / 101,053.68= $48,489.08 b Buy a certain pound amount spot today and invest the amount in the U.K for three months: PV = £35,000 / (1 + 0.02/4)^3 = £34,480.20 the cost of the car in dollars would be: £35,000 x $1.45/£ = $50,750 £34,480.20x (1 + 0.02/4)^3 = £35,000 £35,000x $1.40/£ = $49,000 Therefore, the cost of the car in dollars would be $49,000 Currently, the spot exchange rate is $1.50/£ and the three-month forward exchange rate is $1.52/£ The three-month interest rate is 8.0 percent per annum in the U.S and 5.8 percent per annum in the U.K Assume that you can borrow as much as $1,500,000 or £1,000,000 a Determine whether interest rate parity is currently holding b If IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the arbitrage profit c Explain how IRP will be restored as a result of covered arbitrage activities a $1.52/£ / $1.50/£ = (1 + 0.058/4) / (1 + 0.08/4) 1.013333 = 0.979629 Since the left-hand side is not equal to the right-hand side, IRP is not currently holding b To carry out covered interest rate arbitrage, we can follow the steps below: Step 1: Borrow the domestic currency We can borrow $1,500,000 at the domestic interest rate of 8.0% per annum, which is 2.0% for three months Interest expense = $1,500,000 x 2% x 3/12 = $7,500 Step 2: Convert the domestic currency to the foreign currency We can convert $1,500,000 to pounds at the spot rate of $1.50/£, which gives us: £1,000,000 = $1,500,000 / $1.50/£ Step 3: Invest the foreign currency We can invest £1,000,000 at the foreign interest rate of 5.8% per annum, which is 1.45% for three months Interest income = £1,000,000 x 1.45% x 3/12 = £3,625 Step 4: Enter into a forward contract At the same time, we can enter into a forward contract to sell pounds and buy dollars in three months at the forward rate of $1.52/£ Step 5: Convert back to the domestic currency After three months, we receive £1,000,000 from the investment and enter into the forward contract to sell pounds and buy dollars at the forward rate of $1.52/£ This gives us: $1,520,000 = £1,000,000 x $1.52/£ Step 6: Repay the domestic currency loan We can use the $1,520,000 to repay the domestic currency loan of $1,500,000 and pay the interest expense of $7,500 This leaves us with a profit of: Profit = $1,520,000 - $1,500,000 - $7,500 = $12,500 c Covered interest rate arbitrage activities will cause the demand for the higher interest rate currency to increase, causing its value to appreciate, and the demand for the lower interest rate currency to decrease, causing its value to depreciate As a result, the forward exchange rate will adjust to restore IRP In this case, covered interest rate arbitrage activities would cause an increase in demand for pounds and a decrease in demand for dollars, causing the pound to appreciate and the dollar to depreciate This would cause the forward exchange rate to decrease, reducing the potential profit from covered interest rate arbitrage activities Eventually, the forward exchange rate would decrease to a level where IRP is restored Currently, the spot exchange rate is $0.85/A$ and the one-year forward exchange rate is $0.81/A$ One-year interest is 3.5 percent in the United States and 4.2 percent in Australia You may borrow up to $1,000,000 or A$1,176,471, which is equivalent to $1,000,000 at the current spot rate a Determine if IRP is holding between Australia and the United States b If IRP is not holding, explain in detail how you would realize certain profit in U.S dollar terms c Explain how IRP will be restored as a result of the arbitrage transactions you carry out above a $0.81/A$ / $0.85/A$ = (1 + 0.042) / (1 + 0.035) 0.95294 = 0.95122 Since the left-hand side is not equal to the right-hand side, IRP is not holding b Step 1: Borrow the domestic currency Interest expense = $1,000,000 x 0.875% = $8,750 Step 2: Convert the domestic currency to the foreign currency A$1,176,471 = $1,000,000 / $0.85/A$ Step 3: Invest the foreign currency Interest income = A$1,176,471 x 4.2% = A$49,411.81 Step 4: Enter into a forward contract At the same time, we can enter into a forward contract to sell Australian dollars and buy U.S dollars in one year at the forward rate of $0.81/A$ Step 5: Convert back to the domestic currency $952,941.18 = A$1,176,471 x $0.81/A$ Step 6: Repay the domestic currency loan Profit = $952,941.18 - $1,000,000 - $8,750 = -$55,808.82 As we can see, we would make a loss of $55,808.82 by carrying out this transaction, so it is not profitable c The arbitrage transactions above would cause an increase in demand for Australian dollars and a decrease in demand for U.S dollars, causing the Australian dollar to appreciate and the U.S dollar to depreciate This would cause the forward exchange rate to increase, reducing the potential profit from covered interest rate arbitrage activities Eventually, the forward exchange rate would increase to a level where IRP is restored Suppose that the current spot exchange rate is €0.80/$ and the three-month forward exchange rate is €0.7813/$ The three-month interest rate is 5.6 percent per annum in the United States and 5.40 percent per annum in France Assume that you can borrow up to $1,000,000 or €800,000 a Show how to realize a certain profit via covered interest arbitrage, assuming that you want to realize profit in terms of U.S dollars Also determine the size of your arbitrage profit b Assume that you want to realize profit in terms of euros Show the covered arbitrage process and determine the arbitrage profit in euros a Interest expense=800,000 x 1.35% x 3/12 = 2,700 1/0.80 x 800,000 = 1,000,000 Interest income = 1,000,000 x 1.40% x 3/12 = 3,500 Sell ẻuos after months = 80,000 /( 0.7813/1) = 1,023,934.468 Profit in USD= 1,023,934.468 – 1,000,000 – 3,500 – 2,700 = 17,734.468 b Interest expense in euros = 800,000 x 1.35% x 3/12 = 2,700 profit in euros= 1,000,000 x 0.7813/1 – 800,000 – 2,700 = 477,218.0852 In the October 23, 1999, issue, The Economist reports that the interest rate per annum is 5.93 percent in the United States and 70.0 percent in Turkey Why you think the interest rate is so high in Turkey? On the basis of the reported interest rates, how would you predict the change of the exchange rate between the U.S dollar and the Turkish lira? According to the international Fisher Effect (IFE) the high interest rate reflects a high expected rate of inflation in Turkey 5.93% - 70% = -64.07% This means that the Turkish Lira is expected to depreciate by 64.07% against the US dollar As of November 1, 1999, the exchange rate between the Brazilian real and U.S dollar was R$1.95/$ The consensus forecast for the U.S and Brazil inflation rates for the next one-year period was 2.6 percent and 20.0 percent, respectively What would you have forecast the exchange rate to be at around November 1, 2000? Since the inflation rate is quite high in Brazil, we may use the purchasing power parity to forecast the exchange rate E(e) = E($) - E(R$) = 2.6% - 20.0% = -17.4% $) - E($) - E(R$) = 2.6% - 20.0% = -17.4% R$) = 2.6% - 20.0% = -17.4% E(ST) = So(1 + E(e)) = (R$1.95/$) (1 + 0.174)= R$2.29/$ Omni Advisors, an international pension fund manager, uses the concepts of purchasing power parity (PPP) and the International Fisher Effect (IFE) to forecast spot exchange rates Omni gathers the financial information as follows: Calculate the following exchange rates (ZAR and USD refer to the South African rand and U.S dollar, respectively) a The current ZAR spot rate in USD that would have been forecast by PPP b Using the IFE, the expected ZAR spot rate in USD one year from now c Using PPP, the expected ZAR spot rate in USD four years from now a The current ZAR spot rate in USD that would have been forecast by PPP (1.05/1.11) x (0.158) = $0.1494/rand b Using the IFE, the expected ZAR spot rate in USD one year from now (1.10/1.08) x (0.158) = $0.1609/rand c Using PPP, the expected ZAR spot rate in USD four years from now [(1.07)4 / (1.05)4] x (0.158) = $0.1704/rand Suppose that the current spot exchange rate is €1.50/£ and the one-year forward exchange rate is €1.60/£ The one-year interest rate is 5.4 percent in euros and 5.2 percent in pounds You can borrow at most €1,000,000 or the equivalent pound amount, that is, £666,667, at the current spot exchange rate a Show how you can realize a guaranteed profit from covered interest arbitrage Assume that you are a euro-based investor Also determine the size of the arbitrage profit 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 Show the covered arbitrage process and determine the pound profit amount 10 Due to the integrated nature of their capital markets, investors in both the United States and the U.K require the same real interest rate, 2.5 percent, on their lending There is a consensus in capital markets that the annual inflation rate is likely to be 3.5 percent in the United States and 1.5 percent in the U.K for the next three years The spot exchange rate is currently $1.50/£ a Compute the nominal interest rate per annum in both the United States and the U.K., assuming that the Fisher effect holds b What is your expected future spot dollar-pound exchange rate in three years from now? c Can you infer the forward dollar-pound exchange rate for one-year maturity?