1

Section 2The Foreign Exchange Market

2

Content

• Objectives

• Exchange Rates

• The Foreign Exchange Market

• Interest Parity Conditions

• Equilibrium in the ForEx Market

• Imperfect Markets

• Summary

3

Objectives

• To know how to define and quote an exchange rate.

• To know how to classify exchange rates by types of transactions and by maturity.

• To know about triangular arbitrage• To understand the interest parity conditions.• To know how to determine the spot exchange rate

in the foreign exchange market equilibrium.

4

Exchange Rates

• An exchange rate is the price of a currency in terms of another currency.– The price of a car is $20 000/car.

– The price of a Canadian dollar is USD 0.7649/CAD.– The price of a US dollar in CAD is CAD 1.3074/USD– So, S(USD/CAD) = 1/S(CAD/USD)

• An exchange rate quote is an announcement of a price at which a currency can be traded for another.

5

Exchange Rates

• Direct versus Indirect Quotes– A direct quote is the amount of home currency

per unit of foreign currency.– An indirect quote is the amount of foreign

currency per unit of home currency.

• Example: In the U.S., S(USD/CAD) = USD 0.72/CAD is a direct quote for the Canadian dollar, but an indirect quote

for the U.S. dollar.

6

Exchange Rates

• Terminology:– Depreciation: A fall in the foreign exchange value of a

floating currency.

– Devaluation: A fall in the foreign exchange value of a currency pegged to another currency.

– Soft or Weak: A currency that is expected to devalue or depreciate relative to major currencies.

– The exchange rate is the price of the currency in the denominator: S = USD 0.75/CAD

7

Exchange Rates

• Exchange rate by types of transactions:– Bid rate: exchange rate at which financial institutions

will buy a foreign currency from you. We denote it Sb.

– Ask rate: exchange rate at which financial institutions will sell a foreign currency to you. We denote it Sa.

– The bid and ask rate are related by:ab SS

8

Exchange Rates

– The bid rate is use to sell a foreign currency or purchase the home currency:

– The ask rate is use to purchase a foreign currency or sell the home currency:

)/(/1)/( USDCADSCADUSDS ba

)/(/1)/( USDCADSCADUSDS ab

9

Exchange Rates

– The spread (Sa – Sb) ensures that financial institutions make revenues from foreign exchange transactions.

• These revenues are required to cover transaction costs incurred by acting as a financial intermediary between parties buying and selling currencies.

• These revenues are also essential to make some profits.

10

Exchange Rates

• Triangular Arbitrage and Cross Rates:– I trade EUR z to obtain USD x:

• USDx = EUR z S(USD/EUR)

– I trade USD x to obtain CAD y:

• CAD y = USD x/S(USD/CAD)

– I trade EUR z to obtain CAD y:

• CAD y = EUR z S(CAD/EUR)

– So,

)/(

)/()/(

CADUSDS

EURUSDSEURCADS

11

Exchange Rates

)/(

)/()/(

CADUSDS

EURUSDSEURCADS

12

Exchange Rates

• Domestic and Foreign Prices– The exchange rate enables us to compute the

foreign currency price of goods in terms of home currency.

– Example: The USD price of a CAD 20 compact disc with an exchange rate of USD 0.75/CAD is (USD 0.75/CAD) x (CAD 20) = USD 15 .

13

Exchange Rates

• A depreciation of the home country’s currency– A rise in the price of a foreign currency – Raises the home currency price of foreign

goods– Example: If the exchange rate is USD 0.80/CAD, the

USD price of a CAD 20 compact disc is (USD 0.80/CAD) x (CAD 20) = USD 16 .

14

Exchange Rates

• An appreciation of the home country’s currency– A reduction in the price of a foreign currency – Reduces the home currency price of foreign

goods– Example: If the exchange rate is USD 0.70/CAD, the

USD price of a CAD 20 compact disc is (USD 0.70/CAD) x (CAD 20) = USD 14 .

15

Exchange Rates

• An appreciation of a country’s currency:– Raises the relative price of its goods (exports)

– Lowers the relative price of foreign goods (imports)

• Depreciation of a country’s currency:– Lowers the relative price of its goods (exports)

– Raises the relative price of foreign goods (imports)

16

The Foreign Exchange Market

• Exchange rates are determined in the foreign exchange market.

• Geographically, the foreign exchange market spans the globe.– The market is most liquid early in the European

afternoon, when the markets of both Europe and the U.S. East coast are open.

– The market is thinnest at the end of the day in California, when the markets in Asia are about to open.

17

The Foreign Exchange Market

• The BIS estimated that in 1992, the daily volume of trading on the foreign exchange market was about 5 to 10 times that of international trade in goods and services.

• The volume has ballooned in recent years.

• New technologies are used in the major trading centers (London, New York, Tokyo, Frankfurt, and Singapore).

• In 2001, around 90% of transactions between banks involved exchanges of foreign currencies for U.S. dollars.

18

The Foreign Exchange Market

• The main functions are:– Transfer of purchasing power

– Provision of credit

– Minimizing Foreign Exchange Risk

19

The Foreign Exchange Market

• The major participants are:– Commercial banks

– International corporations

– Nonbank financial institutions

– Central banks

– Speculators and arbitragers

• Interbank trading accounts for most of the volume.

20

The Foreign Exchange Market

• Spot exchange rates (S)– A spot transaction requires almost immediate

delivery of foreign exchange. 

• Forward exchange rates (F)– A forward transaction requires delivery at a

future date of a specified amount of a currency for a specified amount of another currency.

21

The Foreign Exchange Market

• Foreign Exchange Swaps– A swap transaction involves the simultaneous

purchase and sale of a given amount of foreign exchange for two different value dates.

22

The Foreign Exchange Market

• Futures contract– A promise that a specified amount of foreign currency

will be delivered on a specified date in the future.

• Options contract – Gives the right (not the obligation) to buy or sell a

specified amount of foreign currency at a specified price at any time up to a specified expiration date.

23

Interest Parity Conditions

• Covered Interest Parity– This is an application of the law of one price.– Assets that have same maturity, liquidity, and

risk should have the same price.– The rate of return of an asset is inversely

related to its price.– Example: The rate of return on a risk-free asset that

promises to pay 1 unit tomorrow for a price q units today is: qi /11

24

Interest Parity Conditions

• Consider the return from purchasing a home money market instrument that pays in a year.– I purchase USD x of the asset. I get in a year:

– The return is

tusTtT USDxiUSDX )1( ,

)1( ,usTt

t

T iUSDx

USDX

25

Interest Parity Conditions

• Consider the return from purchasing a Canadian money market instrument that pays in a year.– I purchase CAD y:

– I purchase CAD y of the asset. I get in a year

)/(/ CADUSDSUSDxCADy ttt

tcTtT CADyiCADY )1( ,

26

Interest Parity Conditions

– I sell CADY to obtain USDX

– I use a forward contract to remove or cover foreign exchange risk.

– The return is

TTtT CADYCADUSDFUSDX )/(,

)/(

)/()1( ,

, CADUSDS

CADUSDFi

USDx

USDX

t

TtcTt

t

T

27

Interest Parity Conditions

28

Interest Parity Condition

• Covered Interest Parity:

• Two assets with the same maturity and risk must yield the same return.

t

TtcTt

usTt S

Fii ,

,, )1()1(

29

Interest Parity Conditions

• How are forward contracts priced?

• Forward Premiums?

cTt

cTt

usTt

t

tTt

i

ii

S

SF

,

,,,

1

tcTt

usTt

Tt Si

iF

)1(

)1(

,

,,

30

Interest Parity Conditions

• Efficient Market Hypothesis:

– The forward rate is an unbiased predictor of future spot rates.

– Empirical studies on market efficiency have yielded conflicting results. There appears to be an important risk premium on the forward market.

][, TtTt SEF

31

Interest Parity Conditions

• Uncovered Interest Parity:

• The linear version of UIP is sometimes useful:

t

TtcTt

usTt S

SEii

][)1()1( ,,

t

tTtcTt

usTt S

SSEii

][,,

32

Equilibrium in the ForEx Market

• The uncovered interest parity condition is the workhorse of open-economy macroeconmics.

• It contains:– Home returns:

– Foreign returns:

i1

SSi e /*)1(

33

Equilibrium in the ForEx Market

(1+i*)Se/S

USD Returns

S

S

1+i

(1+i) = (1+i*)Se/S

34

Equilibrium in the ForEx Market

i* + (Se – S)/S

USD Rates of Returns

S

S

i

i = i* + (Se – S)/S

35

Equilibrium in the ForEx Market

• The effect of changing interest rates on the exchange rate– A rise in USD interest rates causes the USD to

appreciate.– A rise in CAD interest rates causes the USD to

depreciate.

36

Equilibrium in the ForEx Market

USD Returns

S

S

S

1+i 1+i

(1+i*)Se/S

An increase in home interest rates

37

Equilibrium in the ForEx Market

USD Returns

S

S

S

(1+i*)Se/S

1+i

An increase in foreign interest rates

38

Equilibrium in the ForEx Market

• The effect of changing expectations on the exchange rate– A rise in the expected future exchange rate raises the

current exchange rate.

– A fall in the expected future exchange rate reduces the current exchange rate.

39

Equilibrium in the ForEx Market

USD Returns

S

S

S

(1+i*)Se/S

1+i

A rise in expected future exchange rates

40

Imperfect Markets

• In reality, we have bid-ask spreads.

• This influences the notion of arbitrage used to construct cross-rates and covered interest parity.

41

Imperfect Markets

• Cross-rates:

)/(

)/()/(

)/(

)/()/(

CADUSDS

EURUSDSEURCADS

CADUSDS

EURUSDSEURCADS

b

aca

a

bcb

42

Imperfect Markets

43

Imperfect Markets

• It must not be possible to make any arbitrage profits.

– Suppose that the relation between the cross rates and actual rates are:

• A) No arbitrage opportunity

Scb--------------Sca

Sb--------------Sa

• B) No arbitrage opportunity

Scb-----------------Sca

Sb--------Sa

44

Imperfect Markets

• C) Arbitrage opportunity

Scb-------Sca

Sb--------Sa

– You can purchase the currency at price Sa and resell it at price Scb, and make a profit of (Scb - Sa) per units of currency purchased.

45

Imperfect Markets

• International investments are also affected.

• It must not be possible to make any arbitrage profits.

• There are bid-ask rates in the foreign exchange market.

• Borrowing rates (ia) are larger than lending rates (ib). So, ia > ib

46

Imperfect Markets

47

Imperfect Markets

• Example: The manager of a U.S. firm intends to buy Canadian maple syrup in 1 year. The syrup is worth CAD 1 m. International prices are as follows:

– Spot rate: USD 0.66----0.80/CAD

– Forward rate: USD 0.65----0.77/CAD

– Interest rates (Canada): 8---10 percent per annum

– Interest rates (U.S.): 5---6 percent per annum

• How much money should the manager put aside today for this purchase?

48

Imperfect Markets

• Investing in the US:CADYT = USDxt (1+ib,us)/ Fa(USD/CAD)

or

USDxt = CADYT Fa(USD/CAD)/(1+ib,us)

USDxt = CAD 1m (USD 0.77/CAD)/(1+0.05)

= USD 0.73 m

49

Imperfect Markets

• Investing in Canada:CADYT = USDxt (1+ib,c)/ Sa(USD/CAD)

USDxt = CADYT Sa(USD/CAD)/(1+ib,c)

= CAD 1m (USD 0.80/CAD)/(1+0.08)

= USD 0.74m

• The manager should set aside USD 0.73 m, and invest it in the US.

50

Imperfect Markets

• Is there an arbitrage opportunity?

• To answer this question, we construct the USD return to borrowing and investing abroad.

• Then, we can compare the rates obtained abroad to those in the US.

51

Imperfect Markets

• Investing at Home: HRb = 1+ib

• Borrowing at Home: HRa = 1+ia

• As expected, HRb < HRa

52

Imperfect Markets

• Investing Abroad: FRb = (1+i*b) Fb/Sa

• Borrowing Abroad: FRa = (1+i*a) Fa/Sb

• As expected, FRb < FRa

53

Imperfect Markets

• It must not be possible to make any arbitrage profits.

– Suppose that the relation between the Home and Foreign returns are:

• A) No arbitrage opportunity

FRb--------------FRa

HRb--------------HRa

• B) No arbitrage opportunity

FRb-----------------FRa

HRb--------FRa

54

Imperfect Markets

• C) Arbitrage opportunity

FRb-------FRa

HRb--------HRa

– You can invest abroad at return FRb and borrow at home

at return HRa and make a profit of (FRb/HRa) per units of home currency invested.

55

Imperfect Markets

• Example: You work for a bank on Wall Street. You face the following prices – Spot rate: USD 0.745----0.765/CAD

– Forward rate: USD 0.750----0.770/CAD

– Interest rates (Canada): 8---10 percent per annum

– Interest rates (U.S.): 5---6 percent per annum

56

Imperfect Markets

• So, the home borrowing and investment returns over a year are:

• HRb = 1+ib =1+ 0.05 = 1.05

• HRa = 1+ia = 1+ 0.06 = 1.06

57

Imperfect Markets

• The foreign investment return over a year is: • FRb = (1+i*b) Fb/Sa

• FRb = (1+0.08) (USD 0.750/CAD)/[USD 0.765/CAD]

• FRb = 1.059

58

Imperfect Markets

• The foreign borrowing return over a year is: • FRa = (1+i*a) Fa/Sb

• FRa = (1+0.10) (USD 0.770/CAD)/[USD 0.745/CAD]

• FRa = 1.137

59

Imperfect Markets

• The rates overlap: FRb=1.059 ----------------FRa=1.137

HRb=1.05 ----------HRa=1.06

• The rates overlap: there is no arbitrage opportunity.

• Where should I borrow?– Borrow at home at 6 percent rather than abroad at 14 percent.

• Where should I invest?– Invest abroad at 5.9 percent rather than at home at 5 percent.

60

Summary

• Exchange rates enable us to translate different countries’ prices into comparable terms.

• A depreciation (appreciation) of a country’s currency against foreign currencies makes its exports cheaper (more expensive) and its imports more expensive (cheaper).

• Exchange rates are determined in the foreign exchange market.

61

Summary

• Covered Interest Parity:

• Uncovered Interest Parity:

t

TtcTt

usTt S

Fii ,

,, )1()1(

t

TtcTt

usTt S

SEii

][)1()1( ,,

62

Summary

• Equilibrium in the foreign exchange market requires uncovered interest parity.

• A rise in USD interest rates causes the USD to appreciate against foreign currencies.

• The exchange rate depends on its expected future level.

• Market imperfections affect both cross-rates and interest rate parity conditions.