Hw chapter 7 - Professor Frega PDF

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Taylor Phelps Chapter 7 Questions and Applications 1. Explain the concept of locational arbitrage and the scenario necessary for it to be plausible. Locational arbitrage occurs when the spot rate of a currency varies among locations. The ask rate at one location is lower than the bid rate at another location. The difference in rates occurs because information is not always immediately available to all banks. 2. Assume the following information: Bid price of New Zealand Dollar Ask price of New Zealand Dollar

Beal Bank $0.401 $0.404

Yardley Bank $0.398 $0.400

Given this information, is locational arbitrage possible? If so, explain the steps involved in locational arbitrage, and compute the profit from this arbitrage if you had $1,000,000 to use. What market forces would occur to eliminate any further possibilities of locational arbitrage? Yes, locational arbitrage is possible by purchasing NZ$ at Yardley Bank for $0.400 and selling them to Beal Bank for $0.401. $1 million would purchase 2.5 million NZ$ at Yardley Bank. They could be sold to Beal Bank for $1,002,500 resulting in a profit of $2,500. Others will realize the opportunity for locational arbitrage and the large demand for NZ$ at Yardley Bank will force the ask price to increase. The large sales going to Beal Bank will force the bid price down. 3. Explain the concept of triangular arbitrage and the scenario necessary for it to be plausible. Triangular arbitrage is possible when the actual cross exchange rate between two currencies differs from what it should be. The appropriate cross rate can be determined given the values of the two currencies with respect to some other currency. 4. Assume the following information: Quoted Price Value of Canadian dollar in U.S. dollars Value of New Zealand dollar in U.S. dollars Value of Canadian dollar in New Zealand dollars

$0.90 $0.30 NZ$3.02

Given this information, is triangular arbitrage possible? If so, explain the steps that would reflect triangular arbitrage, and compute the profit from this strategy if you had $1,000,000 to use. What market forces would occur to eliminate any further possibilities of triangular arbitrage? Yes, locational arbitrage is possible. The cross-exchange rate should be 1 Canadian dollar = 3 New Zealand dollars, so the actual value of the Canadian dollars compared to New Zealand dollars is more than it should be. To profit, you could purchase Canadian dollars with US

dollars, sell the Canadian dollars for New Zealand dollars, then exchange New Zealand dollars for US dollars. This would result in a profit of $6,667. $1,000,000/$.90 = C$1,111,111 × 3.02 = NZ$3,355,556 × $.30 = $1,006,667

5. Explain the concept of covered interest arbitrage and the scenario necessary for it to be plausible. Covered interest arbitrage involves the short-term investment in a foreign currency that is covered by a forward contract to sell that currency when the investment matures. Covered interest arbitrage is plausible when the forward premium does not reflect the interest rate differential between two countries specified by the interest rate parity formula. 6. Assume the following information: Spot rate of Canadian dollar 90-day forward rate of Canadian dollar 90-day Canadian interest rate 90-day US interest rate

Quoted Price $0.80 $0.79 4% 2.5 %

Given this information, what would be the yield to a US investor who used covered interest arbitrage? (Assume the investor invests $1,000,000). What market forces would occur to eliminate any further possibilities of covered interest arbitrage? = $1,000,000/$0.80 = C$1,250,000 = C$1,250,000 • (1+0.04) = C$1,300,000 = C$1,300,000 • 0.79 = $1,027,000 Yield = ($1,027,000 - $1,000,000) / $1,000 = 2.7% which exceeds the yield in the US over the 90 days period 7. Assume the following information: Spot rate of Mexican peso 180-day forward rate of Canadian dollar 180-day Mexican interest rate 180-day US interest rate

Quoted Price $0.100 $0.098 6% 5%

Given this information, is covered interest rate arbitrage worthwhile for Mexican investors who have pesos to invest? Explain the answer. Assumed initial amount is MXP 1,000,000 MXP 1,000,000 • $0.100 = $100,000 $100,000 • (1+0.05) = $105,000 $105,000 / $0.098 = MXP 1,071,429 Yield= (MXP 1,071,429 – MXP 1,000,000) / MXP 1,000,000 = 7.14% which exceeds their domestic yield, so it is worthwhile for the Mexican investor. 8. The terrorist attack on the United States on September 11, 2001, caused expectations of a weaker US economy. Explain how such expectation should have affected US interest

rates and therefore have affected the forward rate premium (or discount) on various foreign currencies. The expectations of a weaker U.S. economy resulted in a decline of short-term interest rates. The U.S. interest rate was reduced but foreign interest rates were not, therefore, the forward premium on foreign currencies decreased. 9. Explain the concept of interest rate parity. Provide the rationale for its possible existence. Interest rate parity states that the forward rate premium (or discount) of a currency should reflect the differential in interest rates between two countries. If interest rate parity did not exist, covered interest arbitrage could occur which should cause market forces to move back toward conditions which reflect interest rate parity. 10. Why do you think currencies of countries with high inflation rates tend to have forward discounts? These currencies have high interest rates causing forward rates to have discounts. 11. Assume that the existing US one-year interest rate is 10% and the Canadian one-year interest rate is 11%. Also assume that interest rate parity exists. Should the forward rate of the Canadian dollar exhibit a discount or a premium? If US investors attempt covered interest arbitrage, what will be their return? If Canadian investors attempt covered interest arbitrage, what will be their return? The Canadian dollar's forward rate should reflect a discount because its interest rate exceeds the US interest rate. US investors would earn a return of 10% using covered interest arbitrage, the same % they would earn in the US. Canadian investors would earn a return of 11% using covered interest arbitrage, the same % they would earn in Canada. 12. Why would UK investors consider covered interest arbitrage in France when the interest rate on euros in France is lower than the UK interest? If the forward premium on euros makes up for the lower interest rate, investors could use covered interest arbitrage by investing in euros and achieve higher returns than in the UK. 13. Consider investors who invest in either US or British one-year Treasury bills. Assume zero transaction costs and no taxes. a. If interest rate parity exists, then the return for UK investors who use covered interest arbitrage will be the same as the return for UK Treasury bills true b. If interest rate parity exists, then the return for British investors who use covered interest arbitrage will be the same as the return for British investors who invest in British Treasury bills true

14. Assume that the Japanese yen’s forward rate currently exhibits a premium of 6% and that interest rate parity exists. If US interest rates decrease, how must this premium change to maintain interest rate parity? Why might we expect the premium to change? The premium will decrease in order to maintain IRP, because the difference between the interest rates is reduced. We would expect the premium to change because as US interest rates decrease, US investors could benefit from covered interest arbitrage if the forward premium stays the same. The return earned by US investors who use covered interest arbitrage would not be any higher than before, but the return would now exceed the interest rate earned in the US. Therefore, there is downward pressure on the forward premium. 15. Assume that the forward rate premium of the euro was higher last month than it is today. What does this imply about interest rate differentials between the US and Europe today compared to those last month? The interest rate differential is smaller now than it was last month. 16. If the relationship that is specified by interest rate parity does not exist at any period but does exist on average, then covered interest arbitrage should not be considered by US firms. Do you agree or disagree with this statement? Explain. I disagree because if at any point in time, interest rate parity does not exist, covered interest arbitrage could earn excess returns. 17. The one-year interest rate in New Zealand is 6%. The one-year US interest rate is 10%. The spot rate of the New Zealand dollar (NZ$) is $0.50. The forward rate of the New Zealand dollar is $.54. Is covered interest arbitrage feasible for U.S. investors? Is it feasible for New Zealand investors? In each case, explain why covered interest arbitrage is or is not feasible. $1,000,000/$.50 = NZ$2,000,000 • (1.06) = NZ$2,120,000 • $.54 =$1,144,800 Yield = ($1,144,800 - $1,000,000)/$1,000,000 = 14.48% US investors can benefit from covered interest arbitrage because this yield exceeds the US interest rate of 10%. NZ$1,000,000 • $.50 = $500,000 • (1.10) = $550,000/$.54 = NZ$1,018,519 Yield = (NZ$1,018,519 - NZ$1,000,000)/NZ$1,000,000 = 1.85% New Zealand investors would not benefit from covered interest arbitrage since 1.85% is less than the 6% that they could receive from investing their funds in New Zealand. 18. Assume that the one-year US interest rate is 11%, while the one-year interest rate in Malaysia is 40%. Assume that a US bank is willing to purchase the currency of that country from you one year from now at a discount of 13%. Would covered interest arbitrage be worth considering? Is there any reason why you should not attempt covered interest arbitrage in this situation? (Ignore tax effects.)

Covered interest arbitrage would be worth considering since the return would be 21.8% which is much higher than the US interest rate. $1,000,000 • (1.40) • 0.87 =$1,218,000 Yield = ($1,218,000 - $1,000,000)/$1,000,000 = 21.8% However, the funds would be invested in Malaysia, which could cause some concern about default risk or government restrictions on convertibility of the currency back to dollars. 19. Assume that the annual US interest rate is currently 8% and Germany’s annual interest rate is currently 9%. The euros one-year forward rate currently exhibits a discount of 2%. a. Does interest rate parity exist? No, because the discount is larger than the interest rate differential. b. Can a U.S. firm benefit from investing funds in Germany using covered interest arbitrage? No, because the discount on a forward sale exceeds the interest rate advantage of investing in Germany. c. Can a German subsidiary of a US firm benefit by investing funds in the United States through covered interest arbitrage? Yes, because even though it would earn 1% less interest over the year by investing in US dollars, it would be able to sell dollars for 2% more than it paid for them 20. The South African rand has a one-year forward premium of 2%. One-year interest rates in the US are 3 percentage points higher than in South Africa. Based on this information, is covered interest arbitrage possible for a US investor if interest rate parity holds? No, covered interest arbitrage is not possible for a US investor. Although the investor can lock in the higher exchange rate in one year, interest rates are 3% lower in South Africa. 21. Assume that annual interest rates in the US are 4%, while interest rates in France are 6% a. According to IRP, what should the forward rate premium or discount of the euro be? p = (1.04) / (1.06) -1 = -0.0189 or -1.89% discount b. If the euros spot rate is $1.10, what should the one-year forward rate of the euro be? F = $1.10 • (1 - 0.0189) = $1.079 22. The following information is available: You have $500,000 to invest The current spot rate of the Moroccan dirham is $0.110. The 60-day forward rate of the Moroccan dirham is $.108.

The 60-day interest rate in the US is 1% The 60-day interest rate in Morocco is 2% a. What is the yield to a US investor who conducts covered interest arbitrage? Did covered interest arbitrage work for the investor in this case? 1. Convert dollars to Moroccan dirham: $500,000/$0.11 = MD 4,545,454.55 2. Deposit the dirham in a Moroccan bank for 60 days. You will have MD 4,545,454.55 • (1.02) = MD 4,636,363.64 in 60 days. 3. In 60 days, convert the dirham back to dollars at the forward rate and receive MD 4,636,363.64 * $.108 = $500,727.27 The yield to the U.S. investor is ($500,727.27/$500,000) - 1 = .15%. b. Would covered interest arbitrage be possible for a Moroccan investor in this case? Yes, covered interest arbitrage would be possible for a Moroccan investor. The investor would convert dirham to dollars, invest the dollars at a 1% interest rate in the US, and sell the dollars forward 60 days. Even though the Moroccan investor would earn an interest rate that is 1% lower in the US, the forward rate discount of the dirham more than offsets that differential....