The Foreign Exchange Market Copyright 2013 by Diane S. Docking1 KM.

The Foreign Exchange Market

Copyright 2013 by Diane S. Docking 1

€KM

Learning Objectives• What is meant by a foreign exchange rate• Different ways that a foreign exchange rate can be quoted

– (direct versus indirect; American versus European)• Conventions for quoting foreign exchange rates• What foreign exchange risk is• Cross rates and how to calculate theoretical cross rates• IRP & PPP• What a forward exchange rate is• What arbitrage is:

– Triangle arbitrage– Covered interest arbitrage


Exchange Rates


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Foreign Exchange

• In the foreign exchange markets—every currency has a price in terms of other currencies

• Foreign Exchange Rate: a price for a currency denominated in another currency.

• Foreign exchange rates are the conversion rates between currencies– Spot rate– Forward rate

Copyright 2013 by Diane S. Docking4

Foreign Exchange Transactions


Spot foreign exchange transaction: 0 1 2 3 mo

Exchange Rate Agreed/Paid + Currency Delivered bybetween Buyer and Seller Seller to Buyer

Forward exchange transaction 0 1 2 3 mo

Exchange Rate Agreed Buyer Pays Forward Pricebetween Buyer and Seller Seller delivers currency

Spot foreign exchange transaction: 0 1 2 3 mo

Exchange Rate Agreed/Paid + Currency Delivered bybetween Buyer and Seller Seller to Buyer

Forward exchange transaction 0 1 2 3 mo

Exchange Rate Agreed Buyer Pays Forward Pricebetween Buyer and Seller Seller delivers currency

The Foreign Exchange Market

• While you can buy small amounts of FX at any currency exchange such as those found in international airports, much larger sums of currencies are bought and sold around the clock on the foreign exchange market.

• The foreign exchange (FX or forex) market:– where currencies are traded,– is a market that is open 24 hours a day during the week,– has no central physical location, and– experiences daily turnover of over $3 trillion.


FX Rate Quotation Conventions

• Direct vs. Indirect quote:• _________quote is the number of units of local

currency (LC) needed to buy one foreign unit, e.g., # U.S. dollars per 1 Swiss franc

• _________quote is the number of units of a foreign currency (FC) needed to buy one unit of LC, e.g., # Swiss francs per $1– Given a direct quote, we can calculate an indirect

quote, which is the reciprocal of the direct quote


FX Rate Quotation Conventions

• American vs. European quote:• ____________ terms - quoting in terms of U.S.

dollars per unit of foreign currency• _____________terms - quoting in terms of the

number of units of the foreign currency per U.S. dollar is called

• If local currency is U.S. dollars, then Direct quote = American terms and Indirect quote = European terms


15-9 Copyright 2013 by Diane S. Docking

U.S. Dollar Foreign Exchange Rate Quotations

Current foreign exchange rateshttp://www.federalreserve.gov/releases/H10/hist

For example:

One Euro can be purchased for $1.2310, or equivalently,

0.8123 Euros buy one U.S. dollar.

#$/1FCDirect Quote or American Terms

#FC/$1Indirect Quote orEuropean Terms

http://www.federalreserve.gov/releases/H10/hist

http://www.federalreserve.gov/releases/H10/hist

US $ Spot Rates

Copyright 2013 by Diane S. Docking

10

#$/1FCDirect Quoteor American Terms

#FC/$1Indirect Quote orEuropean Terms

US Dollar 1 USD In USD

Euro 0.7518 1.3302

British Pound 0.6576 1.5207

Indian Rupee 60.635 0.01649

Australian Dollar 1.1131 0.8984

Canadian Dollar 1.0277 0.9731

UAE Emirati Dirham 3.6730 0.2723

Swiss Franc 0.9262 1.0796

Chinese Yuan Renminbi 6.1290 0.1632

Malaysian Ringgit 3.2500 0.3077

New Zealand Dollar 1.2524 0.7985

Top 10 July 31, 2013

FX Cross Rates

• Cross Rates• The exchange rate between two countries

other than the U.S. can be inferred from their exchange rates with the U.S. dollar

• The rates thus obtained are known as cross rates


Key Currency Cross Rates

Copyright 2013 by Diane S. Docking

12

Dollar Euro Pound SFranc Peso Yen CdnDlr

Canada 1.0277 1.3670 1.5628 1.1095 0.0807 0.0105 ...

Japan 97.8891 130.2121 148.8636 105.6846 7.6891 ... 95.2539

Mexico 12.7309 16.9347 19.3604 13.7448 ... 0.1301 12.3882

Switzerland 0.9262 1.2321 1.4086 ... 0.0728 0.0095 0.9013

U.K. 0.6576 0.8747 ... 0.7099 0.0517 0.0067 0.6399

Euro 0.7518 ... 1.1432 0.8116 0.0591 0.0077 0.7315

U.S. ... 1.3302 1.5207 1.0796 0.0785 0.0102 0.9731

July 31, 2013 Snapshot of foreign exchange cross rates at 5 p.m. Eastern time.Source: ICAP plc ; historical data prior to 6/9/11: Thomson Reuters http://online.wsj.com/mdc/public/page/2_3023-keyrates.html

http://www.icap.com/market-commentary.aspx

http://online.wsj.com/mdc/public/page/2_3023-keyrates.html

FX Cross Rates


B

C

C

A

CB

CA

B

A

= €1.143248 = €1.1432 £ £

€0.7518 x $1 = €0.7518 =$1 £0.6576 £0.6576

FX Cross Rates (cont.)

• Cross-exchange rates are foreign exchange rates of two currencies relative to a currency.

• Value of one unit of currency A in units of currency B = value of currency A in C divided by value of currency B in C

• Arbitrage assures that the exchange rates will be the same between the countries


B

C

C

A

CB

CA

B

A

Foreign Exchange Risk


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FOREIGN EXCHANGE RISK

• Foreign exchange risk, or currency risk, is the risk that a currency’s value may change adversely

• Most exchange rates are a floating rate, which means it changes constantly depending on the quantity supplied and demanded for each currency in the market.


Appreciation/Depreciation

• If depreciation of the domestic currency ($) occurs, then– FC cost more $’s– a _____________ of the $

• If appreciation of the domestic currency ($) occurs– FC costs less $’s– a _____________ of the $



• When a country’s currency appreciates (rises in value relative to other currencies), the country’s goods in that country become cheaper (holding domestic prices constant in the two countries).

• Appreciation of a country’s currency can make it harder for domestic manufacturers to sell their goods abroad

• Exports __________; imports ___________



• Conversely, when a country’s currency depreciates, its goods abroad become cheaper and foreign goods in that country become more expensive

• exports ___________; imports ___________


$/Euro: August 1, 2008 – August 1, 2013http://tools.currenciesdirect.net/currency-chart/


http://tools.currenciesdirect.net/currency-chart/

$/Pound: August 1, 2008 – August 7, 2013 http://tools.currenciesdirect.net/currency-chart/


http://tools.currenciesdirect.net/currency-chart/

Example FX Risk: L-T Purchase Contract with Foreign Currency

Problem:• In May 2XX1, when the exchange rate was $1.35 per euro,

Mason ordered parts for next year’s production from Campco. They agreed to a price of 500,000 euros, to be paid when the parts were delivered in one year’s time.

• One year later, the exchange rate was $1.55 per euro.

• What was the actual cost in dollars for Mason when the payment was due?

• If the price had instead been set at $675,000 (which had equivalent value at the time of the agreement), how many euros would Campco have received?


Solution:• Right now, May 2XX1 cost is $1.35 x 500,000 euros = $675,000• With the price set at 500,000 euros, Mason had to pay

($1.55/euro) (500,000 euros) = ___________one year later May 2XX2

• This cost is $100,000 higher than it would have been if the price had been set in dollars.

Conclusion:• Whether the price was set in euros or dollars, one of the parties would

have suffered a substantial loss. Since neither knows which will suffer the loss ahead of time, each has an incentive to hedge.


Example FX Risk: L-T Purchase Contract with Foreign Currency (cont.)

Example FX Risk: Traveling and Exchange Rates

Problem:• Lina was planning a trip to tour Europe for three weeks. The exchange

rate cost when she was planning was $1.32 per euro. She planned on expenses and souvenir costs in Europe to be about €7,000.

• Five months later, when she actually went on her trip, the exchange rate cost had increased to $1.65 per euro.

• What was Lina’s estimated cost in euros equal to in U.S. dollars at the time of planning?

• How many euros did Lina actually end up having once she was on her trip?

• How could Lina have planned for the differences in exchange rate cost?


Solution:• With her costs being in euros, her dollar equivalent cost at

planning is:($1.32/€) × (€7,000) = ________

• On her trip the cost of euro had increased so her final amount was:($9,240) ÷ ($1.65/€) = _________

• Or($9,240) ×[1/($1.65/€)] = ($9,240) × (€.61/$) = €5,600

• Lina ended up having €1,400 less euros once she got to Europe.


Example FX Risk: Traveling and Exchange Rates (cont.)

Conclusion:• Lina could have looked at rates, and current

rate patterns to estimate the exchange rate cost at her time of the trip to ensure that she had enough money for her costs and souvenirs.

• However, this is the risk of traveling overseas, since rates are so volatile.


Example FX Risk: Traveling and Exchange Rates (cont.)

Pricing of FX Rates


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Example FX Pricing: Triangle Arbitrage for Cross-Rates

• The following quotations are available to you for US dollars ($), Canadian Dollars (CD), and Mexican pesos (Peso). You may either buy or sell at the stated rates:– BancOne: $.76/CD– Imperial Bank: 1.40 pesos/CD– Domino Bank: $.55 / peso

• Given this information, is a triangle arbitrage possible?• If so, explain the steps and compute the profit,

assuming you have an initial US $1,000,000 to use.


Example FX Pricing: Triangle Arbitrage for Cross-Rates (cont.)

• Is it possible?• Evaluate


BancOne ImperialBank

DominoBank

$0.761 CD

1.40 pesos1 CD

$0.551 peso

Cross Rates Theoretical Actual

1.40 pesos1 CD

x $0.551 peso

= $0.771 CD

> $0.761 CD

At Bank One

Therefore, BankOne X-rate is too LOW. So want to take $→CD at BankOne→pesos at Imperial Bank→$ at Domino Bank

YES

Example FX Pricing: Triangle Arbitrage for Cross-Rates

Steps in Triangle Arbitrage


Con

vert

$1

mill

. to

CD

s at

Ban

cOne

@

$0.7

6/CD

= $

1 m

ill. /

0.76

= 1

,315

,789

CD

s

Convert 1,315,789 C

Ds to pesos at Im

perial Bank

@ 1.40 peso/C

D =

1,315,789 CD

s x 1.40 =

1,842,105 pesos

Convert 1,842,105 pesos to $s at Domino Bank @ $0.55/peso = 1,842,105 pesos x 0.55 = $1,013,158

1

2

3

BancOne$ → CD

Imperial BankCD → peso

Domino Bankpeso → $

Riskless Arbitrage Profit: $1,013,158- $1,000,000 $ 13,158

Purchasing Power Parity


The theory explaining the change in foreign currencyexchange rates as inflation rates in the countries change.

The PPP theorem states that the change in the exchange rate between two countries’ currencies is proportional to the difference in the inflation rates in the countries

Formula using Direct quote & $ as domestic currency:

The theory explaining the change in foreign currencyexchange rates as inflation rates in the countries change.

The PPP theorem states that the change in the exchange rate between two countries’ currencies is proportional to the difference in the inflation rates in the countries


FC

FCFCUS S

S

1$

1$

Purchasing Power Parity


Formula using Indirect quote & $ as domestic currency:

Formula using Indirect quote & $ as domestic currency:

1$#

1$#

FC

FCUSFC S

S

Fundamental Determinant of FX rates

• The basic fundamental determinant of exchange rates between countries is purchasing power parity, or the relative degrees of inflation among countries

– E.g.: If the U.S. has greater inflation than the European Union, the dollar will ____________ relative to the euro (will take more $s to buy a euro)


Example: PPP

Given the following and based on PPP: S$/£ = $2/£ or S£/$ = 0.50£/$

E(InflationUK )= 4%

E(InflationUS )= 3%

1) Will you expect the dollar to appreciate or depreciate against the pound? By how much (percentage change)? What would be the expected new Spot rate to be, i.e.: S$/£ ?

2) What is expected Forward exchange rate; i.e.: F$/£ as given by PPP?


1) Since expecting inflation is England to be greater than inflation in US, then it should take fewer $s to buy a £ (or more £s to buy a $). The $ should appreciate against the £ by 1%.

Since current S$/£ = $2 /£ then expected new rate should be $1.98/£.

The dollar has appreciated against the pound.


£ eagainst th $ ofon appreciati 1%01.

04.03.

£1$

£1$

£1$

£1$

1$

1$

S

S

S

S

S

S

FC

FCFCUS

Example: PPP (cont.)

£_____/$02.0$2$

02.0$2$

01.

£1$£1$£1$

£1$£1$

SSF

SS

2) What is expected Forward exchange rate; i.e.: F$/1£ as given by PPP?

Conclusion: • If πUS is expected to be > πFC ; then $ will depreciate against the FC (the

FC appreciates against the $)• If πUS is expected to be < πFC ; then $ will appreciate against the FC (the

FC depreciates against the $)


1£$1.9800F

£$1

02.2

02.201.

204.03.

£1$01

£1$£1$

£1$

£1$

1$

1$

£$£$SSF

SS

S

S

S

FC

FCFCUS

Example: PPP (cont.)

Interest Rate Parity


The theory that the domestic interest rate should equal the foreign interest rate minus the expected appreciation of the domestic currency.


The theory that the domestic interest rate should equal the foreign interest rate minus the expected appreciation of the domestic currency.


FC

FCFC

FC

FCUS

S

SF

i

ii

1$

1$1$

1



Formula using Indirect quote & $ as domestic currency:Formula using Indirect quote & $ as domestic currency:

1$#

1$#1$#

1 FC

FCFC

US

USFC

S

SF

i

ii



Rearranging this formula:

Direct quote & $ as domestic currency. Used to find theoretical Forward rates. Helpful with determining arbitrage opportunities.

Indirect quote & $ as domestic currency.

Rearranging this formula:

Direct quote & $ as domestic currency. Used to find theoretical Forward rates. Helpful with determining arbitrage opportunities.

Indirect quote & $ as domestic currency.

FC

USFCFC i

iSF

1

11$1$

US

FCFCFC i

iSF

1

1$$

• Theoretical parity is rarely attained, since it is based on several assumptions– There are no transactions costs for executing an

arbitrage strategy– Investors can borrow and lend at the same rate– There are no tax differences between different

economies– There are no barriers to capital mobility between

economies



Example: Computing Forward Rates Using IRP

Given the following and based on IRP:S$/£ = $2/£ ( S£/$ = .50 £/$ )

iUK = 6%

iUS = 5%• What is the 1-year Forward rate?

Conclusion: • If iUS are expected to be > iFC ; then $ will depreciate against the FC (the FC

appreciates against the $)• If iUS are expected to be < iFC ; then $ will appreciate against the FC (the FC

depreciates against the $)Copyright 2013 by Diane S. Docking 41

£/$

06.1

05.12

1

1

1$

1$

1$1$

FC

FC

FC

USFCFC

F

F

i

iSF

Example: Computing Interest Rates Using IRP

Given the following and based on IRP: S$/£ = $2/£; ( S£/$ = .50 £/$)

F$/£ = $1.98/£; ( F£/$ = .50505 £/$)

iUK = 6%

• What are current interest rates in the US?


%94.40494.

06.06.12

02.

1

£100.2$

£100.2$

£198.1$

06.1

06.

1$

1$1$

US

US

FC

FCFC

FC

FCUS

i

i

S

SF

i

ii

USi

Covered Interest Arbitrage• Covered interest arbitrage activity makes Forward rate

approximately equal to the differential in interest rates between two countries

• Given actual spot and interest rates, compute the “theoretical” Forward rate {E(F$/FC)} using the IRP formula:

• If the “theoretical” forward rate does not equal the “actual” forward rate, covered interest arbitrage is possible

• If the “theoretical” forward rate equals the “actual” forward rate, there are no opportunities for arbitrage


FC

USFCFC i

iSFE

1

11$1$

Covered Interest Arbitrage (cont.)

• Covered interest arbitrage activity creates a relationships between spot rates, interest rates and forward rates.

• Today:– Borrow dollars in US at iUS

– Convert the dollars to the foreign currency (FC) using the spot rate (S)– SELL forward contract for return of FC back into dollars at forward rate (F)– Invest FC in foreign country at iForeign Country

• Later:– Receive FC principal and interest from investment in foreign country– Exercise forward contract and convert FC back to $ at forward rate (F)– Repay US loan principal and interest in dollars

• Could do the reverse - depends• Ideally no profit should exist due to arbitrage forces.


Example: Covered Interest Arbitrage/Parity

• In May 2XX1, the current spot exchange rate (S0) is $1.35/€ and the current 1-year forward rate (F1) is $1.40/€ . Current 1-year interest rates are 4.9% for dollars and 4.3% for euros.

• Explain how one can make an arbitrage profit assuming you either borrow $675,000 or 675,000 euros.

• What must the 1-year Forward FX rate must be to create parity.


• For no-arbitrage opportunity to exist, the 1-yr forward exchange (F1 ) must equal:

• Since the actual F1 of $1.40/€ > the theoretical F1 of $1.35776606/€ , an arbitrage opportunity exists.

• Actual rate is too high, so want to borrow $, convert to euros, invest in euros, then convert back to $ at F1.

• Interest rates in U.S. are too low.Copyright 2013 by Diane S. Docking 46

Solution to Example: Covered Interest Arbitrage/Parity

TFC

TUS

i

iSF

FCFC

1

11$1$ 01

_____________________043.1

049.135.1$ 1

1

1 1$

FCF

Solution to Example: Covered Interest Arbitrage/Parity (cont.)

Do a cash-and-carry strategy.


Today May 2XX1: CFs

Borrow $675,000 in US at iUS = 4.9% for 1-yr.

Convert the $675,000 to €s @ S0 = $1.35/€: $675,000/$1.35 = 500,000 €s

Invest 500,000 €s in foreign country at iFor.Ctry= 4.3% for 1 year.

____________ a 1-yr. forward contract for return of 521,500€sA back into $ at forward rate (F1=$1.40/€)AP+I on investment = 500,000 (1.043)1 = 521,500€s

Solution to Example: Covered Interest Arbitrage/Parity (cont.)

• You made an arbitrage profit of $730,100 – 708,075 = ______________


1 Year later on May 2XX2: CFsReceive 521,500€s P&I from investment in foreign country

Exercise forward contract and convert 521,500€s back to $s @ (F1=$1.40/€) 521,500€ x $1.40/€ = $730,100

Repay US loan P&I = $675,000 x (1.049)1 = $708,075

Arbitrage profit

9-49Copyright 2013 by Diane S.

Docking

Foreign Exchange Risk

• Firms can hedge their foreign exchange exposure either on or off the balance sheet

• On-balance-sheet hedging involves matching foreign assets and liabilities– as foreign exchange rates move any decreases in foreign asset

values are offset by decreases in foreign liability values (and vice versa)

• Off-balance-sheet hedging involves the use of forward contracts– forward contracts are entered into (at t = 0) that specify

exchange rates to be used in the future (i.e., no matter what the prevailing spot exchange rates are at t = 1)

• Firms can hedge their foreign exchange exposure either on or off the balance sheet

• On-balance-sheet hedging involves matching foreign assets and liabilities– as foreign exchange rates move any decreases in foreign asset

values are offset by decreases in foreign liability values (and vice versa)

• Off-balance-sheet hedging involves the use of forward contracts– forward contracts are entered into (at t = 0) that specify

exchange rates to be used in the future (i.e., no matter what the prevailing spot exchange rates are at t = 1)

The Foreign Exchange Market Copyright 2013 by Diane S. Docking1 KM.

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