International Macroeconommics - Chapter 2: Introduction to...

Exchange Rate EssentialsForeign Exchange Market

Arbitrage and Spot Exchange RateNo Arbitrage Conditions

International MacroeconommicsChapter 2: Introduction to Exchange Rates and Foreign

Exchange Market

Instructor: Yuan Liu

Department of Economics, UCDavis

Instructor: Yuan Liu CH2



Outline

1 Exchange Rate Essentials

2 Foreign Exchange Market

3 Arbitrage and Spot Exchange Rate

4 No Arbitrage ConditionsCIPUIP




Outline








Defining the Exchange Rate

An Exchange Rate (E) is the Price of one currency in terms ofanother.

Conventional WayUnits of home currency per foreign currencyUS is the home country, E: $/€(American Term)Europe is the home country, E: €/$ (European Term)E$/euro = 1

Eeuro/$

E$/euro = 1.33Eeuro/$ = 0.75





Compare goods price across country:

NewYork Hongkong LondonPrice of a tux $4000 HK$ 30,000 £2,500Exchange-rate E$/£ = 1.53 E$/HK$ = 0.1

Price in £ £2614 £3000 £2500





Compare goods price across country:

NewYork Hongkong LondonPrice of a tux $4000 HK$30, 000 £2, 500Exchange-rate E$/£ = 1.63 E$/HK$ = 0.1

Price in £ £2454 £3000 $2500




Appreciation and Depreciation

E$/£ :1.53→ 1.63

It takes more $ to buy one unit £.£appreciates relative to $, $ depreciates relative to £.Price of Tux in N.Y: $4000.£2614 → £2454.





E$/£ :1.53→ 1.63It takes more $ to buy one unit £.

£appreciates relative to $, $ depreciates relative to £.Price of Tux in N.Y: $4000.£2614 → £2454.





E$/£ :1.53→ 1.63It takes more $ to buy one unit £.£appreciates relative to $, $ depreciates relative to £.

Price of Tux in N.Y: $4000.£2614 → £2454.





E$/£ :1.53→ 1.63It takes more $ to buy one unit £.£appreciates relative to $, $ depreciates relative to £.Price of Tux in N.Y: $4000.£2614 → £2454.





Appreciation: increase in the value of a currency relativeto another.Depreciation: decrease in the value of a currency relativeto another.Given exchange rtae is expressed as units of Homecurrency per foreign currency.

Exchange rate increases: home currency depreciationExchange rate decreases: home currency appreciation




Multilateral Exchange Rates

According to bilateral exchange rate, dollar can beappreciating against one currency at the same timedepreciating against another currency.

1

1Aug 3rd, 2013, The EconomistInstructor: Yuan Liu CH2



Multilateral Exchange Rates

Nominal Effective Exchange Rate: a weighted average ofseveral bilateral exchange rates, usually using trade sharesas weights to reflect the relative importance of each ofthe bilateral pairs involved.Example: Suppose US only trade with Britian and EU.

∆E$/£ = −10%,trade share of UK in US trade is 40%.∆E$/euro = 30%, trade share of EU in US trade is 60%.−10%× 40% + 30%× 60% = +0.14




Outline








Features

Foreign Exchange Market (FOREX) is a collection of privateindividuals, corporations, and some public institutions that buyand sell currencies.

Volume is enormous:2010 $4 trilion per day. US GDP?Highly integrated internationally:there is not a moment in the day when foreign exchangeis not being traded somewhere in the world.Concentrated in major FOREX centers:London, New York, Tokyo: half of the tradeOther important centers?




Actors

Private ActorsCommercial Banks

interbank trading is 3/4 of all FOREX transactionsglobally.Highly concentrated in a few international banks:Deutsche Bank, Citigroup, Barclay.

CorporationsNon-bank Financial Institutions

GovernmentCapital ContralIntervention




Spot exchange rate: the exchange rate for currencytransactions that takes place immediately.Derivatives

Forward: fix the price today, but deliver currency in thefuture.





US#Bestbuy#

Japan#Sony#

TV#(1#month#later)#

Yen#(1#month#later)#

FOREX#

Forward#contract# If#$depreciaFon/#¥appreciaFon#1#month#later,#bestbuy#pay#more.#

To#avoid#the#risk,#buy#forward,#fix#the#exchange#rate#today##actually#delivery#of#¥#and#payment#happens#1#month#later##





Swap: combination of a spot contract and a forwardcontract.





US#Bestbuy#

Japan###Receive#Yen#now##

Yen#(1#month#later)#

FOREX#

swap#contract# Don’t#want#hang#on#to#Yen,#need#use#$#

A#swap#contract#include#a#spot#sell#of#¥#for#$,##And#a#forward#buy#of#¥#using#$#





Futures: standardized forward contract, can be tradedon an organized futures exchange and thus delivery ofcurrency is not necessary.





Options: An option provides the buyer with the right tobuy (call) or sell (put) a currency in exchange foranother at a prespecitiedexchange rate at a future date.




Outline








Arbitrage: buy low and sell high.If arbitrage opportunity exists, market is out ofequilibrium.If arbitrage opportunity not exists, market is inequilibrium because it satisfies no-arbitrage condistion.highly integrated market, arbitrage opportunity will beimmediately spotted and exploited by traders. marketgoes back to equilibrium immediately.




E N.Y .$/£ = 2, E London

$/£ = 1.8.

buy £ in London, sell them in N.Y.in the FOREX market, this transaction:increases demand of £ in London, E London

$/£ ↑increases supply of £ in N.Y., E N.Y .

$/£ ↓until E N.Y .

$/£ = E London$/£ no arbitrage opportunity, market

back to equilibrium.





$/£ = 1.8.buy £ in London, sell them in N.Y.

in the FOREX market, this transaction:increases demand of £ in London, E London









$/£ = 1.8.buy £ in London, sell them in N.Y.in the FOREX market, this transaction:increases demand of £ in London, E London


$/£ ↓

until E N.Y .$/£ = E London

$/£ no arbitrage opportunity, marketback to equilibrium.





$/£ = 1.8.buy £ in London, sell them in N.Y.in the FOREX market, this transaction:increases demand of £ in London, E London








CIPUIP

Outline








CIPUIP

example

has $100 can deposit in US (i$ = 2%) or UK (i£ = 8%).option1: deposit in US, earn 2% interests.option2: convert $100 to £, and deposit £in UK, earn 8%

interests. 1 year later, convert £back to $.




CIPUIP

example


interests. 1 year later, convert £back to $.E$/£ = 1.8 and F$/£ = 1.7




CIPUIP

No Arbitrage Condition: CIP

E$/£ = 1.8 $100

E$/£= £55.556

F$/£ = 1.7

i$ = 2% i£ = 8%

£55.556(1 + i£) = £60

$100(1 + i$) = $102

£60F$/£ = $102

$100




CIPUIP

No Arbitrage Condition: CIP

Gross rate of return of $ deposite: 1 + i$.Gross rate of return of £deposite: F$/£

E$/£(1 + i£).

Covered Interest Parity: 1 + i$ =F$/£E$/£

(1 + i£)

In equilibrium:Total Gross Return on $ Deposit=Total Gross Return on£Deposit




CIPUIP

What Determines the Forward Rate?

CIP: 1 + i$ =F$/£E$/£

(1 + i£)

Rearrange CIP: F$/£ = E$/£1+i$1+i£

i$, i£, E$/£ →F$/£In practice, this is exactly how the price of a forward contractis set.? →i$, i£, E$/£




CIPUIP

Equilibrating ProcessE$/£ = 1.8 $100

E$/£= £55.556

i$ = 2% i£ = 8%

£55.556(1 + i£) = £60

$100(1 + i$) = $102

$100

F$/£ = 1.8£60F$/£ = $108

Arbitrage opportunity: 1 + i$ <F$/£E$/£

(1 + i£)

Demand of £increases in spot market, E$/£ ↑Supply of £increases in forward market, F$/£ ↓Until 1 + i$ =

F$/£E$/£

(1 + i£). Back to equilibrium.Instructor: Yuan Liu CH2



CIPUIP

Test of CIP




CIPUIP

Example


interests. 1 year later, convert £back to $.E$/£ = 1.8 and E e

$/£ = 1.7




CIPUIP

No Arbitrage Condition: UIP

E$/£ = 1.8 $100

E$/£= £55.556

i$ = 2% i£ = 8%

£55.556(1 + i£) = £60

$100(1 + i$) = $102

£60F$/£ = $102

$100

Ee$/£ = 1.7




CIPUIP

No Arbitrage Condition: UIP

Gross rate of return of $ deposite: 1 + i$.Expected gross rate of return of £deposite: E e

$/£E$/£

(1 + i£).

Uncovered Interest Parity: 1 + i$ =E e

$/£E$/£

(1 + i£)

In equilibrium:Total Gross Return on $ Deposit=Expected Total GrossReturn on £Deposit




CIPUIP

What Determines the Spot Rate?

UIP: 1 + i$ =E e

$/£E$/£

(1 + i£)

Rearrange CIP: E$/£ = E e$/£

1+i£1+i$

i$, i£, E e$/£ →E$/£

? →i$, i£, E e$/£




CIPUIP

UIP: A Useful Approximationi$ = i£ +

∆E e$/£

E$/£

Net rate of return on $ deposit=Net Rate of return on£deposit.Return on £deposit include the £interest rate and theexpected appreciation of £against $.i$ − i£ =

∆E e$/£

E$/£

Interest Rate Differential = Expected percentage changeof exchange rate.How much higher $ interest rate is than £interest rate =Expected depreciation of $ against £.How much lower $ interest rate is than £interest rate =Expected appreciation of $ against £.




CIPUIP

Test of UIP

i$ = i£ +∆E e

$/£

E$/£?

Hard to measure expectations.Maybe errors with the measure of expectations.Risk premium.Expected return is risky. Investors ask for a premiumassociate with the risk that they undertake.




CIPUIP

Test of UIP




CIPUIP

Short-run Exchange Rate Determination


Date post:	11-May-2020
Category:	Documents
Upload:	others
View:	3 times
Download:	0 times

International Macroeconommics - Chapter 2: Introduction to...

Documents