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Section 2The Foreign Exchange Market

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Content

• Objectives• Exchange Rates• The Foreign Exchange Market• Interest Parity Conditions• Equilibrium in the ForEx Market• Imperfect Markets• Summary

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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.

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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.

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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.

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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

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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 <

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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 =

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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.

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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,

)/()/()/(

CADUSDSEURUSDSEURCADS =

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Exchange Rates

)/()/()/(

CADUSDSEURUSDSEURCADS =

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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 .

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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 .

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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 .

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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)

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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.

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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.

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The Foreign Exchange Market

• The main functions are:– Transfer of purchasing power– Provision of credit– Minimizing Foreign Exchange Risk

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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.

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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.

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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.

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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.

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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 =+

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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 iUSDxUSDX

+=

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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( ,

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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

USDxUSDX

t

TtcTt

t

T +=

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Interest Parity Conditions

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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( +=+

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Interest Parity Conditions

• How are forward contracts priced?

• Forward Premiums?

cTt

cTt

usTt

t

tTt

iii

SSF

,

,,,

1+−

=−

tcTt

usTt

Tt Sii

F)1()1(

,

,, +

+=

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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 =

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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 −+=

][,,

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Equilibrium in the ForEx Market

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

• It contains:– Home returns:

– Foreign returns:

i+1

SSi e /*)1( +

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Equilibrium in the ForEx Market

(1+i*)Se/SUSD Returns

S

S

1+i

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

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Equilibrium in the ForEx Market

i* + (Se – S)/SUSD Rates of Returns

S

S

i

i = i* + (Se – S)/S

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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.

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Equilibrium in the ForEx Market

USD Returns

S

S

S

1+i 1+i

(1+i*)Se/S

An increase in home interest rates

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Equilibrium in the ForEx Market

USD Returns

S

S

S

(1+i*)Se/S

1+i

An increase in foreign interest rates

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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.

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Equilibrium in the ForEx Market

USD Returns

S

S

S

(1+i*)Se/S

1+i

A rise in expected future exchange rates

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Imperfect Markets

• In reality, we have bid-ask spreads.• This influences the notion of arbitrage used

to construct cross-rates and covered interest parity.

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Imperfect Markets

• Cross-rates:

)/()/()/(

)/()/()/(

CADUSDSEURUSDSEURCADS

CADUSDSEURUSDSEURCADS

b

aca

a

bcb

=

=

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Imperfect Markets

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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

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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.

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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

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Imperfect Markets

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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?

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Imperfect Markets

• Investing in the US:CADYT = USDxt (1+ib,us)/ Fa(USD/CAD)orUSDxt = CADYT Fa(USD/CAD)/(1+ib,us)USDxt = CAD 1m (USD 0.77/CAD)/(1+0.05)

= USD 0.73 m

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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.

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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.

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Imperfect Markets

• Investing at Home: HRb = 1+ib

• Borrowing at Home: HRa = 1+ia

• As expected, HRb < HRa

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Imperfect Markets

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

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

• As expected, FRb < FRa

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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

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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.

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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

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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

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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

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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

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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.

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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.

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Summary

• Covered Interest Parity:

• Uncovered Interest Parity:t

TtcTt

usTt S

Fii ,

,, )1()1( +=+

t

TtcTt

usTt S

SEii ][)1()1( ,, +=+

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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.