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Chapter 10 Foreign Exchange Conceptual and Analytical Problems If the U.S. dollar-British pound exchange rate is $1.50 per pound, and the U.S. dollar-euro rate is $0.90 per euro: What is the pound-per-euro rate? How could you profit if the pound-per-euro rate were above the rate you calculated in part a? What if it were lower? Answer: a. £0.6/€ b. If the pound per euro rate were above £0.6/€, you could profit by converting dollars to euros, euros to pounds, and then pounds to dollars. For example, if the rate were £0.7/€ and you started with $90, you could exchange the $90 for €100. Then you could exchange €100 for £70, and £70 for $105, making a profit of $15. If the pound per euro rate were below £0.6/€, you could make a profit by converting dollars to pounds, pounds to euros, and then euros to dollars. If a computer game costs $30 in the United States and £26 in United Kingdom, what is the real “computer game” exchange rate? Look up the current dollar-pound exchange rate in a newspaper or an online source, and compare the two prices. What do you conclude? Answer: As of November 23, 2016, the dollar-pound exchange rate was $1.2432 per pound. The real computer game exchange rate is $30/(£26 × 1.2432) = 0.93. This is the ratio of the cost of a computer game in the United States to the cost of a game in the U.K. Since the real computer game exchange rate is less than one, it implies that this game is cheaper in the United States than in the U.K; you can exchange one U.S. computer game for 0.93 of a U.K. computer game. Suppose the euro-dollar exchange rate moves from $0.90 per euro to $0.92 per euro. At the same time, the prices of European made goods and services rise 1 percent, while prices of American made goods and services rise 3 percent. What has happened to the real exchange rate between the dollar and the euro? Assuming the same change in the nominal exchange rate, what if inflation were 3 percent in Europe and 1 percent in the United States? Answer: In the first case there is (approximately) no change in the real exchange rate because inflation in the U.S. is 2 percent higher than in Europe and the dollar has depreciated about 2 percent against the euro. In this case, assume that initially the cost of goods in the U.S. is $100 and that the cost of goods in Europe is 100€. The real exchange rate is: (Dollar price of U.S.goods)/(Euro price of European goods*($/€)) So, we would have 100 / (100 × 0.90) = 1.11 as the real exchange rate at the initial exchange rate. If prices in the U.S. rise by 3 percent and those in Europe by 2 percent while at the same time the dollar price of the euro changed to $.92, then the real exchange rate would be 103 / (101 × 0.92) = 1.108, about the same. Using similar computations, it can be shown that in the second case the real dollar/euro exchange rate has risen by 4 percent. The same television set costs $500 in the United States, €450 in France, £300 in the United Kingdom, and ¥100,000 in Japan. If the law of one price holds, what are the euro-dollar, pound-dollar, and yen-dollar exchange rates? Why might the law of one price fail? Answer: If the law of one price holds, then the euro/dollar exchange rate should be €450/$500 = €0.9/$, the pound/dollar exchange rate should be £300/$500 = £0.6/$, and the yen/dollar exchange rate should be ¥100,000/$500 = ¥200/$. The law of one price may fail because of transportation costs, tariffs, and technical specifications. What does the theory of purchasing power parity predict in the long run regarding the inflation rate of a country that fixes its exchange rate to the U.S. dollar? Answer: According to the theory of purchasing power parity, changes in exchange rates are tied to differences in inflation from one country to another. If, as in the case of a fixed exchange rate, there are no exchange rate changes, it predicts that the inflation rate in that country should be the same as the U.S. rate of inflation in the long run. Can purchasing power parity help predict short-term movements in exchange rates? Answer: Purchasing power parity doesn’t hold on a day-to-day basis – or even on a month-to-month or year-to-year basis. It tells us how exchange rates will move over long periods like decades. In the short run, exchange rates can deviate substantially from their purchasing power parity levels. In the short run, exchange rates are determined by a host of factors affecting supply and demand for currencies and are effectively unpredictable. You need to purchase Japanese yen and have called two brokers to get quotes. The first broker offered you a rate of 125 yen per dollar. The second broker, ignoring market convention, quoted a price of 0.0084 dollars per yen. To which broker should you give your business? Why? Answer: An exchange rate of 0.0084 dollars per yen is equivalent to 119 yen per dollar (¥1/$0.0084 = ¥119/$), so you should get yen from the first broker. During the 1990s, the U.S. Secretary of the Treasury often stated, “a strong dollar is in the interest of the United States.” Is this statement true? Explain your answer. What can the Secretary of the Treasury actually do about the value of the dollar relative to other currencies? Answer: a. When the dollar is strong, foreign goods are relatively cheap for consumers in the United States. This helps keep inflation in check. A strong dollar also attracts foreign investment. However, when the dollar is strong, U.S. goods are more expensive for foreigners, and U.S. exports fall. So, a strong dollar benefits some people and hurts others. What is more beneficial is a stable dollar, so that there is not much exchange rate risk. b. Without the cooperation of the Federal Reserve, the Secretary of the Treasury can’t do anything about the value of the dollar. He or she can buy and sell foreign currencies, but this is not usually effective in changing the value of the dollar because it does not influence the interest rate. And it is the interest rate that influences investors’ demand for and supply of dollars. The following table gives selective data on nominal exchange rates, price levels, and real exchange rates for Country A and several other countries. Country A uses the dollar (A$) as its currency. Fill in the blanks in the table.
Nominal Exchange Rate (A$ per unit of other currency) Price Level in Country A Price Level in Other Country Real Exchange Rate
Country B $1.25 per unit of currency B 114.5 88.3
Country C 114.5 95.6 1.23
Country D $0.55 per unit of currency D 114.5 0.80
Answer: Nominal Exchange Rate (A$ per unit of other currency) Price Level in Country A Price Level in Other Country Real Exchange Rate
Country B $1.25 per unit of currency B 114.5 88.3 114.5/(88.3 × 1.25) = 1.04
Country C 114.5/(95.6 × 1.23) = $0.973/unit of currency C 114.5 95.6 1.23
Country D $0.55 per unit of currency D 114.5 114.5/(.80 × $0.55) = 260.23 0.80
If the price (measured in a common currency) of a particular basket of goods is 10 percent higher in the U.K. than it is in the United States, which country’s currency is undervalued, according to the theory of purchasing power parity? (LO2) Answer: According to the theory of purchasing power parity, the real exchange rate should equal 1. If we look at the ratio of the cost of the basket of goods in the United States to the cost in the U.K., that ratio (which is the real exchange rate taking the United States to be the home country), is less than one. The U.S. dollar is therefore undervalued. If the dollar were to strengthen, the dollar price of the U.K. basket of goods would fall, bringing the real exchange rate back towards 1. You hear an interview with a well-known economist who states that she expects the U.S. dollar to strengthen against the British pound over the next five to ten years. This economist is known for her support of the theory of purchasing power parity. Using an equation to summarize the relationship predicted by purchasing power parity between exchange-rate movements and the inflation rates in the two countries, explain whether you expect inflation in the United States to be higher or lower on average compared with that in the U.K. over the period in question. Answer: The economist’s comments were about exchange rate movements in the long run. Purchasing power parity tells us that, in the long run, changes in exchange rates are related to inflation rate differentials across countries. (Take a look at Figure 10.4). We can represent this idea by the equation: Change in exchange rate (dollars per pound) = Inflation (U.S.) – Inflation (U.K.) If the dollar is expected to strengthen, this means it takes fewer dollars to purchase a pound, so the change in the exchange rate is negative. Therefore, inflation in the United States is expected to be lower than in the U.K. Using the model of demand and supply for U.S. dollars, what would you expect to happen to the U.S. dollar exchange rate if, in light of a worsening geopolitical situation, Americans viewed foreign bonds as more risky than before? (You should quote the exchange rate as number of units of foreign currency per U.S. dollar.) Answer: If Americans view foreign bonds as more risky than before, they will reduce their demand for these bonds. There will be a fall in the supply of dollars Americans use to purchase foreign assets, shifting the supply curve to the left. The exchange rate, quoted as the number of units of foreign currency per U.S. dollar, will rise, reflecting an appreciation of the U.S. dollar. Suppose that the Chinese central bank has been intervening in the foreign exchange market, buying U.S. dollars in an effort to keep its own currency, the yuan, weak. Use the model of demand and supply for dollars to show what the immediate effect would be on the Chinese yuan- U.S. dollar exchange rate of a decision by China to allow its currency to float freely. Answer: Suppose initially that the Chinese central bank had maintained the exchange rate at E0 in the diagram below. If the Chinese central bank then stopped purchasing U.S. dollars in the market, there would be a shift to the left in the demand curve for dollars, leading to a fall in the number of yuan per dollar in equilibrium. In other words, the yuan would appreciate against the U.S. dollar and the dollar will depreciate. Consider again the situation described in Problem 13 where China decided to allow its currency (the renminbi) to float. What would you expect to happen to U.S. exports to China? U.S. imports from China/ the U.S. trade deficit with China? Explain your answers. Answer: If the yuan is undervalued and is allowed to float freely, market forces will cause the yuan to appreciate. Thus, U.S. exports to China should increase. The appreciation of the yuan would make U.S. exports more competitive in China, as the amount of yuan that would have to be given up for any given dollar price of a good would fall. U.S. imports from China should fall. The appreciation of the yuan would make imports from China more expensive in the U.S., as more dollars would have to be given up to purchase the yuan needed for the imports. The trade deficit measures the excess of imports from China over exports to China from the U.S. With exports rising and imports falling, the trade deficit should narrow. 15. Suppose that, driven by waves of national pride, consumers across the world (including in the United States), decide to buy home-produced products where possible. Explain how the demand and supply for dollars would be affected? What can you say about the impact on the equilibrium dollar exchange rate? Answer: A fall in foreign demand for U.S. goods would shift the demand curve for dollars to the left while the fall in U.S. demand for foreign goods would shift the supply curve for dollars to the left. The overall impact on the dollar exchange rate depends on which shift dominates. As the economy of the world outside the U.S. is larger than the U.S. economy, you might expect the demand shift to dominate, leading to a depreciation of the dollar. Suppose an Italian bank has short-term borrowings of 400 million euro and 100 million U.S. dollars and made long term loans of 300 million euro and 250 million U.S. dollars. The euro-dollar exchange rate is initially $1.50 per euro. Ignoring other assets and liabilities, place each item on the appropriate side of the bank’s balance sheet. List the risks that this bank faces. If the euro-dollar exchange rate moved to $1.60 per euro, would the bank gain or lose? Provide calculations to support your answer. Answer: In addition to other assets and liabilities, the items appear on the balance sheet as: In addition to the usual default risk, the bank faces both currency risk and rollover risk arising from the currency and maturity mismatches between its assets and liabilities. The gap between the bank’s lending and borrowing in foreign currency - its currency mismatch - is $150 million. The maturity mismatch arises because its long-term lending is financed by short-term borrowing, giving rise to risk associated with its ability to rollover this short-term borrowing as it matures. This rollover risk adds to the currency risk: in the event the bank cannot rollover its dollar borrowings, it would have to sell dollar loans or borrow euro. The bank has more dollar-denominated assets than dollar-denominated liabilities, so when the dollar weakens (the euro strengthens), the bank loses. At the initial exchange rate of $1.50 per euro, the currency gap is 100 million euro. If the euro appreciates to $1.60 per euro, the bank loses 6.25 million euro. The loss due to the currency movement is found by converting the dollar entries to euros at the initial exchange rate and finding the net value of the dollar assets in euros, and then re-computing the net value at the new exchange rate. Suppose government officials in a small open economy decided they wanted their currency to weaken in order to boost exports. What kind of foreign exchange market intervention would they have to make to cause their currency to depreciate? What would happen to domestic interest rates in that country if its central bank doesn’t take any action to offset the impact on interest rates of the foreign exchange intervention? Answer: The government officials would have to sell domestic currency in exchange for foreign currency in order for their domestic currency to weaken. This increases the supply of domestic currency, pushing down domestic interest rates. Suppose the interest rate on a one-year U.S. bond is 10 percent and the interest rate on an equivalent Canadian bond is 8 percent. If the interest-rate parity condition holds (see Appendix to Chapter 10), is the U.S. dollar expected to appreciate or depreciate relative to the Canadian dollar over the next year? Explain your choice. Answer: You would expect the U.S. dollar to depreciate. If the interest parity condition holds, the return on the two bonds should be equal. The holder of the Canadian bond must gain on the exchange rate to compensate for the lower interest rate to equate the two returns. Most countries do not attempt to manage their exchange rates with intervention in the foreign currency markets, but some do. Under which circumstances is such an intervention likely to be ineffective? Answer: First, the intervention may fail if the government lacks sufficient resources to maintain the intended exchange rate. For example, it may need a large quantity of foreign exchange if it wishes to convince foreign exchange market participants that its exchange rate commitment is credible. Second, the exchange rate policy will likely fail if it is offset by the central bank’s interest rate policy. Put differently, the central bank must be willing to allow interest rates to adjust consistently with the exchange rate objective.
Suppose you see the following newspaper headline: “Japan’s Finance Ministry Sells Yen for U.S. Dollars.” What is the objective of this policy? If the policy goal is achieved, what will happen to the prices of Japanese imports to the United States? What will happen to the prices of U.S. goods purchased by residents of Japan? Answer: The policy intervention by the Ministry aims to lower the value of the yen versus the U.S. dollar by increasing the quantity of yen relative to dollars in the foreign exchange market. For this policy to work over any sustained period of time, Japan's central bank would have to be willing to lower its policy interest rate (otherwise, the central bank would reverse the Ministry's market intervention). A depreciation of the yen (or appreciation of the dollar) will make Japanese goods cheaper in the United States and will make U.S. goods more expensive for residents of Japan. Immediately following the June 2016 U.K. referendum vote to leave the European Union, the value of the British pound plummeted versus the U.S. dollar. Using a demand and supply framework for British pounds, identify two factors that might have contributed to this decline by shifting the demand curve for British pounds. Illustrate the shift graphically. Answer: Two factors that may have shifted the demand curve for British pounds to the left are: i) an increase in the perceived riskiness of U.K. assets (relative to foreign assets) and ii) an expected future depreciation of the British pound. The leftward shift of the demand curve results in a lower equilibrium exchange rate, as measured by the amount of foreign currency that one must give up to acquire a British pound. The U.K. referendum vote described in Problem 21 also affected currencies other than the British pound. For example, the Japanese Yen strengthened as investors sought a “safe-haven” in the wake of the vote. How would this development affect Japanese exporters and Japan’s immediate economic growth prospects? What currency policy tool might Japan’s Ministry of Finance utilize to counter these effects? Is it likely to be effective? Answer: A rising yen would hurt the competitiveness of Japanese exports and consequently dampen Japan’s immediate growth prospects. Japan’s Ministry of Finance could choose to intervene in the foreign exchange market, selling yen in exchange for a foreign currency such as the U.S. dollar. However, this kind of policy intervention is unlikely to be effective without the support of a monetary policy easing by the Bank of Japan Data Exploration Exchange rates can experience sudden changes as well as long-run patterns. Plot the daily U.S. dollar-British pound exchange rate (FRED code: DEXUSUK) for the first half of 2016 and identify the short-term spike. What caused this spike? Which currency is appreciating when the plotted exchange rate falls? Plot since 1971 the monthly Japanese yen-U.S. dollar exchange rate (FRED code: EXJPUS) without recession bars. Which currency is appreciating when the plotted exchange rate falls? Answer: The plot for the U.S. dollar-British pound is below. The spike at the end of June, 2016 followed the vote by the British people in a referendum to leave the European Union, popularly known as “Brexit.” Concerns about the impact on the British economy diminished the value of the pound; its sharp drop is mirrored by an appreciation of the U.S. dollar. The plot for the Japanese yen-U.S. dollar exchange rate is below. Periods of sudden changes include the sharp downward movement in 1973 and again in 1985 and 1986. A long downward trend appears over the entire period through the mid-1990s. Downward movements in the plot represent appreciations of the Japanese yen and depreciations of the dollar. For example, in the early 1970s, it took nearly 360 yen to buy one U.S. dollar; recently, it took less than 100 yen to buy one U.S. dollar. Note: In part (a), downward movement represents a U.S. dollar appreciation; in (b) downward movement represents a U.S. dollar depreciation. It is important to note which currency is in the numerator of the exchange rate. Plot since 1999, without recession bars, the real exchange rate between U.S. goods and euro-area goods according to equation (2) in the text. Use the consumer price index (divided by 2.37 to set a common base year of 2015 = 100 for the U.S. and euro-area indexes) for the price of U.S. goods (FRED code: CPIAUCSL). Use the harmonized index of consumer prices for the euro area goods (FRED code: CP0000EZ19M086NEST), and the U.S. dollar-euro exchange rate (FRED code: EXUSEU). Why might this measure of the real exchange rate be persistently below unity since 2003?
Answer: A plot of the data is below. Several reasons may explain the appearance that U.S. goods are persistently cheap compared to euro-area goods. First, non-traded goods and services–such as haircuts and restaurant meals – are included in the price indexes. Second, industrial goods are excluded from the indexes of consumer prices. Third, euro-area consumer prices are affected by relatively high value-added taxes. Fourth, the period may not be long enough to capture the forces that establish purchasing power parity (PPP). Eurostat, Harmonized Index of Consumer Prices: All Items for Euro area (19 countries)© [CP0000EZ19M086NEST], retrieved from FRED, Federal Reserve Bank of St. Louis; Write in algebraic form a calculation of U.K pounds per euro that uses U.S. dollars per U.K pound (FRED code: EXUSUK) and U.S. dollars per euro (FRED code: EXUSEU). Then plot since 1999 (without recession bars) the exchange rate of U.K. pounds per euro using these two U.S. dollar exchange rates. What happened to the exchange rate in 2016? Answer: To find the indicated exchange rate, pay attention to the units in the computation. The British pound-euro exchange rate can be found by dividing the number of dollars per euro by the number of dollars per pound to find the number of pounds per euro. Symbolically, ($/€)/($/£) = $/€ £/$ = £/€ The data plot is below. Note that the British pound depreciated versus the euro in 2016. One cause was the uncertainty about the British economic outlook both before and after the June vote to exit the European Union. Examine an episode of large-scale interventions by the Bank of Japan (BoJ) in the yen-dollar foreign exchange market. Plot between January 2003 and January 2005 a measure of BoJ intervention (FRED code: JPINTDUSDJPY). Do positive values of the intervention indicator reflect purchases or sale of yen by the BOJ? What was the BOJ’s policy objective? To investigate whether the intervention of 2003-2004 was effective, add the Japanese yen-U.S. dollar exchange rate (FRED code: EXJPUS) to the chart, but scaled on the right axis. Answer: The data plot is below. Positive values mean that the Bank of Japan was buying U.S. dollars (selling yen) in the foreign exchange market. The objective was to cause a depreciation of the yen and stimulate demand for Japanese goods. The yen depreciated temporarily in early 2004 but then appreciated again as the year progressed. Bank of Japan, Japan Intervention: Japanese Bank purchases of USD against JPY© [JPINTDUSDJPY], retrieved from FRED, Federal Reserve Bank of St. Louis; indicates more difficult problems. Solution Manual for Money, Banking and Financial Markets Stephen G. Cecchetti, Kermit L. Schoenholtz 9781259746741, 9780078021749, 9780077473075

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