BUS330: International Finance Workshop 04
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BUS330: International Finance
Workshop 04 (Chapter 6): Relationships among Inflation, Interest Rates and Exchange Rates
Solutions to Problems
7. Implications of IFE Assume Australian interest rates are generally above foreign interest rates. What does this suggest about the future strength or weakness of the Australian dollar based on the IFE? Should Australian investors invest in foreign securities if they believe in the IFE? Should foreign investors invest in Australian securities if they believe in the IFE?
ANSWER: The IFE would suggest that the Australian dollar will depreciate over time if Australian interest rates are currently higher than foreign interest rates. Consequently, foreign investors who purchased Australian securities would on average receive a similar yield as what they receive in their own country, and Australian investors that purchased foreign securities would on average receive a yield similar to Australian rates.
8. Real interest rate One assumption made in developing the IFE is that all investors in all countries have the same real interest rate. What does this mean?
ANSWER: The real return is the nominal return minus the inflation rate. If all investors require the same real return, then the differentials in nominal interest rates should be solely due to differentials in anticipated inflation among countries.
9. Interpreting inflationary expectations If investors in the Australia and Singapore require the same real interest rate, and the nominal rate of interest is 2 per cent higher in Singapore, what does this imply about expectations of Australian inflation and Singaporean inflation? What do these inflationary expectations suggest about future exchange rates?
ANSWER: Expected inflation in Singapore is 2 per cent above expected inflation in Australia. If these inflationary expectations come true, PPP would suggest that the value of the Singaporean dollar should depreciate by 2 per cent against the Australian dollar.
11. Source of weak currencies Currencies of some South Asian countries, such as Indian and Bangladesh, frequently weaken against most other currencies. What concept in this chapter explains this occurrence? Why don’t all Australia-based MNCs use forward contracts to hedge their future remittances of funds from South Asian countries to Australia if they expect depreciation of the currencies against the Australian dollar?
ANSWER: South Asian countries typically have very high inflation more than 150 per cent compared to Australian inflation rate. PPP theory would suggest that currencies of these countries will depreciate against the Australian dollar (and other major currencies) in order to retain purchasing power across countries. The high inflation discourages demand for South Asian imports and places downward pressure in their South Asian currencies. Depreciation of the currencies offsets the increased prices on South Asian goods from the perspective of importers in other countries.
Interest rate parity forces the forward rates to contain a large discount due to the high interest rates in South Asia, which reflects a disadvantage of hedging these currencies. The decision to hedge makes more sense if the expected degree of depreciation exceeds the degree of the forward discount. Also, keep in mind that some remittances cannot be perfectly hedged anyway because the amount of future remittances is uncertain.
12. PPP Japan has typically had lower inflation than Australia. How would one expect this to affect the Japanese yen’s value? Why does this expected relationship not always occur?
ANSWER: Japan’s low inflation should place upward pressure on the yen’s value. Yet , other factors can sometimes offset this pressure. For example, Japan heavily invests in Australian securities, which places downward pressure on the yen’s value.
13. IFE Assume that the nominal interest rate in India is 12 per cent and the interest rate in Australia is 4 per cent for one-year securities that are free from default risk. What does the IFE suggest about the differential in expected inflation in these two countries? Using this information and the PPP theory, describe the expected nominal return to Australian investors who invest in India.
ANSWER: If investors from Australia and India required the same real (inflation-adjusted) return, then any difference in nominal interest rates is due to differences in expected inflation. Thus, the inflation rate in India is expected to be about 8 per cent above the Australian inflation rate. According to PPP, the Indian rupee should depreciate by the amount of the differential between Australia and India inflation rates. Using an 8 per cent differential, the Indian rupee should depreciate by about 8 per cent. Given a 12 per cent nominal interest rate in Indian and expected depreciation of the rupees of 8 per cent, Australian investors will earn about 4 per cent. (This answer used the in exact formula, since the concept is stressed here more than precision.)
17. Estimating depreciation due to PPP Assume that the spot exchange rate of the New Zealand dollar is A$0.75. How will this spot rate adjust according to PPP if New Zealand experiences an inflation rate of 7 per cent while Australia experiences an inflation rate of 3 per cent?
ANSWER: According to PPP, the exchange rate of the New Zealand dollar will depreciate by -3.74 [(1.03/1.07) – 1] per cent.. Therefore, the spot rate would adjust to A$0.75 x [1+ (-0.0374)] = A$0.7219.
18. Forecasting the future spot rate based on IFE Assume that the spot exchange rate of the Singapore dollar is A$0.95. The one-year interest rate is 9 per cent in Australia and 5 per cent in Singapore. What will the spot rate be in one year according to the IFE? What is the force that causes the spot rate to change according to the IFE?
ANSWER: According to PPP, the exchange rate of the Singapore dollar will be appreciate by 3.81 [(1.09/1.05) – 1] per cent. Therefore, the spot rate will be A$0.9862 [A$0.95 x (1+ 0.0381)] in one- year. The force that causes this expected effect on the spot rate is the inflation differential. The anticipated inflation differential can be derived from interest rate differential.
19. Deriving forecasts of the future spot rate As of today, assume the following information is available:
Australia India
Real rate of interest required
by investors 2% 2%
Nominal interest rate 5% 11%
Spot rate — A$.20
One-year forward rate — A$.19
a. Use the forward rate to forecast the percentage change in the Indian rupee over the next year. ANSWER: (A$.19 – A$.20)/A$.20 = – .05, or –5%
b. Use the differential in expected inflation to forecast the percentage change in the Indian rupee over the next year.
ANSWER: [1.03 (1+5%-2%) / 1.09 (1+11%-2%)] – 1 = - 0.055 or -5.50% ; the negative sign represents depreciation of the Indian rupee.
c. Use the spot rate to forecast the percentage change in the Indian rupee over the next year.
ANSWER: zero per cent change
20. Inflation and interest rate effects The opening of Russia's market has resulted in a highly volatile Russian currency (the ruble). Russia's inflation has commonly exceeded 20 per cent per month. Russian interest rates commonly exceed 150 per cent, but this is sometimes less than the annual inflation rate in Russia.
a.Explain why the high Russian inflation rate has put severe pressure on the value of the ruble.
ANSWER: As Russian prices were increasing, the purchasing power of Russian consumers was declining. This would encourage them to purchase goods in the US and elsewhere, which results in a large supply of rubles for sale. Given the high Russian inflation, foreign demand for rubles to purchase Russian goods would be low. Thus, the ruble’s value should depreciate against the dollar, and against other currencies.
b. Does the effect of Russian inflation on the decline in the ruble’s value support the PPP theory? How might the relationship be distorted by political conditions in Russia?
ANSWER: The general relationship suggested by PPP is supported, but the ruble’s value will not normally move exactly as specified by PPP. The political conditions that could restrict trade or currency convertibility can prevent Russian consumers from shifting to foreign goods. Thus, the ruble may not decline by the full degree to offset the inflation differential between Russia and the US. Furthermore, the government may not allow the ruble to float freely to its proper equilibrium level.
c. Does it appear that the prices of Russian goods will be equal to the prices of US goods from the perspective of Russian consumers (after considering exchange rates)? Explain.
ANSWER: Russian prices might be higher than US prices, even after considering exchange rates , because the ruble might not depreciate enough to fully offset the Russian inflation. The exchange rate cannot fully adjust if there are barriers on trade or currency convertibility.
d. Will the effects of the high Russian inflation and the decline in the ruble offset each other for US importers? That is, how will US importers of Russian goods be affected by the conditions?
ANSWER: US importers will likely experience higher prices, because the Russian inflation may not be completely offset by the decline in the ruble’s value. This may cause a reduction in the US demand for Russian goods.
21. IFE application to Asian crisis Before the Asian crisis, many investors attempted to capitalise on the high interest rates prevailing in the South-East Asian countries, although the level of interest rates primarily reflected expectations of inflation. Explain why investors behaved in this manner. Why does the IFE suggest that the South-East Asian countries would not have attracted foreign investment before the Asian crisis despite the high interest rates prevailing in those countries?
ANSWER: The investors' behaviour suggests that they did not expect the international Fisher effect (IFE) to hold. Since central banks of some Asian countries were maintaining their currencies within narrow bands, they were effectively preventing the exchange rate from depreciating in a manner that would offset the interest rate differential. Consequently, superior profits from investing in the foreign countries were possible.
If investors believed in the IFE, the Asian countries would not attract a high level of foreign investment because of exchange rate expectations. Specifically, the high nominal interest rate should reflect a high level of expected inflation. According to purchasing power parity (PPP), the higher interest rate should result in a weaker currency because of the implied market expectations of high inflation.
23. IFE. Beth Miller does not believe that the international Fisher effect (IFE) holds. Current one- year interest rates in Europe are 5 per cent, while one-year interest rates in Australia are 3 per cent. Beth converts A$100,000 to euros and invests them in Germany. One year later, she converts the euros back to Australian dollars. The current spot rate of the euro is A$1.35.
a. According to the IFE, what should the spot rate of the euro in one year be?
b. If the spot rate of the euro in one year is A$1.00, what is Beth’s percentage return from her strategy?
c. If the spot rate of the euro in one year is A$1.15, what is Beth’s percentage return from her strategy?
d. What must the spot rate of the euro be in one year for Beth’s strategy to be successful?
ANSWER:
a.
= − 1
(1.03)
= − 1 = −1.90%
If the IFE holds, the euro should depreciate by 1.90 per cent in one year. This translates to a spot rate of A$1.35 x (1-1.90%) = A$1.3244.
b.
1. Convert dollars to euros: A$100,000/A$1.35 = €74074.07
2. Invest euros for one year and receive €74,074.07 x 1.05 = €77,777.77
3. Convert euros back to Australian dollars and receive €77,777.77 x A$1 = A$77,777.77 The percentage return is (A$77,777.77/A$100,000) -1 = 22.22%
c.
1. Convert dollars to euros: A$100,000/A$1.35 = €74074.07
2. Invest euros for one year and receive €74,074.07 x 1.05 = €77,777.773.
3. Convert euros back to Australian dollars and receive €77,777.77 x A$1.15 = A$89,444.44 The percentage return is (A$89,444.44/A$100,00) – 1 = 10.56%
d. Beth’s strategy would be successful if the spot rate of the euro in one year is greater than A$1.3244.
28. Arbitrage and PPP Assume that locational arbitrage ensures that spot exchange rates are properly aligned. Also assume that you believe in purchasing power parity. The spot rate of the Singapore dollar (S$) is A$0.95.. The spot rate of the Malaysian ringgit (MYR) is 0.45 Singapore dollars. You expect that the one-year inflation rate is 7 per cent in Singapore, 5 per cent in Malaysia and 1 per cent in Australia. The one-year interest rate is 6 per cent in Singapore, 2 per cent in Malaysia and 4 per cent in Australia. What is your expected spot rate of the Malaysian ringgit in one year with respect to Australian dollar? Show your work.
ANSWER: MYR spot rate in A$ = (A$0.95/S$) x (S$0.45/MYR) = A$0.4275/MYR. Expected % change in MYR in one year = (1.01)/(1.05) – 1 = –3.8%
Expected spot rate of MYR in one year = A$0.4275/MYR x (1- 0.038) = A$0.4113/MYR.
29. PPP and real interest rates The nominal (quoted) Australia one-year interest rate is 6 per cent, while the nominal one-year interest rate in Malaysia is 5 per cent. Assume you believe in purchasing power parity. You believe the real one-year interest rate is 2 per cent in Australia, and that the real one-year interest rate is 3 per cent in Malaysia. Today, the Malaysian ringgit (MYR) spot rate is A$0.35. What do you think the spot rate of the Malaysian ringgit will be in one year?
ANSWER: Expected inflation in Australia = 6% - 2%= 4%.
Expected inflation in Malaysia = 5% - 3% = 2%.
Expected % change in MYR = [(1 + .04)]/[(1 + .02)] – 1 = .0196 or 1.96%.
Future spot rate of MYR in one year = A$0.35 x (1 + .0196) = A$0.3569
31. PPP and cash flows BHP Billiton will receive 1 million Chinese yuan in one year from selling iron ore. It did not hedge this future transaction. BHP believes that the future value of the yuan will be determined by purchasing power parity (PPP). It expects that inflation in China will be 12 per cent next year, while inflation in Australia will be 7 per cent next year. Today, the spot rate of the yuan is A$0.21 and the one-year forward rate is A$0.25.
a. Estimate the amount of Australian dollars that BHP will receive in one year when converting its yuan (CNY) receivables into Australian dollars (A$).
b. Today, the spot rate of the Hong Kong dollar is A$0.17. BHP believes that the Hong Kong dollar will remain pegged to the Australian dollar for the next year. If BHP decides to convert its 1 million yuan into Hong Kong dollars instead of Australian dollars at the end of one year, estimate the amount of Hong Kong dollars that BHP will receive in one year when converting its yuan receivables into Hong Kong dollars.
ANSWER:
a. Expected appreciation of yuan = (1+.07)/(1+.12)-1=-.04464
Expected spot rate of yuan in one year = A$0.21 x (1 - .04464) = A$0.2006/CNY
Expected Australian dollars received from receivables = CNY1,000,000 x A$0.2006. = A$200,600
b. Expected spot rate of HK$ in one year = A$0.17/HK$ since it will remain pegged. Expected cross rate in one year = [(A$0.2006/CNY)/(A$0.17/HK$)] = HK$1.18/CNY So 1 million yuan will convert to 1,000,000 x 1.18 = HK$1,180,000
33. IFE and forward rate The one-year Treasury (risk-free) interest rate in Australia is presently 6 per cent, while the one-year Treasury interest rate in India is 13 per cent. The spot rate of the Indian rupee is A$0.21. Assume that you believe in the international Fisher effect. You will receive
1 million Indian rupee in one year.
a. What is the estimated amount of Australian dollars you will receive when converting the rupees to Australian dollars in one year at the spot rate at that time?
b. Assume that interest rate parity exists. If you hedged your future receivables with a one-year forward contract, how many dollars will you receive when converting the rupees to Australia dollars in one year?
a. Expected movement in Indian rupee = [(1.06)/(1.13) - 1]= -6.19% A$0.21 x (1 - .0619) = A$0.1970
1,000,000 x A$0.1970 = A$197,000
b. The forward rate premium = [(1.06)/(1.13) - 1]= -6.19%
A$0.21 x (1 - .0619) = A$0.1970
1,000,000 x A$0.1970 = A$197,000
34. PPP. You believe that the future value of the Australian dollar will be determined by purchasing power parity (PPP). You expect that inflation in Australia will be 6 per cent next year, while inflation in the United States will be 2 per cent next year. Today the spot rate of the Australian dollar is US$.81, and the one-year forward rate is US$.77. What is the expected spot rate of the Australian dollar in one year?
ANSWER:
Expected depreciation of A$ = [(1+ 2%)/(1+6%)] – 1 = -0.0377
Expected spot rate of A$ in one year = $0.81 x (1 - 0.0377) = $0.7794.
36. Influence of PPP Australia has expected inflation of 2 per cent, while Country A, Country B, and Country C have expected inflation of 7 per cent. Country A engages in much international trade with Australia. The products that are traded between Country A and Australia can easily be produced by either country. Country B engages in much international trade with the Australia. The products that are traded between Country B and Australia are important health products, and there are not substitutes for these products that are exported from Australia to Country B or from Country B to Australia. Country C engages in much international financial flows with Australia but very little trade. If you were to use PPP to predict the future exchange rate over the next year for the local currency of each country against the Australian dollar, do you think PPP would provide the most accurate forecast for the currency of Country A, Country B, or Country C? Briefly explain.
ANSWER: PPP should provide the most accurate forecast for the currency of Country A, because there is much international trade, so price changes can affect the volume of foreign exchange in each direction. Also, the products have substitutes, which cause each country to shift its demand in response to price movements, which causes a shift in the trade. This is not possible in the case of Country B, because substitute products are not available. Therefore, price movements of Country B will not have a major impact on trade flows, and will not have a major impact on the exchange rate. Country C does not have much trade with Australia, so its exchange rate is influenced by factors other than PPP forces.
37. Australia–Malaysia IFE Assume that one-year interest rates are 4 per cent in Australia and 6 per cent in Malaysia. The spot rate between the Australian dollar and the Malaysian ringgit is A$0.3546/MYR. Assuming that the international Fisher effect holds, what should be the exchange rate in one year?
ANSWER:
Malaysian ringgit (MYR) depreciates by - 1.89% [(1.04/1.06) -1]
If IFE holds, then the exchange rate in one year A$0.3478/MYR [A$0.3546/MYR x (1-0.0189)]
2022-03-21
Relationships among Inflation, Interest Rates and Exchange Rates