lecture2_22.pdf

International Finance (Prof. G. Bellettini) Lecture 2: Exchange rates and the foreign exchange market Introduction (part 1) Exchange rates affect large flows of international trade by influencing the prices of goods in different currencies, and they affect international trade in...

International Finance (Prof. G. Bellettini) Lecture 2: Exchange rates and the foreign exchange market Introduction (part 1) Exchange rates affect large flows of international trade by influencing the prices of goods in different currencies, and they affect international trade in assets via the prices of stocks, bonds, and other investments. In the foreign exchange market, trillions of dollars are traded each day, and the economic implications of shifts in the market can be dramatic. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 3 Introduction (part 2) In this chapter, we begin to study the nature and impact of activity in the foreign exchange market. The topics we cover include: Exchange rate basics Basic facts about exchange rate behavior The foreign exchange market Two key market mechanisms: arbitrage and expectations © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 4 1) Exchange Rate Essentials (part 1) An exchange rate (E) is the price of some foreign currency expressed in terms of a home (or domestic) currency. Because an exchange rate is the relative price of two currencies, it may be quoted in either of two ways: – The number of home currency units that can be exchanged for one unit of foreign currency – The number of foreign currency units that can be exchanged for one unit of home currency To avoid confusion, we must specify which country is the home country and which is the foreign country. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 5 1) Exchange Rate Essentials (part 2) Defining the Exchange Rate When we refer to a particular country’s exchange rate, we will quote it in units of home currency per units of foreign currency. E1/2 will denote the exchange rate of country 1, in units of country 1’s currency per unit of country 2’s currency. For example: o The U.S. exchange rate with the Eurozone is denoted as E$/€ or U.S. dollars per euro. o Denmark’s exchange rate with the Eurozone is denoted as Ekr/€ or Danish krone per euro. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 6 1) Exchange Rate Essentials (part 3) TABLE 2(13)-1 Exchange Rate Quotations This table shows major exchange rates as they might appear in the financial media. Columns (1) to (3) show rates on November 15, 2019. For comparison, columns (4) to (6) show rates on November 15, 2018. For example, column (1) shows that at in 2019, one U.S. dollar was worth 1.3230 Canadian dollars, 6.7661 Danish krone, 0.9054 euros, and so on. The euro–dollar rates appear in bold type. EXCHANGE RATES ON EXCHANGE RATES ON NOVEMBER 15, 2019 NOVEMBER 15, 2018 ONE YEAR PREVIOUSLY Currency Country (currency) Symbol Per $ Per € Per £ Per $ Per € Per £ Canada (dollar) C$ 1.3230 1.4613 1.7067 1.3192 1.4940 1.6825 Denmark (krone) DKr 6.7661 7.4731 8.7285 6.5890 7.4619 8.4035 Eurozone (euro) € 0.9054 — 1.1680 0.8830 — 1.1262 Japan (yen) ¥ 108.81 120.17 140.36 113.45 128.48 144.69 Norway (krone) NKr 9.0870 10.0366 11.7226 8.4790 9.6023 10.8140 Sweden (krona) SKr 9.6489 10.6572 12.4474 9.0519 10.2511 11.5446 Switzerland (franc) SFr 0.9904 1.0939 1.2776 1.0056 1.1388 1.2825 United Kingdom (pound) £ 0.7752 0.8562 — 0.7841 0.8880 — United States (dollar) $ — 1.1045 1.2900 — 1.1325 1.2754 E$/€ = 1.1045 = U.S. exchange rate (American terms) 1 1 𝐸𝐸$/€ = 1.1045 = E€/$ = 0.9054 = Eurozone exchange rate (European terms) 𝐸𝐸€/$ 0.9054 © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 7 1) Exchange Rate Essentials (part 4) Appreciations and Depreciations If one currency buys more of another currency, we say it has experienced an appreciation. – We also might say it has risen in value, appreciated, or strengthened against the other currency. If a currency buys less of another currency, we say it has experienced a depreciation. – We also might say it has fallen in value, depreciated, or weakened against the other currency. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 8 1) Exchange Rate Essentials (part 5) Appreciations and Depreciations In U.S. terms, the following holds true: When the U.S. exchange rate E$/€ rises, the price of one euro goes up in dollar terms, and the U.S. dollar depreciates. When the U.S. exchange rate E$/€ falls, the price of one euro goes down in dollar terms, and the U.S. dollar appreciates. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 9 1) Exchange Rate Essentials (part 6) Appreciations and Depreciations Similarly, in European terms, the following holds true: When the Eurozone exchange rate E€/$ rises, the price of one dollar goes up in euro terms, and the euro depreciates. When the Eurozone exchange rate E€/$ falls, the price of one dollar goes down in euro terms, and the euro appreciates. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 10 1) Exchange Rate Essentials (part 7) Appreciations and Depreciations To determine the size of an appreciation or depreciation, we compute the proportional change, as follows: In 2018, at time t, the dollar value of the euro was E$/€,t = $1.1325. In 2019, at time t + 1, the dollar value of the euro was E$/€,t+1 = $1.1045. The change in the dollar value of the euro was ΔE$/€,t = 1.1045 - 1.1325 = -$0.0280. The percentage change was ΔE$/€,t / E$/€,t = -0.0280 / 1.1325 = -2.47%. Thus, the dollar appreciated against the euro by 2.47%. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 11 1) Exchange Rate Essentials (part 8) Appreciations and Depreciations Similarly, over the same year: In 2018, at time t, the euro value of the dollar was E€/$,t = €0.8830. In 2019, at time t + 1, the euro value of the dollar was E€/$,t+1 = €0.9054. The change in the euro value of the dollar was ΔE€/$,t = 0.9054 - 0.8830 = +€0.0224. The percentage change was ΔE€/$,t / E€/$,t = 0.0224 / 0.8830 = +2.53%. Thus, the euro depreciated against the dollar by 2.53%. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 12 1) Exchange Rate Essentials (part 9) Multilateral Exchange Rates Economists calculate multilateral exchange rate changes by aggregating bilateral exchange rates using trade weights to construct an average for each currency in the basket. The resulting measure is called the change in the effective exchange rate. For example: Suppose 40% of Home trade is with country 1 and 60% is with country 2. Home’s currency appreciates 10% against 1 but depreciates 30% against 2. To find the change in Home’s effective exchange rate, multiply each exchange rate change by the trade share and sum: (-10% × 40%) + (30% × 60%) = (-0.1 × 0.4) + (0.3 × 0.6) = -0.04 + 0.18 = 0.14 = +14%. Home’s effective exchange rate has depreciated by 14%. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 13 1) Exchange Rate Essentials (part 10) Multilateral Exchange Rates In general, suppose there are N currencies in the basket, and Home’s trade with all N partners is: Trade = Trade1 + Trade2 +... + TradeN Applying trade weights to each bilateral exchange rate change, the home country’s effective exchange rate (Eeffective) will change according to the following weighted average: Δ𝐸𝐸effective Δ𝐸𝐸1 Trade1 Δ𝐸𝐸2 Trade2 Δ𝐸𝐸𝑁𝑁 Trade𝑁𝑁 = + +⋯ + 𝐸𝐸effective 𝐸𝐸1 Trade 𝐸𝐸2 Trade 𝐸𝐸𝑁𝑁 Trade Trade−weighted average of bilateral nominal exchange rate changes © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 14 1) Exchange Rate Essentials (part 11) Multilateral Exchange Rates FIGURE 2(13)-1 Effective Exchange Rates: Change in the Value of the U.S. Dollar, 2002–19 The chart shows the value of the dollar using two different baskets of foreign currencies. Against a basket of 7 major currencies, the dollar had depreciated by 35% by early 2008. Against a broad basket of 26 currencies, the dollar had lost only 25% by 2008. This is because the dollar was floating against the major currencies, but the broad basket included important U.S. trading partners (such as China and other Asian economies) that maintained fixed or tightly managed exchange rates against the dollar. These trends only briefly reversed during the global financial crisis of 2008 before continuing up to 2019. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 15 1) Exchange Rate Essentials (part 12) Example: Using Exchange Rates to Compare Prices in a Common Currency TABLE 2(13)-2 Using the Exchange Rate to Compare Prices in a Common Currency Now pay attention, 007! This table shows how the hypothetical cost of James Bond’s next tuxedo in different locations depends on the exchange rates that prevail. Scenario 1 2 3 4 Cost of the tuxedo in London £2,000 £2,000 £2,000 £2,000 local currency Hong Kong HK$30,000 HK$30,000 HK$30,000 HK$30,000 New York $4,000 $4,000 $4,000 $4,000 Exchange rates HK$/£ 15 16 14 14 $/£ 2.0 1.9 2.1 1.9 Cost of the tuxedo in London £2,000 £2,000 £2,000 £2,000 pounds Hong Kong £2,000 £1,875 £2,143 £2,143 New York £2,000 £2,105 £1,905 £2,105 © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 16 1) Exchange Rate Essentials (part 13) Example: Using Exchange Rates to Compare Prices in a Common Currency Generalizing The same logic applies to any exchange rate. All else equal, when the prices of goods are constant in each country, the following conclusions will apply: Changes in the exchange rate cause changes in prices of foreign goods expressed in the home currency. Changes in the exchange rate cause changes in the relative prices of goods produced in the home and foreign countries. When the home country’s exchange rate depreciates, home exports become less expensive as imports to foreigners, and foreign exports become more expensive as imports to home residents. When the home country’s exchange rate appreciates, home exports become more expensive as imports to foreigners, and foreign exports become less expensive as imports to home residents. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 17 2) Exchange Rates in Practice (part 1) Exchange Rate Regimes: Fixed Versus Floating There are two major types of exchange rate regimes— fixed and floating: A fixed (or pegged) exchange rate fluctuates in a narrow range (or not at all) against some base currency over a sustained period. The exchange rate can remain fixed for long periods only if the government intervenes in the foreign exchange market in one or both countries. A floating (or flexible) exchange rate fluctuates in a wider range, and the government makes no attempt to fix it against any base currency. Appreciations and depreciations may occur yearly, monthly, by the day, or even every minute. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 18 APPLICATION: Exchange Rate Behavior (part 1) FIGURE 2(13)-2 (1 of 2) Exchange Rate Behavior: Selected Developed Countries, 1996–2019 This figure shows the exchange rates of three currencies against the U.S. dollar. The U.S. dollar is in a floating relationship with the yen, the pound, and the Canadian dollar (or loonie). The U.S. dollar is subject to a great deal of volatility because it is in a floating regime, or free float. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 19 APPLICATION: Exchange Rate Behavior (part 2) FIGURE 2(13)-2 (2 of 2) Exchange Rate Behavior: Selected Developed Countries, 1996–2019 This figure shows exchange rates of three currencies against the euro, which was introduced in 1999. The pound and the yen float against the euro. The Danish krone provides an example of a fixed exchange rate. There is only a tiny variation around this rate, no more than plus or minus 2%. This type of fixed regime is known as a band. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 20 APPLICATION: Exchange Rate Behavior (part 3) FIGURE 2(13)-3 (1 of 2) Exchange Rate Behavior: Selected Developing Countries, 1996–2019 Selected Developing Countries, 1996–2019 Exchange rates in developing countries show a wide variety of experiences and greater volatility. Pegging is common but is punctuated by periodic crises (you can see the effects of these crises in graphs for Thailand, South Korea, and India). © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 21 APPLICATION: Exchange Rate Behavior (part 4) FIGURE 2(13)-3 (2 of 2) Exchange Rate Behavior: Selected Developed Countries, 1996–2019 Colombia is an example of a crawling peg. The Colombian peso was allowed to crawl gradually, and it steadily depreciated at an almost constant rate for several years from 1996 to 2002. Dollarization occurred in Ecuador in 2000, a process that occurs when a country unilaterally adopts the currency of another country. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 22 3) The Market for Foreign Exchange (part 1) Exchange rates the world over are set in the foreign exchange market (or forex or FX market). The forex market is not an organized exchange: trade is conducted “over the counter” and in many locations. In April 2019, the global forex market traded $6.6 trillion per day; this was 29% more than in 2016, over three times more than in 2004, and over six times more than in 1992. Four major foreign exchange centers are London, New York, Singapore, and Hong Kong. Other important centers for forex trade include Tokyo, Zurich, Paris, and Frankfurt. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 26 Annexes A Tables Table 1 OTC foreign exchange turnover by instrument.................................................................................................. 9 Table 2 OTC Foreign exchange turnover by instrument, counterparty and maturity....................................... 10 Table 3 OTC foreign exchange turnover by currency and counterparty................................................................ 11 Table 4 OTC foreign exchange turnover by currency..................................................................................................... 12 Table 5 OTC foreign exchange turnover by currency pair............................................................................................ 13 Table 6 Geographical distribution of OTC foreign exchange turnover................................................................... 14 OTC foreign exchange turnover by instrument "Net-net" basis,1 daily averages in April in billions of US dollars Table 1 Instrument 2010 2013 2016 2019* 2022 Foreign exchange instruments 3,973 5,357 5,066 6,581 7,508 Spot transactions 1,489 2,047 1,652 1,979 2,107 Outright forwards 475 679 700 998 1,163 Foreign exchange swaps 1,759 2,240 2,378 3,198 3,810 Currency swaps 43 54 82 108 124 Options and other products² 207 337 254 298 304 Memo: Turnover at April 2022 exchange rates 3 3,542 4,727 4,851 6,446 7,508 Exchange-traded derivatives 4 144 145 115 127 152 1 2 Adjusted for local and cross-border inter-dealer double-counting (ie “net-net” basis). The category “other FX products” covers highly leveraged transactions and/or trades whose notional amount is variable and where a 3 decomposition into individual plain vanilla components was impractical or impossible. Non-US dollar legs of foreign currency transactions were converted into original currency amounts at average exchange rates for April of each survey year and then reconverted into US dollar amounts at average April 2022 exchange rates. 4 Euromoney Tradedata; Futures Industry Association; The Options Clearing Corporation; BIS derivatives statistics. Foreign exchange futures and options traded worldwide. * Revised data. BIS Triennial Central Bank Survey 2022 9 2019 to 2.6% in 2022. By contrast, the shares for the Canadian dollar and Singapore dollar increased noticeably. 7 Foreign exchange market turnover by currency and currency pairs1 Net-net basis, daily averages in April, as a percentage of total turnover Graph 4 Selected currencies2 Selected currency pairs 1 Adjusted for local and cross-border inter-dealer double-counting, ie “net-net” basis. 2 As two currencies are involved in each transaction, the sum of shares in individual currencies will total 200%. 3 Emerging market economy currencies excluding the Chinese renminbi and Russian rouble: AED, ARS, BGN, BHD, BRL, CLP, COP, CZK, HKD, HUF, IDR, ILS, INR, KRW, MXN, MYR, PEN, PHP, PLN, RON, SAR, SGD, THB, TRY, TWD and ZAR. Source: BIS Triennial Central Bank Survey. For additional data by currency and currency pairs, see Tables 4 and 5. See our Statistics Explorer for access to the full set of published data. Geographical distribution of turnover FX trading continues to be concentrated in major financial centres. In April 2022, sales desks in five locations – the United Kingdom, the United States, Singapore, Hong Kong SAR and Japan – intermediated 7 While FX markets globally can be characterised as OTC markets, a large share of trading in the Brazilian real and, to a lesser extent, the Indian rupee is done via exchange-traded derivatives (XTD) (see Table 4). Taking XTD markets into account would boost the relative ranking of both currencies. BIS Triennial Central Bank Survey 2022 7 3) The Market for Foreign Exchange (part 2) The Spot Contract The simplest forex transaction is a contract for the immediate exchange (“on the spot”) of one currency for another between two parties. This is known as a spot contract. The exchange rate for this transaction is referred to as the spot exchange rate. The use of the term “exchange rate” always refers to the spot rate for our purposes, unless otherwise noted. The spot contract is the most common type of trade and appears in more than 80% of all forex transactions. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 27 3) The Market for Foreign Exchange (part 3) Transaction Costs The difference between the “buy at” and “sell for” prices in foreign exchange transactions is known as the spread. These differences may be large, perhaps 2% to 5% in a retail transaction. For big firms or banks that exchange millions of dollars, the spreads are very small, usually less than 0.10%, and approximately 0.01% to 0.03% for major currencies. Spreads are an important example of market frictions or transaction costs that create a wedge between the price paid by the buyer and the price received by the seller. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 28 3) The Market for Foreign Exchange (part 4) Derivatives FIGURE 2(13)-5 Spot and Forward Rates In addition to the spot contracts, other forex contracts include forwards, swaps, futures, and options. Collectively, all these related forex contracts are termed derivatives. In a forward contract, the two parties make the contact today, but the settlement date is in the future. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 29 3) The Market for Foreign Exchange (part 5) Private Actors Most forex traders work for commercial banks. More than half of all forex transactions globally are handled by just 10 banks. The exchange rates for these trades underlie quoted market exchange rates. Some corporations may trade in the market if they are engaged in extensive transactions in foreign markets. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 30 3) The Market for Foreign Exchange (part 6) Government Actions Some governments engage in policies that restrict trading, movement of forex, or cross-border financial transactions. These are called a form of capital control. In lieu of capital controls, the central bank must stand ready to buy or sell its own currency to maintain a fixed exchange rate. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 31 4) Arbitrage and Spot Exchange Rates (part 1) FIGURE 2(13)-6 Arbitrage and Spot Rates Arbitrage ensures that the trade of currencies in New York along the path AB occurs at the same exchange rate as via London along path ACDB. At B the pounds received must be the same, regardless of the route taken to get to B: 𝐸𝐸 N.Y. = 𝐸𝐸 London. £/$ £/$ © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 32 4) Arbitrage and Spot Exchange Rates (part 2) Arbitrage with Three Currencies In general, three outcomes are again possible. 1. The direct trade from dollars to pounds has a better rate: E£/$ > E£/€ × E€/$ 1. The indirect trade has a better rate: E£/$ < E£/€ × E€/$ 2. The two trades have the same rate and yield the same result: E£/$ = E£/€ E€/$. Only in the last case are there no profit opportunities. This is the no-arbitrage condition: 𝐸𝐸£/€ 𝐸𝐸 £/$ = 𝐸𝐸£/€ × 𝐸𝐸€/$ = 𝐸𝐸 $/€ Direct exchange rate Cross rate The right-hand expression, a ratio of two exchange rates, is called a cross rate. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 33 4) Arbitrage and Spot Exchange Rates (part 3) FIGURE 2(13)-7 Arbitrage and Cross Rates Triangular arbitrage ensures that the direct trade of currencies along the path AB occurs at the same exchange rate as via a third currency along path ACB. The pounds received at B must be the same on both paths: 𝐸𝐸£/$ = 𝐸𝐸£/€ × 𝐸𝐸€/$ © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 34 5) Arbitrage and Interest Rates (part 1) Cross Rates and Vehicle Currencies The majority of the world’s currencies trade directly with only one or two of the major currencies, such as the dollar, euro, yen, or pound. Many countries do a lot of business in major currencies such as the U.S. dollar, so individuals always have the option to engage in a triangular trade at the cross rate. When a third currency, such as the U.S. dollar, is used in these transactions, it is called a vehicle currency because it is not the home currency of either of the parties involved in the trade and is just used for intermediation. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 35 5) Arbitrage and Interest Rates (part 2) An important question for investors is in which currency they should hold their liquid cash balances. Would selling euro deposits and buying dollar deposits make a profit for a banker? These decisions drive demand for dollars versus euros and the exchange rate between the two currencies. The Problem of Risk A trader in New York cares about returns in U.S. dollars. A dollar deposit pays a known return, in dollars. But a euro deposit pays a return in euros, and one year from now we cannot know for sure what the dollar–euro exchange rate will be. Riskless arbitrage and risky arbitrage lead to two important implications, called parity conditions. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 36 5) Arbitrage and Interest Rates (part 3) Riskless Arbitrage: Covered Interest Parity Contracts to exchange euros for dollars in one year’s time carry an exchange rate of F$/€ dollars per euro. This is known as the forward exchange rate. If you invest in a dollar deposit, your $1 placed in a U.S. bank account will be worth (1 + i$) dollars in one year’s time. The dollar value of principal and interest for the U.S. dollar bank deposit is called the dollar return. If you invest in a euro deposit, you first need to convert the dollar to euros. Using the spot exchange rate, $1 buys 1/E$/€ euros today. These 1/E$/€ euros would be placed in a euro account earning i€, so in a year’s time they would be worth (1 + i€)/E$/€ euros. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 37 5) Arbitrage and Interest Rates (part 4) Riskless Arbitrage: Covered Interest Parity To avoid exchange rate risk, you engage in a forward contract today to make the future transaction at a forward rate F$/€. The (1 + i€)/E$/€ euros you will have in one year’s time can then be exchanged for (1 + i€)F$/€/E$/€ dollars, or the dollar return on the euro bank deposit. The no-arbitrage condition is: 𝐹𝐹$/€ 1 + 𝑖𝑖$ = 1 + 𝑖𝑖€ 𝐸𝐸$/€ Dollar return on dollar deposits Dollar return on euro deposits This expression is called covered interest parity (CIP) because all exchange rate risk on the euro side has been “covered” by use of the forward contract. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 38 5) Arbitrage and Interest Rates (part 5) FIGURE 2(13)-8 Arbitrage and Covered Interest Parity Under CIP, returns to holding dollar deposits accruing interest going along the path AB must equal the returns from investing in euros going along the path ACDB with risk removed by use of a forward contract. Hence, at B, the riskless payoff must be the same on both paths: 𝐹𝐹$/€ 1 + 𝑖𝑖$ = 1 + 𝑖𝑖€ 𝐸𝐸$/€ © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 39 APPLICATION: Evidence on Covered Interest Parity (part 1) FIGURE (2)13-9 (1 of 2) Financial Liberalization and Covered Interest Parity Financial Liberalization and Covered Interest Parity: Arbitrage Between the United Kingdom and Germany The chart shows the difference in monthly pound returns on deposits in British pounds and German marks using forward cover from 1970 to 1995. In the 1970s, the difference was positive and often large: traders would have profited from arbitrage by moving money from pound deposits to mark deposits, but capital controls prevented them from freely doing so. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 40 APPLICATION: Evidence on Covered Interest Parity (part 2) FIGURE (2)13-9 (2 of 2) Financial Liberalization and Covered Interest Parity After financial liberalization, these profits essentially vanished, and no arbitrage opportunities remained. The CIP condition held, aside from small deviations resulting from transaction costs and measurement errors. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 41 5) Arbitrage and Interest Rates (part 6) Risky Arbitrage: Uncovered Interest Parity In this case, traders face exchange rate risk and must make a forecast of 𝑒𝑒 the future spot rate. We refer to the forecast as 𝐸𝐸$/€ , which we call the expected exchange rate. Based on the forecast, you expect that the 1 + 𝑖𝑖€ /𝐸𝐸$/€ euros you will have in one year’s time will be worth 1 + 𝑖𝑖€ × 𝐸𝐸$/€ 𝑒𝑒 /𝐸𝐸$/€ when converted into dollars; this is the expected dollar return on euro deposits. The no-arbitrage expression here is called uncovered interest parity (UIP) is: 𝑒𝑒 𝐸𝐸$/€ 1 + 𝑖𝑖$ = 1 + 𝑖𝑖€ 𝐸𝐸$/€ Dollar return on dollar deposits Expected dollar return on euro deposits © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 42 5) Arbitrage and Interest Rates (part 7) Risky Arbitrage: Uncovered Interest Parity What Determines the Spot Rate? Uncovered interest parity is a no-arbitrage condition that describes an equilibrium in which investors are indifferent between the returns on unhedged interest-bearing bank deposits in two currencies. If we know the expected future exchange rate, we can rearrange the terms in the uncovered interest parity expression to solve for the spot rate: 𝑒𝑒 1 + 𝑖𝑖€ 𝐸𝐸$/€ = 𝐸𝐸$/€ 1 + 𝑖𝑖$ © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 43 5) Arbitrage and Interest Rates (part 8) FIGURE 2(13)-10 Arbitrage and Uncovered Interest Parity Under UIP, returns to holding dollar deposits accruing interest going along the path AB must equal returns from investing in euros going along the risky path ACDB. Hence, at B, the expected payoff must be the same on both paths: 𝑒𝑒 𝐸𝐸$/€ 1 + 𝑖𝑖$ = 1 + 𝑖𝑖€. 𝐸𝐸$/€ © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 44 APPLICATION: Evidence on Uncovered Interest Parity (part 1) Dividing UIP by CIP, we obtain 𝑒𝑒 1 = 𝐸𝐸$/€ /𝐹𝐹$/€ , or 𝑒𝑒 𝐸𝐸$/€ = 𝐹𝐹$/€ Although the expected future spot rate and the forward rate are used in two different forms of arbitrage—risky and riskless―in equilibrium they should be exactly the same! If both covered interest parity and uncovered interest parity hold, the forward rate must equal the expected future spot rate. Intuition: Risk-neutral investors have no reason to prefer to avoid risk by using the forward rate versus embracing risk by awaiting the future spot rate. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 46 APPLICATION: Evidence on Uncovered Interest Parity (part 2) If the forward rate equals the expected spot rate, the expected rate of depreciation equals the forward premium (the proportional difference between the forward and spot rates): 𝑒𝑒 𝐹𝐹$/€ 𝐸𝐸$/€ − 1 = − 1 𝐸𝐸$/€ 𝐸𝐸$/€ Forward premium Expected rate of depreciation As a useful scale-free expression independent of currency, both sides are typically measured in percent per year. While the left-hand side is easily observed, the expectations on the right-hand side are typically unobserved, except for survey data. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 47 APPLICATION: Evidence on Uncovered Interest Parity (part 3) FIGURE 2(13)-11 Evidence on Interest Parity When UIP and CIP hold, the 12-month forward premium should equal the 12-month expected rate of depreciation. A scatterplot showing these two variables should be close to the diagonal 45-degree line. Using evidence from surveys of individual forex traders’ expectations over the period 1988 to 1993, UIP finds some support, as the line of best fit is close to the diagonal.a © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 48 5) Arbitrage and Interest Rates (part 9) Uncovered Interest Parity: A Useful Approximation 𝑒𝑒 Δ𝐸𝐸$/€ 𝑖𝑖⏟$ = 𝑖𝑖⏟€ + 𝐸𝐸$/€ Interest rate Interest rate on dollar deposits on euro deposits Expected rate of depreciation = of the dollar Dollar rate of return on dollar deposits Expected dollar rate of return on euro deposits This approximate equation for UIP says that the home interest rate equals the foreign interest rate plus the expected rate of depreciation of the home currency. Suppose the dollar interest rate is 4% per year and the euro 3%. If UIP is to hold, the expected rate of dollar depreciation over a year must be 1%. The total dollar return on the euro deposit is approximately equal to the 4% that is offered by dollar deposits. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 49 5) Arbitrage and Interest Rates (part 10) Summary FIGURE 2(13)-12 How Interest Parity Relationships Explain Spot and Forward Rates In the spot market, UIP provides a model of how the spot exchange rate is determined. To use UIP to find the spot rate, we need to know the expected future spot rate and the prevailing interest rates for the two currencies. In the forward market, CIP provides a model of how the forward exchange rate is determined. When we use CIP, we derive the forward rate from the current spot rate (from UIP) and the interest rates for the two currencies. © 2021 Worth Publishers International Economics, 5e | Feenstra/Taylor 50