1 Determinants of the Exchange Rate

2 Determinants of the Exchange Rate Under a flexible rate system, the exchange rate is determined by supply and demand. –The dollar demand for foreign exchange originates from American demand for foreign goods, services, & assets (real or financial). –The supply of foreign exchange originates from sales of goods, services, & assets from Americans to foreigners. –The foreign exchange market brings the quantity demanded and quantity supplied into balance. As it does so, it brings the purchases by Americans from foreigners into equality with the sales of Americans to foreigners.

3 Quantity of foreign exchange (pounds) Q $1.20 $1.50 $1.80 Dollar price of foreign exchange (for pounds ) Foreign Exchange Market Equilibrium S (sales to foreigners) Excess demand for pounds Excess supply of pounds The dollar price of the English pound is measured on the vertical axis. The horizontal axis indicates the flow of pounds to the foreign exchange market. The demand and supply of pounds are in equilibrium at the exchange rate of $1.50 = 1 English pound. At this price, quantity demanded equals quantity supplied. A higher price of pounds (like $1.80 = 1 pound), would lead to an excess supply of pounds... causing the dollar price of the pound to fall (depreciate). A lower price of pounds (like $1.20 = 1 pound), would lead to an excess demand for pounds … causing the dollar price of the pound to rise (appreciate). D (purchases from foreigners) e

4 Changes in the Exchange Rate Factors that cause a currency to depreciate: –A rapid growth of income (relative to trading partners) that stimulates imports relative to exports. –A higher rate of inflation than one's trading partners. –A reduction in domestic real interest rates (relative to rates abroad).

5 Quantity of foreign exchange (pounds) Q1Q1 $1.50 $1.80 Dollar price of foreign exchange (for pounds ) a Foreign Exchange Market Equilibrium S (sales to foreigners) Other things constant, if incomes increase in the United States, U.S. imports of foreign goods and services will grow. The increase in imports will increase the demand for pounds (in the foreign exchange market) causing the dollar price of the pound to rise from $1.50 to $1.80. D1D1 Q2Q2 D2D2 b

6 Quantity of foreign exchange (pounds) Q1Q1 $1.50 Dollar price of foreign exchange (for pounds ) Inflation With Flexible Exchange Rates S1S1 If prices were stable in England while the price level in the U.S. increased by 50 percent … the U.S. demand for British goods (and pounds) would increase … D1D1 D2D2 a $2.25 S2S2 as U.S. exports to Britain would be relatively more expensive they would decline and thereby cause the supply of pounds to fall. These forces would cause the dollar to depreciate relative to the pound. b

7 Changes in the Exchange Rate Factors that cause a currency to appreciate: –A slower growth rate relative to one’s trading partners. –A lower inflation than one's trading partners. –An increase in domestic real interest rates (relative to rates abroad).

8 Growth of Trade and Foreign Exchange Transactions

9 Exchange Rates and Asset Prices Exchange rates are determined by the relative supplies and demands for currencies. Since buyers and sellers are ultimately interested in purchasing something with the currency - goods, services, or investments - their prices and returns must indirectly influence the demand for a given currency. So far, we have focused on the relationship between exchange rates and the demand and supply of goods and services. Now we turn to the prices that determine the demand for assets - their returns.

10 Law of One Price for Assets Assume: Absent frictions, identical goods must trade for identical prices in different countries when converted into a common currency. The same condition should hold for assets. One important difference between goods and assets: Price is not paid immediately - it is paid over time in the form of returns. This introduces the primary friction for exchanging assets - a friction not found in goods. Risk

11 Law of One Price for Assets Hence, there must exist a corresponding version of the Law of One Price for assets which requires returns to be identical across countries once this friction has been removed: Covered Interest Parity Covered Interest Parity requires frictionless markets to offer identical rates of returns for identical assets.

12 Law of One Price for Assets Arbitrageurs will guarantee that the following two strategies will generate the exact same common-currency return: 1.a. Purchasing $1 worth of U.S. short-term treasuries. b. Obtain an n-period return of 1+R t,t+n. 2. a. Convert $1 into foreign currency at rate 1/s t (FC/$). b. Purchase corresponding foreign short-term treasuries. c. Receive an n-period foreign currency return of 1+R* t,t+n. d. Eliminate the currency risk of the foreign return by locking in an exchange rate of F t,t+n ($/FC).

13 Law of One Price for Assets Arbitrageurs will guarantee that the following two strategies will generate the exact same common-currency return: 1.a. Purchasing $1 worth of U.S. short-term treasuries. b. Obtain an n-period return of 1+R t,t+n. 2. a. Convert $1 into foreign currency at rate 1/s t (FC/$). b. Purchase corresponding foreign short-term treasuries. c. Receive an n-period foreign currency return of 1+R* t,t+n. d. Eliminate the currency risk of the foreign return by locking in an exchange rate of F t,t+n ($/FC). e. Obtain an overall n-period return of: F t,t+n (1+R* t,t+n ) s t

14 Covered Interest Parity Covered Interest Parity maintains that the returns from strategies 1 and 2 will always be equal: 1+R t,t+n = F t,t+n (1+R* t,t+n ) s t Cooked example: R t,t+n = 5% R* t,t+n = 4% s t = $2 / FC What is F t,t+n ?

15 Cooked example: R t,t+n = 5% R* t,t+n = 4% s t = $2 / FC What is F t,t+n ? 1+R t,t+n = F t,t+n (1+R* t,t+n ) s t Covered Interest Parity Covered Interest Parity maintains that the returns from strategies 1 and 2 will always be equal: 1+R t,t+n = F t,t+n (1+R* t,t+n ) s t

16 Covered Interest Parity Covered Interest Parity maintains that the returns from strategies 1 and 2 will always be equal: 1+R t,t+n = F t,t+n (1+R* t,t+n ) s t Cooked example: R t,t+n = 5% R* t,t+n = 4% s t = $2 / FC What is F t,t+n ? 1.05 = F t,t+n (1+R* t,t+n ) s t

17 Covered Interest Parity Covered Interest Parity maintains that the returns from strategies 1 and 2 will always be equal: 1+R t,t+n = F t,t+n (1+R* t,t+n ) s t Cooked example: R t,t+n = 5% R* t,t+n = 4% s t = $2 / FC What is F t,t+n ? 1.05 = F t,t+n 1.04 s t

18 Covered Interest Parity Covered Interest Parity maintains that the returns from strategies 1 and 2 will always be equal: 1+R t,t+n = F t,t+n (1+R* t,t+n ) s t Cooked example: R t,t+n = 5% R* t,t+n = 4% s t = $2 / FC What is F t,t+n ? 1.05 = F t,t+n 1.04 $2 / FC

19 Covered Interest Parity Covered Interest Parity maintains that the returns from strategies 1 and 2 will always be equal: 1+R t,t+n = F t,t+n (1+R* t,t+n ) s t Cooked example: R t,t+n = 5% R* t,t+n = 4% s t = $2 / FC What is F t,t+n ? 1.05 = F t,t+n 1.04 $2 / FC F t,t+n = $ 2.02 / FC - Investors in R* require a guaranteed currency appreciation to compensate for lower interest rate.

20 Real Example: Not so long ago, 90-day U.S. and Japanese Treasury Notes had the following returns: R US = 5.03% R J = 3.77% The spot exchange rate was s t = $ / Yen. What was the 90-day forward exchange rate F? $ / Yen. Investors demanded less compensation for holding Yen-denominated returns since they expected the Yen to appreciate.

21 Uncovered Interest Parity The Forward exchange rate is what the market expects the future spot exchange rate to be: F t,t+n = E (s t+n ). If the market has ‘rational expectations,’ then it should predict the future spot accurately (on average): F t,t+n = E (s t+n ) = s t+n This is know as the Unbiased Forward Hypothesis. Does the market have rational expectations? Robert Lucas said ‘yes’ and won a prize (Nobel).

22 Uncovered Interest Parity If so, this implies that an ‘unhedged’ version of covered interest parity should hold as well.

23 Uncovered Interest Parity If so, this implies that an ‘unhedged’ version of covered interest parity should hold as well. If this is the case: 1+R t,t+n = E(s t,t+n )(1+R* t,t+n ) s t

24 Uncovered Interest Parity If so, this implies that an ‘unhedged’ version of covered interest parity should hold as well. On average: 1+R t,t+n = s t,t+n (1+R* t,t+n ) s t

25 Uncovered Interest Parity If so, this implies that an ‘unhedged’ version of covered interest parity should hold as well. On average: 1+R t,t+n = s t,t+n (1+R* t,t+n ) s t Which can be closely approximated by the Uncovered Interest Parity equation: R t,t+n - R* t,t+n = %  s t,t+n.

26 Uncovered Interest Parity Example (cooked): If British short-term interest rates are 5%, German short-term interest rates are 10%, and the current exchange rate is 0.5 P/ Euro, what will be the Pound/Euro exchange rate one year from now? R t,t+n - R* t,t+n = %  s t,t+n. The Euro should depreciate by 5% to P / Euro. Also, the one-year forward exchange rate better be P / Euro

27 To Review: Exchange Rate Arbitrage Two kinds of Arbitrage: 1. Riskless arbitrage will ensure: Covered Interest Parity: 1+R t,t+n = F t,t+n (1+R* t,t+n )/s t or: R t,t+n - R* t,t+n = F t,t+n - s t If difference between forward and spot rates do not equal differences in interest rates, arbitrageurs will make money every time - relationship holds instantaneously and therefore is risk-free.

28 Exchange Rate Arbitrage 2. Risky arbitrage should ensure: A. Forward rate is unbiased - it differs from spot by expected exchange rate changes: F t,t+n - s t = E(%  s t,t+n ), B. That these expectations are rational: E(%  s t,t+n ) = %  s t,t+n C. So that Uncovered Interest Parity holds on average: R t,t+n - R* t,t+n = F t,t+n - s t = E(%  s t,t+n ) = %  s t,t+n

29 Exchange Rate Arbitrage 2. Risky arbitrage should ensure: A. Forward rate is unbiased - it differs from spot by expected exchange rate changes: F t,t+n - s t = E(%  s t,t+n ), B. That these expectations are rational: E(%  s t,t+n ) = %  s t,t+n C. So that Uncovered Interest Parity holds on average: R t,t+n - R* t,t+n = F t,t+n - s t = E(%  s t,t+n ) = %  s t,t+n Differences between interest rates forecast exchange rate changes.

30 Exchange Rate Arbitrage 2. Risky arbitrage should ensure: A. Forward rate is unbiased - it differs from spot by expected exchange rate changes: F t,t+n - s t = E(%  s t,t+n ), B. That these expectations are rational: E(%  s t,t+n ) = %  s t,t+n C. So that Uncovered Interest Parity holds on average: R t,t+n - R* t,t+n = F t,t+n - s t = E(%  s t,t+n ) = %  s t,t+n Differences between interest rates forecast exchange rate changes. Why?

31 Exchange Rate Arbitrage R t,t+n - R* t,t+n = %  s t,t+n If s generally doesn’t change sufficiently to offset interest differential, (say R US t,t+n > R J t,t+n and R US t,t+n -R J t,t+n > %  s t,t+n ) arbitrageurs will: 1. Borrow in low-interest rate currency (Yen). 2. Convert to the high-interest rate currency (Dollars). 3. Deposit in the high-interest rate currency. 4. Convert back to repay low-interest rate loan at an insufficiently appreciated exchange rate. 5. Earn a profit - on average - of: R US t,t+n - R J t,t+n - %  s t,t+n

32 Exchange Rate Arbitrage R t,t+n - R* t,t+n = %  s t,t+n Example: R US = 5.03% R J = 3.77% s t = $ / Yen. F t,t+n says Yen should appreciate to: $ / Yen. But if, on average, s t+n = s t, can a speculator can make profits, on average? Of course: By borrowing in Yen at 3.77%, depositing in Dollars at 5.03%, and converting after 1 year back into yen at the same exchange rate. This will earn - on average % on a zero-wealth investment.

33 Exchange Rate Arbitrage This activity - if widespread - will have the following effects: 1.Increase demand for dollars currency at time t - causing s t ($/Yen) to decline. 2.Increase demand for U.S. deposits - causing R US t,t+n to decline. 3.Increase demand for Japanese borrowing - causing R J t,t+n to increase. 4.Increase demand for Yen at time t+n - causing s t+n to increase.

34 Key International Relationships

35 Exchange Rate Change Relative Inflation Rates Key International Relationships

36 RPPP:  -  * = %  s Inflation differentials are offset by changes in spot exchange rate. Relative Inflation Rates Key International Relationships Exchange Rate Change

37 Relative Inflation Rates Key International Relationships Purchasing Power Parity Exchange Rate Change

38 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships Purchasing Power Parity Exchange Rate Change

39 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships CIP: F t,t+n - s t = R - R* Forward differs from spot by interest rate differential Purchasing Power Parity Exchange Rate Change

40 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships Covered Interest Parity Purchasing Power Parity Exchange Rate Change

41 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships Covered Interest Parity Purchasing Power Parity Exchange Rate Change

42 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships Unbiased Forward: F t,t+n - s t = E(%  s t,t+n ) Forward differs from spot by expected change in spot Covered Interest Parity Purchasing Power Parity Exchange Rate Change

43 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships Unbiased Forward Rate Covered Interest Parity Purchasing Power Parity Exchange Rate Change

44 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships Unbiased Forward Rate Covered Interest Parity Purchasing Power Parity Exchange Rate Change

45 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships Fisher Effect: 1+R = (1+r)(1+E(  )) Nominal interest rate equals real rate plus expected inflation Unbiased Forward Rate Covered Interest Parity Purchasing Power Parity Exchange Rate Change

46 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships 1+R = (1+r)(1+E(  )) Unbiased Forward Rate Covered Interest Parity Purchasing Power Parity Exchange Rate Change R - R* = E(  ) - E(  *) With RIP, interest rates reflect expected inflation differential.

47 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships Fisher Effect and Real Interest Parity Unbiased Forward Rate Covered Interest Parity Purchasing Power Parity Exchange Rate Change

48 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships F t,t+n - s t = R - R* Unbiased Forward Rate Purchasing Power Parity Exchange Rate Change Fisher Effect and Real Interest Parity

49 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships F t,t+n - s t = R - R* F t,t+n - s t = E(%  s t,t+n ) Purchasing Power Parity Exchange Rate Change Fisher Effect and Real Interest Parity

50 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships F t,t+n - s t = R - R* Uncovered Interest Parity: R - R* = %  s Exchange rate changes offset interest differentials Purchasing Power Parity Exchange Rate Change Fisher Effect and Real Interest Parity F t,t+n - s t = E(%  s t,t+n )

51 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships 1+R = (1+r)(1+E(  )) R - R* = E(  ) - E(  *) Unbiased Forward Rate Covered Interest Parity Purchasing Power Parity Exchange Rate Change

52 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships  -  * = %  s 1+R = (1+r)(1+E(  )) R - R* = E(  ) - E(  *) Unbiased Forward Rate Covered Interest Parity Exchange Rate Change

53 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships 1+R = (1+r)(1+E(  )) R - R* = E(  ) - E(  *) Uncovered Interest Parity: R - R* = %  s Exchange rate changes offset interest differentials  -  * = %  s Unbiased Forward Rate Covered Interest Parity Exchange Rate Change

54 Relative Inflation Rates Forward Exchange Premium Relative Interest Rates Key International Relationships Uncovered Interest Parity Unbiased Forward Rate Covered Interest Parity Purchasing Power Parity Exchange Rate Change Fisher Effect and Real Interest Parity

55 Key International Relationships These relationships are at the heart of international financial management. They are used in many dimensions of a multinational’s operations. 1. Deciding which currency to borrow or lend in. 2. Determining an appropriate project rate of return. 3. Analyzing a firm’s foreign exchange exposure. 4. etc...