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Derivation of Interest Rate Parity Determining the Forward Premium Graphic Analysis of Interest Rate Parity How to Test Whether Interest Rate Parity Exists Interpretation of Interest Rate Parity Does Interest Rate Parity Hold? Considerations When Assessing Interest Rate Parity Changes in Forward Premiums
This chapter illustrates how three types of arbitrage (locational, triangular, and covered interest) are executed. Emphasize that the key to arbitrage from an MNC’s perspective is not the potential profits, but the relationships that should exist due to arbitrage.
The linkage between covered interest arbitrage and interest rate parity is critical.
1. Why are quoted spot rates very similar across all banks? 2. Why don’t arbitrage opportunities exist for long periods of time? 3. Present a scenario and ask whether any type of international arbitrage is possible. If so, how would it be executed and how would market forces be affected? 4. Provide current interest rates of two countries and ask students to determine the forward rate that would be expected according to interest rate parity.
Critical debate Should arbitrage be more regulated? Proposition Yes. Large financial institutions have the technology to recognize when one participant in the foreign exchange market is trying to sell a currency for a higher price than another participant. They also recognize when the forward rate does not properly reflect the interest rate differential. They use arbitrage to capitalize on these situations, which results in large foreign exchange transactions. In some cases, their arbitrage involves taking large positions in a currency and then reversing their positions a few minutes later.
This jumping in and out of currencies can cause abrupt price adjustments of currencies and may create more volatility in the foreign exchange market. Regulations should be created that would force financial institutions to maintain their currency positions for at least one month. This would result in a more stable foreign exchange market. Opposing view No. When financial institutions engage in arbitrage, they create pressure on the price of a currency that will remove any pricing discrepancy. If arbitrage did not occur, pricing discrepancies would become more pronounced. Consequently, firms and individuals who use the foreign exchange market would have to spend more time searching for the best exchange rate when trading a currency.
The market would become fragmented, and prices could differ substantially among banks in a region, or among regions. If the discrepancies became large enough, firms and individuals might even attempt to conduct arbitrage themselves. The arbitrage conducted by banks allows for a more integrated foreign exchange market, which ensures that foreign exchange prices quoted by any institution are in line with the market. With whom do you agree? State your reasons.
Use InfoTrac or search engines recommended by your institution to access academic journals subscribed to by your institution. The keyword “arbitrage” is probably the best means of selecting relevant articles. Such articles often conduct statistical tests of some sophistication. It is the conclusions from these tests and the debate surrounding their design and the literature review that is the real contribution to the debate. Do not be put off by the rather more obscure aspects of the statistical tests. For this subject, newspapers are not a good source as they often confuse speculation with arbitrage. Speculation is considered in the next chapter.
ANSWER: The opposing is correct assuming market efficiency. The type of arbitrage mentioned in this chapter is necessary to have consistent foreign exchange quotations among the financial institutions that serve as dealers in the foreign exchange market. Only if one believes in inefficient markets and speculative attacks on currencies that a case can be made out for regulating arbitrage type operations.
1. Locational Arbitrage. Explain the concept of locational arbitrage and the scenario necessary for it to be plausible. ANSWER: Locational arbitrage can occur when the spot rate of a given currency varies among locations. Specifically, the ask rate at one location must be lower than the bid rate at another location. The disparity in rates can occur since information is not always immediately available to all banks. If a disparity does exist, locational arbitrage is possible; as it occurs, the spot rates among locations should become realigned. 2. Locational Arbitrage. Assume the following information: Beal Bank Yardley Bank Bid price of New £0.020 £0.018 Zealand dollar Ask price of New £0.022 £0.019 Zealand dollar 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 invest. What market forces would occur to eliminate any further possibilities of locational arbitrage? ANSWER: Yes! Generally, an ask (you buy) price must be lower than a bid price (you sell). You could therefore buy from Yardley at £0.019 and sell to Beal at £0.020. With £1,000,000 buy 52,631,579 NZ dollars and sell them for £0.02 ie 52,631,579 x 0.02 = £1,052,632 a profit of £52,632. This is not the NZ dollar rate incidentally! A quicker way to the solution is £1m x (0.2/0.19 – 1) = £52,632 The large demand for New Zealand dollars at Yardley Bank will force this bank’s ask price on New Zealand dollars to increase.
The large sales of New Zealand dollars to Beal Bank will force its bid price down. Once the ask price of Yardley Bank is no longer less than the bid price of Beal Bank, locational arbitrage will no longer be beneficial. 3. Triangular Arbitrage. Explain the concept of triangular arbitrage and the scenario necessary for it to be plausible. ANSWER: 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. Triangular Arbitrage. Assume the following information: Quoted Price Value of Canadian dollar in £0.60 British pounds Value of New Zealand dollar $0.20 in British pounds Value of Canadian dollar in NZ$3.02 New Zealand dollars Given this information, is triangular arbitrage possible? If so, explain the steps that would reflect triangular arbitrage, and compute the profit from this strategy if you had £1,000,000 to invest. What market forces would occur to eliminate any further possibilities of triangular arbitrage? ANSWER: Yes. The appropriate cross exchange rate should be 1 Canadian dollar = 3 New Zealand dollars. Thus, the actual value of the Canadian dollars in terms of New Zealand dollars is more than what it should be. One could go around the triangle by obtaining Canadian dollars with pounds converting the Canadian dollars to NZ dollars and then converting the NZ dollars to pounds. £1,000,000 >>>1,000,000 /0.6 >>>(1,000,000 /0.6)x3.02>>>1,000,000 /0.6×3.02 x 0.20 = £1,006,667 a profit of £6,667 or 0.67%. If one goes the other war around ie £>>NZ$>>C$>>£ one ends up with £993,377.
One should have gone in the other direction! Alternatively, one may say suppose you had 993,377 to start with, you would end up with £1,000,000 a return of £1,000,000/993,377 – 1 = 0.67% Any one or all of the rates may adjust such that triangular arbitrage is no longer possible. Looking at the complete calculation ie 1,000,000 /0.6×3.02 x 0.20= £1,006,667 for the sum to equal £1,000,000 the 0.6 rate should rise and the 3.02 and 0.20 rates should fall. 5. Covered Interest Arbitrage. Explain the concept of covered interest arbitrage and the scenario necessary for it to be plausible. ANSWER: 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. If transactions costs or other considerations are involved, the excess profit from covered interest arbitrage must more than offset these other considerations for covered interest arbitrage to be plausible. 6. Covered Interest Arbitrage. Assume the following information: Spot rate of Canadian dollar = £0.4400 90-day forward rate of = £0.4345 Canadian dollar 90-day Canadian interest rate = 4% 90-day UK interest rate = 2.5%
Given this information, what would be the yield (percentage return) to a UK 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? ANSWER: £1,000,000/0.44 = C$2,272,727 C$2,272,727 x 1.04 = C$2,363,636 C$2,363,636 x 0.4345 = £1,027,000 A yield of 2.7% over the 90 day period better than the 2.5% domestic rate. All the rates are co-determined, so any one or all the rates coulod change: the Canadian dollar’s spot rate should rise, and its forward rate should fall; in addition, the Canadian interest rate may fall and the UK interest rate may rise. 7. Covered Interest Arbitrage. Assume the following information: Spot rate of Mexican peso 180-day forward rate of Mexican peso 180-day Mexican interest rate 180-day euro interest rate = 14.00 euros = 13.72 euros = 6% = 5%
Given this information, is covered interest arbitrage worthwhile for Mexican investors who have pesos to invest? Explain your answer. ANSWER: These rates are not realistic but will test the students’ confidence. Converting pesos to euros requires multiplication by 14 and then converting back will mean division by 13.72 so that is a return on the exchange rates of 14/13.72 – 1 = 2.04%. Interest rates will mean that 6% is paid on the original amount and 5% is earned on the converted amount, so that is an approximate return of 1.05/1.06 – 1 = 0.94% The combined return will be in exact terms: (14/13.72 x 1.05) – 0.06 – 1 = 1.14%. ie (convert abroad and earn interst and then convert back) – interest paid – 1 to obtain the return.
To check, take 100 pesos convert to euros >>> 1,400 euros earns 5% >>>1,470 euros >>> convert back to pesos 1470 / 13.72 >>> 107.14 >>> less the 6% on the 100 pesos borrowed ie 6 pesos so 107.14 – 6 = 106.14 a return of 1.14% 8. Effects of September 11. The terrorist attack on the U.S. on September 11, 2001 caused expectations of a weaker U.S. economy. Explain how such expectations could have affected U.S. interest rates, and therefore have affected the forward rate premium (or discount) on various foreign currencies. ANSWER: The expectations of a weaker U.S. economy resulted in a decline of short-term interest rates (in fact, the Fed expedited the movement by increasing liquidity in the banking system). The U.S. interest rate was reduced while foreign interest rates were not. Therefore, the forward premium on foreign currencies increased. 9. Interest Rate Parity. Explain the concept of interest rate parity.
Provide the rationale for its possible existence. ANSWER: Interest rate parity states that the forward rate premium (or discount) of a currency should reflect the differential in interest rates between the two countries. If interest rate parity didn’t exist, covered interest arbitrage could occur (in the absence of transactions costs, and foreign risk), which should cause market forces to move back toward conditions which reflect interest rate parity. The exact formula is provided in the chapter. 10. Inflation Effects on the Forward Rate. Why do you think currencies of countries with high inflation rates tend to have forward discounts? ANSWER: These currencies have high interest rates, which cause forward rates to have discounts as a result of interest rate parity.
11. Covered Interest Arbitrage in Both Directions. Assume that the existing UK one-year interest rate is 10 % and the EU one-year interest rate is 11 %. Also assume that interest rate parity exists. Should the forward rate of the euro exhibit a discount or a premium? If UK investors attempt covered interest arbitrage, what will be their return? If Euro zone investors attempt covered interest arbitrage, what will be their return? ANSWER: Using covered interest rate arbitrage should earn the same return as domestic investment. As the euro is offering a higher rate of interest by 1% so the forward exchange rate must offset that gain by being at a discount of 1%. UK investors return will be 10% ie the same as the domestic rate. Euro investors return will be 11% the same as their domestic rate.
Sounds paradoxical doesn’t it, but remember the 10% is earned in £’s and the 11% in euros. If euros inflation is 1% higher (as it should be according to Fisher) then the real return to both investors should be the same. 12. Interest Rate Parity. Why would UK investors consider covered interest arbitrage in France when the interest rate on euros in France is lower than the U.S. interest rate? ANSWER: If the forward premium on euros more than offsets the lower interest rate, investors could use covered interest arbitrage by investing in euros and achieve higher returns than in the UK. 13. Interest Rate Parity. Consider investors who invest in either U.S. or British one-year Treasury bills. Assume zero transaction costs and no taxes. a. If interest rate parity exists, then the return for U.S. investors who use covered interest arbitrage will be the same as the return for U.S. investors who invest in U.S. Treasury bills. Is this statement true or false? If false, correct the statement.
ANSWER: 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. Is this statement true or false? If false, correct the statement. ANSWER: True 14. Changes in Forward Premiums. Assume that the Japanese yen’s forward rate currently exhibits a premium of 6 percent and that interest rate parity exists. If euro zone interest rates decrease, how must this premium change to maintain interest rate parity? Why might we expect the premium to change? ANSWER: 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 euro interest rates decrease, euro investors could benefit from covered interest arbitrage if the forward premium stays the same. The return earned by euro 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 euro area.
Thus, there is downward pressure on the forward premium. 15. Changes in Forward Premiums. 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 United States and Europe today compared to those last month? ANSWER: The interest rate differential is smaller now than it was last month. 16. Interest Rate Parity. 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 U.S. firms. Do you agree or disagree with this statement? Explain. ANSWER: Disagree. If at any point in time, interest rate parity does not exist, covered interest arbitrage could earn excess returns (unless transactions costs, tax differences, etc., offset the excess returns). 17. Covered Interest Arbitrage in Both Directions. The one-year interest rate in New Zealand is 6 %.
The one-year UK interest rate is 10 %. The spot rate of the New Zealand dollar (NZ$) is £0.25. The forward rate of the New Zealand dollar is £0.27. Is covered interest arbitrage feasible for UK investors? Is it feasible for New Zealand investors? In each case, explain why covered interest arbitrage is or is not feasible. ANSWER: Converting £’s to NZ$’s and converting back will mean division by 0.25 and multiplication by 0.27 a return of 0.27/0.25 – 1 = 8%, the loss on interest rates is about 4% ie 6% – 10% so there should be a net gain of about 8% – 4% = 4% In exact terms £100 /.25 x 1.06 = NZ$424 converted back at £0.27 >>> £114.48 less the 10% owed or £10 giving a net return of £4.48. Not for NZ investors, all the figues are reversed, there is a loss on conversion of about 8% only 4% of which is recovered by getting a higher interest rate earned than the interest rate paid. 18.
Limitations of Covered Interest Arbitrage. Assume that the one-year UK interest rate is 11 percent, while the one-year interest rate in Malaysia is 40 percent. Assume that a UK bank is willing to purchase the currency of that country from you one year from now at a discount of 13 percent. 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.) ANSWER: Covered interest arbitrage would be worth considering since the return would be 21.8 percent, which is much higher than the UK interest rate. Assuming a £1,000,000 initial investment, £1,000,000 × (1.40) × .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 pounds. 19. Covered Interest Arbitrage in Both Directions. Assume that the annual U.S. interest rate is currently 8 percent and Germany’s annual interest rate is currently 9 percent. The euro’s one-year forward rate currently exhibits a discount of 2 percent. a. Does interest rate parity exist? ANSWER: 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? ANSWER: No, because the discount on a forward sale exceeds the interest rate advantage of investing in Germany. c.
Can a German subsidiary of a U.S. firm benefit by investing funds in the United States through covered interest arbitrage? ANSWER: Yes, because even though it would earn 1 percent less interest over the year by investing in U.S. dollars, it would be able to sell dollars for 2 percent more than it paid for them (it would be buying euros forward at a discount of 2 percent). 20. Covered Interest Arbitrage. The South African rand has a one-year forward premium of 2 percent. One-year interest rates in France are 3 percentage points higher than in South Africa.
Based on this information, is covered interest arbitrage possible for a French investor if interest rate parity holds? ANSWER: No, covered interest arbitrage is not possible for a French investor. Although the investor can lock in the higher exchange rate in one year, interest rates are 3 percent lower in South Africa. 21. Deriving the Forward Rate. Assume that annual interest rates in the UK are 4 percent, while interest rates in France are 6 percent. a. According to IRP, what should the forward rate premium or discount of the euro be? b. If the euro’s spot rate is £0.66, what should the one-year forward rate of the euro be? ANSWER: a. p =
(1.04) − 1 = −.0189 = −1.89% (1.06)
b. F = £0.66 (1-0.0189) = £0.648
22. Covered Interest Arbitrage in Both Directions. The following information is available: The following information is available: ☐ You have £500,000 to invest. The current spot rate of the Moroccan dirham is £0.06. The 60-day forward rate of the Moroccan dirham is £0.05. The 60-day interest rate in the United Kingdom is 1 %.
☐ The 60-day interest rate in Morocco is 2 %. a. What is the yield to a UK investor who conducts covered interest arbitrage? Did covered interest arbitrage work for the investor in this case? b. Would covered interest arbitrage be possible for a Moroccan investor in this case? ANSWER: a. Covered interest arbitrage would involve the following steps: Convert to dirham £500,000 / 0.06 = 8,333,333 dirham Interest earned 8,333,333 x 1.02 = 8,500,000 Convert back 8,500,000 x 0.05 = £425,000 so no gain to UK investors b. Yes, covered interest arbitrage would be possible for a Moroccan investor. The investor would receive a return of £0.06/0.05 – 1 = 20% which is much higher that the adverse interest rate differentials.
23. Economic Effects on the Forward Rate. Assume that Mexico’s economy has expanded significantly, causing a high demand for loanable funds there by local firms. How might these conditions affect the forward discount of the Mexican peso? ANSWER: Expansion in Mexico creates a demand for loanable funds, which places upward pressure on Mexican interest rates, which increases the forward discount on the Mexican peso (or reduces the premium).
24. Differences among Forward Rates. Assume that the 30-day forward premium of the euro with the British pound is −1 %, while the 90-day forward premium of the euro is 2 %. Explain the likely interest rate conditions that would cause these premiums. Does this ensure that covered interest arbitrage is worthwhile? ANSWER: These premiums could occur when the euro’s 30-day interest rate is above the UK 30day interest rate, but the euro’s 90-day interest rate is below the UK 90-day interest rate. Covered interest arbitrage is not necessarily worthwhile, since interest rate parity may still hold. 25. Testing Interest Rate Parity. Describe a method for testing whether interest rate parity exists. Why are transactions costs, currency restrictions, and differential tax laws important when evaluating whether covered interest arbitrage can be beneficial? ANSWER: At any point in time, identify the interest rates of the UK versus some foreign country.
Then determine the forward rate premium (or discount) that should exist according to interest rate parity. Then determine whether this computed forward rate premium (or discount) is different from the actual premium (or discount). Even if interest rate parity does not hold, covered interest arbitrage could be of no benefit if transactions costs or tax laws offset any excess gain. In addition, currency restrictions enforced by a foreign government may disrupt the act of covered interest arbitrage. 26. Deriving the Forward Rate. Before the Asian crisis began, Asian central banks were maintaining a somewhat stable value for their respective currencies. Nevertheless, the forward rate of Southeast Asian currencies exhibited a discount. Explain. ANSWER: The forward rate for the Asian currencies exhibited a discount to reflect that differential between the Asian country’s interest rate and the U.S. interest rate, in accordance with interest rate parity (IRP).
If the forward rate had not exhibited a discount, a U.S. investor could have conducted covered interest arbitrage by converting dollars to the foreign currency, investing in the foreign country, and simultaneously selling the foreign currency forward. 27. Interpreting Changes in the Forward Premium. Assume that interest rate parity holds. At the beginning of the month, the spot rate of the Canadian dollar is £0.35, while the one-year forward rate is £0.34. Assume that UK interest rates increase steadily over the month. At the end of the month, the one-year forward rate is higher (foreign currency costs more) than it was at the beginning of the month.
Yet, the one-year forward discount is larger (the one-year premium is more negative) at the end of the month than it was at the beginning of the month. Explain how the relationship between the UK interest rate and the Canadian interest rate changed from the beginning of the month until the end of the month. ANSWER: The forward discount at the beginning of the month implies that the UK interest rate is lower than the Canadian interest rate. During the month, the Canadian interest rate must have increased by a greater degree than the UK interest rate. At the end of the month, the gap between the Canadian dollar and the UK dollar is greater than it was at the beginning of the month. This results in a more pronounced forward discount.
28. Interpreting a Large Forward Discount. The interest rate in Indonesia is commonly higher than the interest rate in the UK, which reflects a higher expected rate of inflation there. Why should Europpean MNCs consider hedging their future remittances from Indonesia to their parent even when the forward discount on the currency (rupiah) is so large? ANSWER: MNCs may still consider hedging under these conditions because the alternative is to be exposed to the risk that the rupiah may depreciate over the six-month period by an amount that exceeds the degree of the discount. A large forward discount implies that the nominal interest rate in Indonesia is much higher than in the UK, which may suggest a higher rate of expected inflation. Thus, there may be severe downward pressure on the rupiah’s spot rate over time.
29. Change in the Forward Premium. At the end of this month, you (owner of a German firm) are meeting with a Japanese firm to which you will try to sell supplies. If you receive an order from that firm, you will obtain a forward contract to hedge the future receivables in yen. As of this morning, the forward rate of the yen and spot rate are the same. You believe that interest rate parity holds. This afternoon, news occurs that makes you believe that the euro-zone interest rates will increase substantially by the end of this month, and that the Japanese interest rate will not change. However, your expectations of the spot rate of the Japanese yen are not affected at all in the future.
How will your expected euro amount of receivables from the Japanese transaction be affected (if at all) by the news that occurred this afternoon? Explain. ANSWER: If euro interest rates increase, then the forward rate of the yen will exhibit a premium. Therefore, if you hedge your receivables at the end of this month, the euro amount to be received would be higher. 30. Testing IRP. The one-year interest rate in Singapore is 11 percent. The one-year interest rate in the U.S. is 6 percent. The spot rate of the Singapore dollar (S$) is $.50 and the forward rate of the S$ is $.46. Assume zero transactions costs. a. Does interest rate parity exist?
ANSWER: No, because the discount is larger than the interest rate differential. b. Can a U.S. firm benefit from investing funds in Singapore using covered interest arbitrage? ANSWER: No, because the discount on a forward sale exceeds the interest rate advantage of investing in Singapore.
Assessment of Potential Arbitrage Opportunities Recall that Blades, a UK manufacturer of roller blades, has chosen Thailand as its primary export target for “Speedos,” Blades’ primary product. Moreover, Blades’ primary customer in Thailand, Entertainment Products, has committed itself to purchase 180,000 Speedos annually for the next three years at a fixed price denominated in baht, Thailand’s currency. Because of quality and cost considerations, Blades also imports some of the rubber and plastic components needed to manufacture Speedos. Lately, Thailand has experienced weak economic growth and political uncertainty. As investors lost confidence in the Thai baht as a result of the political uncertainty, they withdrew their funds from the country. This resulted in an excess supply of baht for sale over the demand for baht in the foreign exchange market, which put downward pressure on the baht’s value.
As foreign investors continued to withdraw their funds from Thailand, the baht’s value continued to deteriorate. Since Blades has net cash flows in baht resulting from its exports to Thailand, a deterioration in the baht’s value will affect the company negatively. Ben Holt, Blades’ finance director, would like to ensure that the spot and forward rates Blades’ bank has quoted are reasonable. If the exchange rate quotes are reasonable, then arbitrage will not be possible. If the quotations are not appropriate, however, arbitrage may be possible. Under these conditions, Holt would like Blades to use some form of arbitrage to take advantage of possible mispricing in the foreign exchange market. Although Blades is not an arbitrageur, Holt believes that arbitrage opportunities could offset the negative impact resulting from the baht’s depreciation, which would otherwise seriously affect Blades’ profit margins.
Ben Holt has identified three arbitrage opportunities as profitable and would like to know which one of them is the most profitable. Thus, he has asked you, Blades’ financial analyst, to prepare an analysis of the arbitrage opportunities he has identified. This would allow Holt to assess the profitability of arbitrage opportunities very quickly. 1. The first arbitrage opportunity relates to locational arbitrage. Holt has obtained spot rate quotations from two banks in Thailand: Minzu Bank and Sobat Bank, both located in Bangkok.
The bid and ask prices of Thai baht for each bank are displayed in the table below: Minzu Sobat Bank Bank Bid £0.0149 £0.0152 Ask £0.0151 £0.0153 Determine whether the foreign exchange quotations are appropriate. If they are not appropriate, determine the profit you could generate by withdrawing £100,000 from Blades’ checking account and engaging in arbitrage before the rates are adjusted. 2. Besides the bid and ask quotes for the Thai baht provided in the previous question, Minzu Bank has provided the following quotations for the pound and the Japanese yen: Quoted Bid Price £0.0057 ¥2.69 Quoted Ask Price £0.0058 ¥2.70
Determine whether the cross exchange rate between the Thai baht and Japanese yen is appropriate. If it is not appropriate, determine the profit you could generate for Blades by withdrawing £100,000 from Blades’ current account and engaging in triangular arbitrage before the rates are adjusted.
3. Ben Holt has obtained several forward contract quotations for the Thai baht to determine whether covered interest arbitrage may be possible. He was quoted a forward rate of £0.015 per Thai baht for a 90-day forward contract. The current spot rate is £0.0151. Ninety-day interest rates available to Blades in the United Kingdom are 2 %, while 90-day interest rates in Thailand are 3.75 % (these rates are not annualized). Holt is aware that covered interest arbitrage, unlike locational and triangular arbitrage, requires an investment of funds. Thus, he would like to be able to estimate the pound profit resulting from arbitrage over and above the pound amount available on a 90-day UK deposit.
Determine whether the forward rate is priced appropriately. If it is not priced appropriately, determine the profit you could generate for Blades by withdrawing £100,000 from Blades’ current account and engaging in covered interest arbitrage. Measure the profit as the excess amount above what you could generate by investing in the UK money market. 4. Why are arbitrage opportunities likely to disappear soon after they have been discovered? To illustrate your answer, assume that covered interest arbitrage involving the immediate purchase and forward sale of baht is possible. Discuss how the baht’s spot and forward rates would adjust until covered interest arbitrage is no longer possible. What is the resulting equilibrium state called?
The first arbitrage opportunity relates to locational arbitrage. Holt has obtained spot rate quotations from two banks in Thailand: Minzu Bank and Sobat Bank, both located in Bangkok. The bid and ask prices of Thai baht for each bank are displayed in the table below: Minzu Sobat Bank Bank Bid £0.0149 £0.0152 Ask £0.0151 £0.0153 Determine whether the foreign exchange quotations are appropriate. If they are not appropriate, determine the profit you could generate by withdrawing £100,000 from Blades’ checking account and engaging in arbitrage before the rates are adjusted. ANSWER: Locational arbitrage is possible: Locational Arbitrage 1. Buy Thai baht from Minzu Bank (£100,000/£0.0151) 2. Sell Thai baht to Sobat Bank (THB 6,622,517× £0.0153) 3. Pound profit (£101,325 – £100,000) 6,622,517 101,325 1,325
2. Besides the bid and ask quotes for the Thai baht provided in the previous question, Minzu Bank has provided the following quotations for the pound and the Japanese yen:
Value of a Japanese yen in British pounds Value of a Thai baht in Japanese yen
Quoted Bid Price £0.0057 ¥2.69
Quoted Ask Price £0.0058 ¥2.70
Determine whether the cross exchange rate between the Thai baht and Japanese yen is appropriate. If it is not appropriate, determine the profit you could generate for Blades by withdrawing £100,000 from Blades’ current account and engaging in triangular arbitrage before the rates are adjusted. ANSWER: Triangular arbitrage is possible. Triangular Arbitrage 1. Exchange pounds for Thai baht (£100,000/£0.0151) 2. Convert the Thai baht into Japanese yen (THB 6,622,517 × ¥2.69) 3. Convert the Japanese yen into pounds (¥17,814,571× £0.0058) 4. Dollar profit (£103,324– £100,000) 6,622,517 17,814,571 103,324 3,324
Ben Holt has obtained several forward contract quotations for the Thai baht to determine whether covered interest arbitrage may be possible. He was quoted a forward rate of £0.015 per Thai baht for a 90-day forward contract. The current spot rate is £0.0151. Ninety-day interest rates available to Blades in the United Kingdom are 2 %, while 90-day interest rates in Thailand are 3.75 % (these rates are not annualized). Holt is aware that covered interest arbitrage, unlike locational and triangular arbitrage, requires an investment of funds. Thus, he would like to be able to estimate the pound profit resulting from arbitrage over and above the pound amount available on a 90-day UK deposit.
Determine whether the forward rate is priced appropriately. If it is not priced appropriately, determine the profit you could generate for Blades by withdrawing £100,000 from Blades’ current account and engaging in covered interest arbitrage. Measure the profit as the excess amount above what you could generate by investing in the UK money market. ANSWER: Covered interest arbitrage is possible. Covered Interest Arbitrage 1. On Day 1, convert pounds to Thai baht and set up a 90-day deposit account at a Thai bank (£100,000/£0.0151) 2. In 90 days, the Thai deposit will mature to THB 6,622,517× 1.0375, which is the amount to be sold forward 3. In 90 days, convert the Thai baht into pounds at the agreed-upon rate (THB 6,870,861× £0.015) 6,622,517 6,870,861 103,063
4. Dollar amount available on a 90-day UK deposit ($100,000 × 1.02) 5. Dollar profit over and above the dollar amount available on a 90-day U.S. deposit (£103,063 – £102,000)
3. Why are arbitrage opportunities likely to disappear soon after they have been discovered? To illustrate your answer, assume that covered interest arbitrage involving the immediate purchase and forward sale of baht is possible. Discuss how the baht’s spot and forward rates would adjust until covered interest arbitrage is no longer possible. What is the resulting equilibrium state called? ANSWER: Arbitrage opportunities are likely to disappear soon after they have been discovered because of market forces. Due to the actions taken by arbitrageurs, supply and demand for the foreign currency adjust until the mispricing disappears. For example, covered interest arbitrage involving the immediate purchase and subsequent sale of Thai baht would place upward pressure on the spot rate of the Thai baht and downward pressure on the Thai baht forward rate until covered interest arbitrage is no longer possible. At that point, interest rate parity exists, and the interest rate differential between the two countries is exactly offset by the forward premium or discount.
Assessment of Prevailing Spot and Forward Rates by the Sports Exports Company As the Sports Exports Company from Ireland exports basketballs to the United Kingdom, it receives British pounds. The cheque (denominated in pounds) for last month’s exports just arrived. Jim Logan (owner of the Sports Exports Company) normally deposits the cheque with his local bank and requests that the bank convert the cheque to euros at the prevailing spot rate (assuming that he did not use a forward contract to hedge this payment). Jim’s local bank provides foreign exchange services for many of its business customers who need to buy or sell widely traded currencies. Today, however, Jim decided to check the quotations of the spot rate at other banks before converting the payment into euros.
1. Do you think Jim will be able to find a bank that provides him with a more favorable spot rate than his local bank? Explain. 2. Do you think that Jim’s bank is likely to provide more reasonable quotations for the spot rate of the British pound if it is the only bank in town that provides foreign exchange services? Explain. 3. Jim is considering using a forward contract to hedge the anticipated receivables in pounds next month. His local bank quoted him a spot rate of 1.45 euros and a one-month forward rate of 1.4435 euros.
Before Jim decides to sell pounds one month forward, he wants to be sure that the forward rate is reasonable, given the prevailing spot rate. A one-month Treasury security in Ireland currently offers a yield (not annualized) of 1 %, while a one-month Treasury security in the United Kingdom offers a yield of 1.4 %. Do you believe that the one-month forward rate is reasonable given the spot rate of 1.45 euros?
ANSWER: No. The higher interest rate in the UK means that there will be a discount in the forward market but the discount is more than it should be. The differences are in any case small and unlikely to transpire. The forward rate should only be used if Jim feels that he cannot afford the possibility of a negative movement below the forward rate that month. As with any insurance, you should only insure if you cannot afford the consequences.: p = [(1 + .01)/(1 + .014)] – 1 = [.996055] – 1 = –.0039448 The actual premium is: p = (F – S)/S = (1.4435 euros – 1.45 euros)/ 1.45 euros = –.00448
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