1/24/2010. Definitions of Exchange Rates PP542. Depreciation and Appreciation. Exchange Rate Quotations. Depreciation and Appreciation (cont.

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1 PP542 The Foreign Exchange Market Definitions of Exchange Rates Exchange rates are quoted as foreign currency per unit of domestic currency or domestic currency per unit of foreign currency. How much can be exchanged for one dollar? 102/$1 How much can be exchanged for one yen? $0.0098/ 1 Exchange rates allow us to denominate the cost or price of a good or service in a common currency. How much does a Honda cost? 3,000,000 Or, 3,000,000 x $0.0098/ 1 = $29,400 K. Dominguez, Winter Exchange Rate Quotations K. Dominguez, Winter Depreciation and Appreciation Depreciation is a decrease in the value of a currency relative to another currency. A depreciated currency is less valuable (less expensive) and therefore can be exchanged for (can buy) a smaller amount of foreign currency. $1/ 1 $1.20/ 1 means that the dollar has depreciated relative to the euro. It now takes $1.20 to buy one euro, so that the dollar is less valuable. The euro has appreciated relative to the dollar: it is now more valuable. K. Dominguez, Winter Depreciation and Appreciation (cont.) Depreciation and Appreciation (cont.) Appreciation is an increase in the value of a currency relative to another currency. An appreciated currency is more valuable (more expensive) and therefore can be exchanged for (can buy) a larger amount of foreign currency. $1/ 1 $0.90/ 1 means that the dollar has appreciated relative to the euro. It now takes only $0.90 to buy one euro, so that the dollar is more valuable. The euro has depreciated relative to the dollar: it is now less valuable. K. Dominguez, Winter A depreciated currency is less valuable, and therefore it can buy fewer foreign produced goods that are denominated in foreign currency. How much does a Honda cost? 3,000,000 3,000,000 x $0.0098/ 1 = $29,400 3,000,000 x $0.0100/ 1 = $30,000 A depreciated currency means that imports are more expensive and domestically produced goods and exports are less expensive. A depreciated currency lowers the price of exports relative to the price of imports. K. Dominguez, Winter

2 Depreciation and Appreciation (cont.) Foreign Exchange Markets An appreciated currency is more valuable, and therefore it can buy more foreign produced goods that are denominated in foreign currency. How much does a Honda cost? 3,000,000 3,000,000 x $0.0098/ 1 = $29,400 3,000,000 x $0.0090/ 1 = $27,000 An appreciated currency means that imports are less expensive and domestically produced goods and exports are more expensive. An appreciated currency raises the price of exports relative to the price of imports. The set of markets where foreign currencies and other assets are exchanged for domestic ones Institutions buy and sell deposits of currencies or other assets for investment purposes. The daily volume of foreign exchange transactions was $3.2 trillion in About 90% of transactions involved US dollars. K. Dominguez, Winter K. Dominguez, Winter Foreign Exchange Markets Foreign Exchange Markets (cont.) The participants: 1. Commercial banks and other depository institutions: transactions involve buying/selling of deposits in different currencies for investment purposes. 2. Non-bank financial institutions (mutual funds, hedge funds, securities firms, insurance companies, pension funds) may buy/sell foreign assets for investment. 3. Non-financial businesses conduct foreign currency transactions to buy/sell goods, services and assets. 4. Central banks: conduct official international reserves transactions. K. Dominguez, Winter Buying and selling in the foreign exchange market are dominated by commercial and investment banks. Inter-bank transactions of deposits in foreign currencies occur in amounts $1 million or more per transaction. Central banks sometimes intervene, but the direct effects of their transactions are small and transitory in many countries (more on this to come). K. Dominguez, Winter The Foreign Exchange Market (cont.) Characteristics of the market: Trading occurs mostly in major financial cities: London, New York, Tokyo, Frankfurt, Singapore. The volume of foreign exchange has grown: in 1989 the daily volume of trading was $600 billion, in 2001 the daily volume of trading was $1.2 trillion, in 2004 the daily volume of trading was $1.9 trillion, in 2007 the daily volume of trading was $3.2 trillion. About 90% of transactions involve US dollars. See K. Dominguez, Winter Forex Turnover K. Dominguez, Winter

3 Foreign Exchange Markets (cont.) Spot Rates and Forward Rates Computer and telecommunications technology transmit information rapidly and have integrated markets. The integration of markets implies that there is no significant arbitrage between markets. Arbitrage: buying at a low price and selling at a high price for a profit. If dollars are cheaper in New York than in Hong Kong, what do you predict will happen? When other factors are the same, people will buy assets in New York and stop buying them in Hong Kong, so that their price in New York rises and their price in Hong Kong falls, until they are equal in the two markets. Spot rates are exchange rates for currency exchanges on the spot, or when trading is executed in the present. Forward rates are exchange rates for currency exchanges that will occur at a future ( forward ) date. Forward dates are typically 30, 90, 180, or 360 days in the future. Rates are negotiated between two parties in the present, but the exchange occurs in the future. K. Dominguez, Winter K. Dominguez, Winter Dollar/Pound Spot and Forward Exchange Rates, Spot and Forward Rate Data There are a number of websites that provide real time and historical spot and forward exchange rate data: ubc ca/ Source: Datastream. Rates shown are 90-day forward exchange rates and spot exchange rates, at end of month. K. Dominguez, Winter K. Dominguez, Winter Cross-Rates (Jan 22, 2010) Price-adjusted Broad Dollar Index ( ) K. Dominguez, Winter K. Dominguez, Winter

4 Dollar Bilateral Rates, 2009 Other Methods of Currency Exchange Foreign exchange swaps: a combination of a spot sale with a forward repurchase. Swaps often result in lower fees or transactions costs because they combine two transactions, and they allow parties to meet each others needs for a temporary amount of time. Futures contracts: a contract designed by a third party for a standard amount of foreign currency delivered/received on a standard date. Contracts can be bought and sold in markets, and only the current owner is obliged to fulfill the contract. K. Dominguez, Winter K. Dominguez, Winter Other Methods of Currency Exchange The Demand of Currency Deposits Options contracts: a contract designed by a third party for a standard amount of foreign currency delivered/received on or before a standard date. Contracts can be bought and sold in markets. A contract gives the owner the option, but not obligation, of buying or selling currency if the need arises. What influences the demand of (willingness to buy) deposits denominated in domestic or foreign currency? Factors that influence the return on assets determine the demand of those assets. K. Dominguez, Winter K. Dominguez, Winter The Demand for Currency Deposits (cont.) e P t+ k - P t P t Calculating Returns As we discussed earlier, the market for foreign exchange is huge. The market is large both because international trade has expanded dramatically in the last few decades, but largely because investors have realized that a foreign exchange deposit can be a valuable asset. The bulk of foreign exchange transactions involve trades that are considered investments. And investors decide whether to purchase of sell a particular currency based on its expected return. The return on any investment is calculated by comparing the price of the asset at the time of sale, to the price at the time of purchase. Because we usually do not know how much we can sell an asset for in the future, the return on the investment will be an estimate or an expectation. The percentage difference between the expected future value of the asset and the price you must pay for the asset today is the asset's expected rate of return over the time period. e t+k - t P P P t K. Dominguez, Winter K. Dominguez, Winter

5 Rate of return: the percentage change in value that an asset offers during a time period. The annual return for $100 savings deposit with an interest rate of 2% is $100 x 1.02 = $102, so that the rate of return = ($102 - $100)/$100 = 2% Real rate of return: inflation-adjusted rate of return, which represents the additional amount of goods & services that can be purchased with earnings from the asset. The real rate of return for the above savings deposit when inflation is 1.5% is: 2% 1.5% = 0.5%. After accounting for the rise in the prices of goods and services, the asset can purchase 0.5% more goods and services after 1 year. If prices are fixed, the inflation rate is 0% and (nominal) rates of return = real rates of return. Because trading of deposits in different currencies occurs on a daily basis, we often assume that prices do not change from day to day. A good assumption to make for the short run. K. Dominguez, Winter K. Dominguez, Winter Risk of holding assets also influences decisions about whether to buy them. Liquidity of an asset, or ease of using the asset to buy ygoods and services, also influences the willingness to buy assets. But we assume that risk and liquidity of currency deposits in foreign exchange markets are essentially the same, regardless of their currency denomination. Risk and liquidity are only of secondary importance when deciding to buy or sell currency deposits. Importers and exporters may be concerned about risk and liquidity, but they make up a small fraction of the market. K. Dominguez, Winter We therefore say that investors are primarily concerned about the rates of return on currency deposits. Rates of return that investors expect to earn are determined by interest rates that the assets will earn expectations about appreciation or depreciation K. Dominguez, Winter A currency deposit s interest rate is the amount of a currency that an individual or institution can earn by lending a unit of the currency for a year. The rate of return for a deposit in domestic currency is the interest rate that the deposit earns. To compare the rate of return on a deposit in domestic currency with one in foreign currency, consider the interest rate for the foreign currency deposit the expected rate of appreciation or depreciation of the foreign currency relative to the domestic currency. Suppose the interest rate on a dollar deposit is 2%. Suppose the interest rate on a euro deposit is 4%. Does a euro deposit yield a higher expected rate of return? Suppose today the exchange rate is $1/ 1, and the expected rate one year in the future is $0.97/ 1. $100 can be exchanged today for 100. These 100 will yield 104 after one year. These 104 are expected to be worth $0.97/ 1 x 104 = $ in one year. K. Dominguez, Winter K. Dominguez, Winter

6 The rate of return in terms of dollars from investing in euro deposits is ($ $100)/$100 = 0.88%. Let s compare this rate of return with the rate of return from a dollar deposit. The rate of return is simply the interest rate. After 1 year the $100 is expected to yield $102: ($102-$100)/$100 = 2% The euro deposit has a lower expected rate of return: thus, all investors should be willing to dollar deposits and none should be willing to hold euro deposits. Note that the expected rate of appreciation of the euro was ($0.97- $1)/$1 = = -3%. We simplify the analysis by saying that the dollar rate of return on euro deposits approximately equals the interest rate on euro deposits plus the expected rate of appreciation of euro deposits 4% + -3% = 1% 0.88% K. Dominguez, Winter K. Dominguez, Winter Notation (book versus me) The Demand for Currency Deposits (cont.) Concept: Domestic Rate of Return on Foreign Assets Book Notation: R + (E e $/ -E $/ )/E $/ My Notation: i* t+k + (S e t+k S t )/ S t Where * denotes foreign; e in the superscript denotes the expectation, t+k in the subscript denotes a time period in the future, i denotes the interest rate, and S denotes the spot exchange rate The reason for the difference: when we go on to model exchange rate behavior we will need this more general notation. K. Dominguez, Winter The difference in the rate of return on domestic deposits and foreign deposits is i t+k -(i* t+k + (S e t+k -S t )/S t ) = i t+k - i* t+k -(S e t+k -S t )/S t expected rate of return = interest rate on domestic deposits interest rate on foreign deposits expected exchange rate expected rate of return on foreign deposits current exchange rate expected rate of appreciation of the foreign currency K. Dominguez, Winter Demand for Currency Assets: Comparing Dollar Rates of Return on Dollar and Euro Deposits Triangular Arbitrage $/Euro = 1.41 Yen/$ = Yen/Euro = $/Euro x Yen/$ = Yen/Euro 1.41 x An arbitrage opportunity would arise if any of these rates got out of line. If the Euro rate were less than $1.41 in NY (say $1) with the other rates unchanged, it would pay to buy Euro in NY, sell it for Yen, and sell Yen for $s in Tokyo. K. Dominguez, Winter K. Dominguez, Winter

7 Triangular Arbitrage (cont) Start with $1000, then sell it for Euro1000 in NY, [$1000 x 1Euro/$ = 1000Euro] Sell the Euro1000 for Yen126,720 in Frankfurt at the cross rate Yen/Euro Sell the Yen126,720 in Tokyo at 89.87Yen/$ for $1,320. [Yen126,720 x.0111$/y = $ ] The arbitrage profit is $ earned because the rates were out of line. If these transactions were possible, hoards of arbitragers would buy Euro in NY driving up the price until the relationship between the $ rates and cross rates was restored. Eurocurrency Rates Eurocurrency rates are interest rates on foreign currency deposits located outside the country in which those currencies are issued as legal tender. The euro-dollar interest rate is the interest rate on dollar-denominated deposits offered by banks outside the US. Why do we use eurocurrency rates in calculating forward rates (or returns across different assets)? Eurocurrency deposits are free from their particular country of currency issue's regulations and capital controls - settlement dates follow the same conventions as in the forward market (a one-month Yen deposit will mature on the same date as does a one-month forward Yen contract). Note: The prefix euro has nothing to do with the European currency (or Europe). K. Dominguez, Winter K. Dominguez, Winter Eurocurrency Rates (cont.) Euro-currency Rates (Jan 22, 2010) Eurocurrency interest rates are always quoted on an annualized basis, so we need to adjust the rate so that it reflects the k-period time frame. The adjustment involves multiplying by the fraction of a 360-day year involved in the time period of the deposit. (For the British Pound and the Belgian Franc one needs to use 365-day years.) For example: the current 30-day euro-dollar rate is listed in the FT as.4%. The 30-day adjustment is:.004 x (30/360) or K. Dominguez, Winter K. Dominguez, Winter Eurocurrency Rates (cont.) In general, if interest rates are higher in the foreign country than in the home country (as is the case in Europe relative to the U.S.), then the home country's currency will be selling at a premium in the forward market. And if interest rates are lower in the foreign country than in the home country, then the home country's currency will be selling at a discount in the forward market. Eurocurrency Rates (cont.) The annualized 30-day euro-yen interest rate is.3% and the (annualized) 30-day eurodollar interest rate is.4%. The spot yen-usd rate and the 30-day yen-usd forward rate is This suggests that the dollar is selling at a (slight) discount relative to the yen, as people expect to get fewer yen for every dollar in the future. See for daily forward and spot exchange rate data. K. Dominguez, Winter K. Dominguez, Winter

8 How is the forward rate determined? We will use an arbitrage argument to analyze this question next class. It turns out that if we know the eurocurrency interest rates for two countries and the spot exchange rate, then a simple formula gives us the forward rate K. Dominguez, Winter