6 Foreign Exchange

University of Texas at Dallas School of Management Finance 6301 Corporate Finance Lecture 7: Exchange Rates and Investment Decisions The Foreign Exchange Market The market for foreign exchange is the world's largest financial market. Trading is conducted through an “over-the-counter” network of traders from major commercial and investment banks linked by phone, computer terminal and other telecommunications devices. Major trading centers include London, New York and Tokyo, with total trading volume in excess of $1.25 trillion dollars of foreign currency per day. More than half of all trading directly involves the exchange of dollars. Participants include importers and exporters, as well as traders, portfolio managers and foreign exchange brokers. The importance of trading other currencies against U.S. dollars arises from the fact that currency dealers quote other currencies against the dollar when trading among themselves. Method of Quotation The are two methods of quotation for exchange rates between the dollar and the currency of another country. The two methods are referred to as the direct (American) and indirect (European) methods of quotation. The exchange rate between any two non-dollar currencies is referred to as a cross rate 1. Direct/American Quotation The dollar price of one unit of foreign currency. For example, a direct quotation of the exchange rate between dollar and the British pound (German mark) is $1.6000/£1 ($0.6000/DM1), indicating that the dollar cost of one British pound (German mark) is $1.6000 ($0.6000). Direct exchange rate quotations are most frequently used by banks in dealing with their non-bank customers. In addition, the prices of currency futures contracts traded on the Chicago Mercantile Exchange are quoted using the direct method. 2. Indirect/European Quotation The number of units of a foreign currency that are required to purchase one dollar. For example, an indirect quotation of the exchange rate between the dollar and the Japanese yen (German mark) is ¥125.00/$1 (DM 1.6667/$1), indicating that one dollar can be purchased for either 125.00 Japanese Yen or 1.6667 German Marks. 3. Cross Rates The exchange rate between any two non-dollar currencies is referred to as a cross rate. A relatively large number of cross rates would be required to trade every currency directly Professor Day Fall 1999 against every other currency. For example, N currencies would require N x (N -1)/2 separate cross rates. For this reason, most exchange rates are quoted in terms of dollars and by far the greatest volume of trading directly involves the dollar. This reduces the number of cross-currency quotes that dealers must keep track of and reduces the potential losses associated with mispricing currencies relative to one another (which permits Triangular Arbitrage). 2 The Relation between Direct and Indirect Exchange Rate Quotations An indirect exchange rate quotation is simply the reciprocal of the direct exchange rate quotation. In other words SF/$ Indirect = 1 Direct S$/F . where the superscripts are actually unnecessary in that we will use the notation F/$ to denote an indirect quotation in terms of units of currency F required to purchase one dollar. Similarly, we will use the notation $/F to denote a direct quotation in terms of the number of dollars required to purchase one unit of currency F. To illustrate this principal, suppose that the direct quotation for the exchange rate between the dollar and the German mark is $0.6000/DM1. Then the indirect quotation for the exchange rate between the dollar and the mark would be SDM/$ = = Currency Markets Foreign exchange transactions that are settled immediately are said to occur in the spot market, while transactions to be settled at a future date occur in either the forward or the futures market. These markets are summarized below: 1. Spot Market The market for currency for immediate delivery. The price of foreign exchange in the spot market is referred to as the spot exchange rate or simply the spot rate. 2. Forward Market The market for the exchange of foreign currencies at a future date. A forward contract usually represents a contract between a large money center bank and a well-known (to the bank) customer having a well-defined need to hedge exposure to fluctuations in exchange rates. Although forward contracts usually call for the exchange to occur in either 30, 90 or 180 days, the contract can be customized to call for the exchange of any desired quantity of currency at any future date acceptable to both parties to the contract. The price of foreign currency for future delivery is typically referred to as a forward exchange rate or simply a forward rate. 3. Futures Market Although the futures market trading is similar to forward market trading in that all transactions are to be settled at a future date, futures markets are actual physical locations where anonymous participants trade standard quantities of foreign currency (e.g., 125,000 DM per contract) for delivery at standard future dates (e.g., March, June, September, and December). 3 1 $0.6000/DM1 DM1.6667/$1 . , The most active forward markets are those for the Japanese yen and the German mark. Active markets also exist for the British pound, the Canadian dollar and the major continental currencies, the Swiss franc, the French franc, the Belgian franc, the Italian Lira and the Dutch guilder. Forward markets for currencies of less developed countries are either limited or nonexistent. The Chicago Mercantile Exchange trades futures contracts on yen, marks, Canadian dollars, British pounds, Swiss francs, Australian dollars, Mexican peso's and euros. 4 Triangular Arbitrage Given the exchange rate between the dollar and the British Pound, S $/£ , and the exchange rate between the dollar and the German Mark, S $/DM , the exchange rate between the German Mark and the British Pound, SDM/£ , should be SDM/£ = S$/£ S$/DM . For example, if the exchange rate between the dollar and the British Pound is $1.50/£1 and the exchange rate between the dollar and the German Mark is $.75/DM1, the exchange rate between the German Mark and the British Pound is SDM/£ = = $1.50/£1 $0.75/DM1 DM2/£1 . , If the exchange rate between the German Mark and the British Pound were either greater or less than DM2/£1, then a triangular arbitrage opportunity will be available. For example, suppose that the Mark/Pound exchange rate were DM2.1/£1. Then a trader with two German Marks would (1) exchange them for $1.50 (2 x $.75/DM1). The $1.5 would then (2) be exchanged for one British Pound, which would then (3) be used to purchase DM 2.1, which is greater than the number of German Marks that the trader started with. Interest Rate Parity The Interest Rate Parity Theorem says that the relation between (a) foreign and domestic interest rates and (b) the forward and spot exchange rates is given by 1 + R US 1 + RF = F$/F S$/F , where F$/F denotes the (direct) forward exchange rate between the dollar and an arbitrary foreign currency F, S$/F denotes the spot rate, with R US and RF respectively denoting the U.S. and foreign interest rates. The Interest Rate Parity Theorem implies that the currency with the higher interest rate will always be at a forward premium to the currency having the lower interest rate. In other words, the forward exchange rate will be greater (less) than the spot rate whenever the U.S. interest rate is greater (less) than the foreign interest rate. Since the direct and indirect exchange rate quotations are reciprocals of one another, the interest rate parity can also be expressed in terms of the indirect quotations for the spot and forward exchange rates, 1 + RF 1 + R US = FF/$ SF/$ . 5 An violation of Interest Rate Parity would allow investors in either the U.S. or the country denoted by F to earn more than their domestic risk-free rate of interest (i.e., RF for a U.S. investor). For example, a violation of interest rate parity may permit a U.S. investor to simultaneously (1) convert dollars to foreign currency at the spot rate, (2) invest in risk-free foreign securities at a rate of RF , and (3) hedge the future value of the investment against fluctuations in the exchange rate by selling the foreign currency to be received in the forward market. Thus, the Interest Rate Parity Theorem essentially states that nn investor must earn the same rate of return by investing in risk-free money market securities at home (e.g., the U.S.) as could be earned from a hedged investment in risk-free foreign money market securities. To explore the implications of interest rate parity further, consider the fact that an investor who wishes to invest $1 in risk-free securities has two alternatives. 1. By investing at home in dollar-denominated money market securities, an investor earns interest at a rate of RF per period. Thus, at the end of one period the investor receives $1 x (1 + R US) . 2. Alternatively, if the investor invests one dollar in foreign bonds, then the investor must $1 a. Convert one dollar to S units of foreign currency, $/F $1 b. Invest S in foreign securities at an interest rate of R F, giving $/F $1 S$/F (1 + RF) units of foreign currency at maturity, c. Eliminate any exchange rate risk by selling the currency to be received in the forward market at the current forward rate of F$/F giving future dollar proceeds of $1 S$/F (1 + RF) F$/F . The search by investors for the highest possible risk-free returns implies that prices must adjust so that the return from investing in dollars is equal to the hedged return from investing in the foreign money market securities. In other words, $1 x (1 + R US) = $1 S$/F (1 + RF) F$/F , which implies that (1 + R US)/(1 + RF) must equal to F$/F /S$/F . 6 Example: Suppose that you can invest in U.S. Government Treasury bill for one year at an interest rate of 5 percent. The spot exchange rate between dollars and French francs (S $/F) is $0.2000/FF1, while the forward exchange rate (F$/F ) is $0.2020/FF1. Assuming that you are able to invest in risk-free French bonds for one year at an interest rate of 4.25 percent , the returns from investing in domestic and foreign bonds are respectively equal to 1. Domestic Investment $1 x (1 + R US) = = 2. Foreign Investment $1 S$/F (1 + RF) F$/F = = $1 $0.2000/FF1 x 1.0425 x $0.2020/FF1 $1.0529 . $1 x 1.05 $1.05 . In other words, we can earn 5.0 percent by investing in the U.S.. However, we could earn 5.29 percent by converting dollars to Francs, investing at 4.25 percent, and purchasing forward cover by selling the French francs to be received one year from now in the forward market for $0.2020/FF1. 7 Creating a Money Market Hedge The Interest Rate Parity relation can be rearranged to show that 1 1 + R US F$/F = S$/F 1 1 + RF . The expression above shows that the present value of the proceeds from selling (or cost of buying) currency for dollars in the forward market shown on the left hand side above should equal the current dollar value (at the spot exchange rate) of the present value (discounted at the foreign interest rate) of the amount to be received or paid that is shown on the right hand side. Therefore, Interest Rate Parity implies that there are two alternative mechanisms for hedging exchange rate risk such as accounts receivable and accounts payable. Hedging an Account Receivable The most simple procedure for hedging an account receivable is to simply to sell the receivable in the forward market at a price of F $/F per unit of foreign currency. The present value of this strategy is simply the left hand side of the expression above 1 1 + R US F$/F . Alternatively, we could borrow an amount equal to the present value (discounted at the interest rate in the foreign country) of the account receivable, . The current dollar value of the proceeds of the loan is represented by the right hand of the above expression, S$/F 1 1 + RF . When the loan comes due, the liability can be repaid using the proceeds from collection of the account receivable. Hedging an Account Payable Similarly, can hedge an account payable by entering into a forward contract to buy the foreign currency at a price of F$/F per unit of foreign currency. The present value of this strategy is 1 1 + R US F$/F . Alternatively, since the present value (discounted at the foreign interest rate) of a liability of one unit of foreign currency is 1/(1+RF) , we can eliminate any exchange rate risk associated with the future liability by immediately converting 1 S$/F 1 + R F 8 dollars to units of foreign currency and investing at the foreign interest rate of R F . When the liability comes due, this number of present dollars is guaranteed to be equal to 1 unit of foreign currency, which can then be used to pay the foreign currency denominated payable. 9 Example: (Hedging an Account Receivable) Assume that your firm has an account receivable of one million Swiss francs that is due to be received in 180 days. The spot exchange rate (S $/F ) is $0.8800/SF1 , while the forward exchange rate ( F$/F ) for delivery in 180 days is $0.8950/SF1. The interest rate in the U.S. for a 180 day period (R US ) is 2.6 percent while the Swiss rate of interest (R F ) for 180 days is 1 percent. The present value of selling the francs in the forward market is 1 1 + R US F$/F SF1,000,000 = = 1 1.026 $0.8950/SF1 SF1,000,000 , $872,319.69 . The present value from borrowing the present value of the receivable (denominated in units of foreign currency) and converting to dollars is 1 S$/F 1 + R F SF1,000,000 = = 1 $0.8800 1.01 $871,287.13 . SF1,000,000 . Since the present value of selling the currency in the forward market is $872,319.69 while the present value of the money market hedge is $871,287.13, it would be better to hedge by selling the currency forward. If we needed to hedge an account payable of SF1,000,000 due in 180 days, the amounts above would represent the present value of the cost of hedging. In this case, we would go with a money-market hedge, since the present value of the money-market hedge ($871,287.13) is less than the cost of hedging in the forward market. 10 The Expectations Theory Applied to Exchange Rates The Expectations theory argues that the forward rates quoted in the market for foreign exchange are useful in forecasting future exchange rates. In particular, the Expectations theory argues that forward rates are exactly equal to the spot exchange rate that is expected on the delivery date specified in the forward contract (30, 60, 90 or 180 days in the future). Thus, the Expectations theory implies that the forward exchange rates quoted in the foreign exchange market are unbiased forecasts of the exchange rates the are expected in the future. While the exact economic circumstances under which the Expectations theory holds are complex to describe, empirical evidence suggests that the Expectations theory is a fairly good description of the true relation between forward exchange rates and expected future exchange rates. The Expectations theory implies that the cost of hedging exchange rate risk is costless. Consider the following alternatives for hedging exchange rate risk: 1. Always invoice in dollars Although invoicing in dollars completely avoids losses (and gains) attributable to fluctuations of the value of foreign currency relative to the dollar, a refusal to invoice in a foreign customer's own currency may result in a loss of sales to competitors willing to invoice in the the customer's own currency. 2. Selling foreign currency forward This alternative is desirable to the extent that exchange rate risk is eliminated. However, selling anticipated receivables denominated in foreign currencies in the forward market is costly whenever the forward rate differs systematically from the spot exchange rate that is expected to prevail when the receivable is scheduled to be collected. Therefore, the cost of the “insurance” obtained by selling currency in the forward market is the difference between the forward rate, F, and the expected spot rate, E(S). If the expectations theory holds (i.e., forward rates are always equal to the expected spot rate), then the cost of hedging (insuring against) the risk of fluctuations in exchange rates is zero. In practice, differences between forward rates and actual future spot rates are small on average. 11 Absolute Purchasing Power Parity (The Law of One Price) The exchange rate between any pair of currencies is roughly equal to the ratio of the domestic and foreign prices of any good that may be freely traded (traded goods) between the two countries with minor (per unit) shipping costs. In other words, the price of a good in dollars should be equal the price of that good in British pounds after the price in British pounds has been converted to a dollar price using the prevailing exchange rate between the dollar and the British pound. Formally, Pt which implies that S$/£ = Pt Pt $ $ = S$/£ Pt £ , £ . For example, if the price of one ton of soybean meal in Chicago is $225 and the price of one ton of soybean meal in London is £150, then the exchange rate between the dollar and the British pound should be S$/£ = = $225 £150 , $1.50/£1 . 12 The Hamburger Standard (The Economist of April 15, 1989) Country France Germany Britain US Japan Big Mac Price in Local Currency FF 17.70 DM 4.30 £ 1.26 $ 2.02 ¥ 370 ¥ 183/$1 ¥ 133/$1 Big Mac Exchange Rate $0.114/FF1 $0.469/DM1 $1.610/£1 Actual Exchange Rate $0.157/FF1 $0.529/DM1 $1.690/£1 Note that you get more Yen for your dollar if you trade Big Macs for yen rather the Dollars for Yen. If we could in fact transport Big Macs from Japan, then we could earn an arbitrage profit by 1. Buy one Big Mac in the U.S. for $2.02, 2. Sell one Big Mac in Tokyo for ¥370 (i.e., [¥183/$1] x $2.02) 3. Convert the Yen to Dollars at ¥133/$1 which implies that you end up with $2.78 = $1 ¥370 ¥133 The arbitrage mechanism required for Purchasing Power Parity is to hold depends on 1. Low per unit cost of trading and shipping commodities from one country to another, 2. Absence of barriers to trade such as taxes and tariffs, 3. Standard definition of the goods in question. The conditions which permit Purchasing Power Parity to hold give rise to the distinction between 1. Traded Goods (e.g., crude oil, wheat, and soybean meal) 2. Non-Traded Goods (e.g., haircuts) 13 Relative Purchasing Power Parity The Relative version of the Purchasing Power Parity theorem states that changes in the exchange rate between two currencies are determined by changes in the relative prices in the two countries in question. In other words, Pt+1 Pt $ $ $ $ = S$/F t t+1 Pt+1 Pt F F S $/F . If we let the ratio P t+1 /P t represent the expected rate of inflation, I $ , then the expected exchange rate can be expressed as E(S$/F ) t+1 = 1 + I$ t S $/F 1 + I F . For example, assume that the exchange rate between the dollar and the French franc is currently $0.1600/FF1. Then if inflation in the U.S. is expected to be 3 percent per year and inflation in France is expected to be 5 percent per year, the exchange rate between the dollar and the French franc in one year should be $0.1570/FF 1 = 1.03 $0.1600/FF1 1.05 . The Relative Purchasing Power Parity relation can be generalized to predict exchange rates N periods in the future (assuming of course that we have forecasts of inflation in the respective countries over the time period covered by the exchange rate in question). This general relation is given by 1 + I US E( S$/F ) t+N = S $/F t [ 1+I F ]N For example, assuming that inflation in the U.S. and France are respectively expected to run at 3 percent and 5 percent per year over the next two years, the exchange rate between the dollar and the French Franc in two years should be $0.1540/FF1 = 1.03 $0.1600/FF1  1.05   2   . Intuitively, if a country experiences higher inflation than its trading partners, then its exports become less competitive overseas and foreign imports become more competitive at home. The resulting deficit in the balance of trade puts downward pressure on the exchange rate. 14 The International Version of the Fisher Equation The Fisher Equation (named after Irving Fisher) expresses the nominal or dollar denominated rate of interest in terms of the expected rate of inflation and the real or purchasing power denominated rate of interest. Although the Fisher Equation is not a precise theory of the relation between interest rates and the expected rate of inflation, it is a fairly close approximation. If we denote the real rate of interest by and the expected rate of inflation by I, the Fisher Equation is given by 1+R = (1 + ) (1 + I) For example, if the real rate of interest is 0.0125 (1.25 percent) and the expected rate of inflation is 4 percent, then the nominal (dollar denominated) rate of interest will be the solution to 1+R which implies that R = = 1.0125 x 1.04 1 = (1 + .0125) (1 + .04) 5.30 percent (.0530) An international version of the Fisher effect is often used to specify how differences in the respective rates of inflation across countries determine the differences in interest rates across countries. If we assume that the Fisher Equation holds simultaneously in both the U.S. and in country FR, then we have 1 + R US 1 + RF = 1 + US 1 + F 1 + I US 1 + IF . If capital flows freely from one country to another, chasing the highest interest rates, then there will be a tendency for real rates to be equalized across countries. If this is the case, then the U.S. and contry F should have the same real rate of interest (i.e., US equals F). Therefore, 1 + R US 1 + RF = 1 + I US 1 + IF . The expression above implies that all we have to do to infer the difference in the expected rates of inflation in two countries is to observer the difference in the nominal interest rates in those two countries. For example, suppose that the nominal rate of interest in the U.S. is 6 percent and that the nominal rate of interest in Japan is 2.5 percent. Then assuming that the real rate of interest in the U.S. is equal to the real rate of interest in Japan, the difference between the expected rates of inflation in the U.S. and Japan is 1 + R US 1 + R¥ = 1 + .060 1 + .025 , 15 = 1.034 , indicating that inflation in the U.S. is approximately 3.4 percent greater in the U.S. than in Japan. 16 In order to forecast future exchange rates using Relative Purchasing Power Parity, we need a good forecast in the difference in the expected rates of inflation in the two countries in question, E(S$/F ) t+N = S $/F t [ 1+I F 1 + I US ]N . Forecasting the inflation rate is always very difficult. However, if we are satisfied that the real interest rates in two countries are approximately equal, then the Fisher Equation allows us to approximate differences in expected inflation rates using the difference in the nominal interest rates. Therefore, we can forecast exchange rates using the nominal rates of interest, E(S$/F ) t+N = S $/F t [ 1+R F 1 + R US ]N . For example, suppose that the exchange rate between the dollar and the Swiss franc is $0.6500/SF1. Further, the U.S. interest rate is 5.3 percent per year and the Swiss interest rate is 2.5 percent per year. Our forecast of the expected exchange rate in one year would be E(S$/SF ) = = t+1 1.053 $0.6500/SF1 x [ 1.025 $0.6678/SF1. ]1 , Similarly, the appropriate forecast for the exchange rate between the dollar and the Swiss franc in 2 years would be E(S$/SF ) = = t+2 1.053 $0.6500/SF1 x [ 1.025 $0.6860/SF1. ]2 , 17 Valuing Direct Foreign Investments The logic underlying the valuation of a capital investment project that generate future cash flows denominated in a foreign currency is similar to that underlying a standard capital budgeting problem. That is, we should identify the incremental cash flows and discount them at the appropriate weighted average cost of capital. Foreign investment decisions are complicated by a. conversion of foreign exchange to dollars, b. restrictions on the repatriation of cash flows. While accounting for the potential impact of unanticipated future restrictions on the repatriation of future cash flows is particularly difficult, converting a stream of future cash flows denominated in a foreign currency to a projected dollar denominated stream is relatively straightforward. The net present value of the projected future cash flows can then be determined using the firm's dollar-denominated weighted average cost of capital. We can summarize this approach to the valuation of investments in foreign countries as follows: a. estimate future foreign currency denominated cash flow, b. convert foreign currency to dollars at the “projected” exchange rate, c. determine the net present value using the domestic (U.S.) cost of capital. Example: Valuation of Foreign Investments Consider the following example. Because of a recent ban on the import of U.S. made tennis rackets to Germany (in retaliation for anticipated restrictions on the import of German-made goods to the U.S.), a U.S. sporting goods manufacturer expects to create a German subsidiary to manufacture and distribute tennis rackets in Germany. The project life is expected to be two years (at which time, an end to protectionist sentiment in the U.S. will lead to an end to trade restrictions). The required investment in the project is a. DM 25,000,000 in plant and equipment, b. DM 5,000,000 in working capital. The projected after-tax cash flows from the project are DM 20,000,000 for the next two years, in addition to DM5,000,000 from the liquidation of working capital in two years. The spot exchange rate (S $/DM) is $0.6500/DM1 . The interest rate in the U.S. (R US ) is 6 percent per year while the German interest rate (RDM ) 11 percent per year. 18 Predicted Exchange Rates If the real rate of interest is the same in all countries (due to the international mobility of capital) the International Fisher Effect implies that differences in nominal interest rates will signal differences in the expected rates of inflation across countries. Given that R US is 6 percent per year and that the German interest rate R DM is 11 percent per year, we would expect the expected rate of inflation in Germany to be roughly 5 percent greater than the expected rate of inflation in the U.S.. Relative Purchasing Power Parity implies that the expected changes in exchange rates should reflect differences the expected rates of inflation in the two countries in question, E( S$/DM(t+N) ) S$/DM 1 + I US [ 1+I DM = ] N where E( S$/DM(t+n) ) denotes the exchange rate expected in n periods. This formula implies that over the next two years we can expect the following exchange rates E( S$/DM(t+1) ) = and E( S$/DM(t+2) ) = = 1.06 2 $0.65/DM1 [ 1.11 ] $0.5928/DM1 . , = 1.06 1 $0.65/DM1 [ 1.11 ] $0.6207/DM1 , , The anticipated structure of exchange rates can be used to convert the anticipated WV denominated cash flows to dollars, which can then be discounted using the US cost of capital. 0 Investment in DM a. Plant and Equipment b. Working Capital DM Cash Flows Total DM Cash Flows Projected Exchange Rate Projected Dollar Cash Flow $0.6500/DM1 <$19,500> 19 DM 20,000 DM 20,000 DM 5,000 DM 20,000 DM 25,000 Cash Flows in 1000s of DM 1 2 3 $0.6207/DM1 $0.5928/DM $12,414 $14,820 Assuming that the firm has a weighted average cost of capital of 12 percent, the net present value of the projected dollar stream of cash flows is $3,398 (1000s), which indicates that the project should be accepted. 20