International Economics #7 The exchange rate · 1. The foreign-exchange market 2. The monetary...

1. The foreign-exchange market2. The monetary approach and purchasing-

International Economics #7The exchange rate

1

2. The monetary approach and purchasing-power parity

3. Interest-rate parities4. Exchange-rate determination

1. The foreign-exchange market

2Bénassy-Quéré & Coeuré

International Economics 2009-2010

What is the foreign-exchange market?

• The market where currencies can be traded– Only convertible currencies

• A global, almost continuousmarket– Very large turnover: USD 3,200 Bn per day

interbank– Mostly interbank: only 17% of turnover involves non-financial agents– Manual transactions only marginal

• Three kinds of transactions:– Spot: delivery within 24 hours– Forward: delivery at a future date at a price set in advance– Swaps: two transactions of opposite directions at different dates; rates set in advance

• A concentrated market– Few currencies (mainly US dollar, euro, yen)– Few marketplaces (mainly London. New York)– Few banks (Ex.: in New York, 10 banks account for 75% of transactions)



A few figures (April 2007)

Transactions quotidiennes sur le marché des changes

Daily transactions: USD 3,210Bn/day = 15 × World GDP ; 48 × World trade

Daily transactions on the foreign-exchange market

In April 2007

× World GDP ; 48 × World trade• Top pairs: EUR/USD 27% ; JPY/USD

13% ; GBP/USD 12%• Top pivotal currencies: USD: 86% of

transactions, EUR: 37%• Top marketplaces: London 34%; New

York 17%

4

Source: Bank of International Settlements, Triennial Survey of Foreign Exchange and Derivatives Markets, December 2007.

Bénassy-Quéré & CoeuréInternational Economics 2009-2010

Why so many transactions?

• A decentralized market (no auctioneer, no consolidation of transactions except on electronic brokerage platforms)

• Arbitrage to take profit from spreads across marketplaces or products• Speculation(gambling): mostly intra-day

– Covered position, ex.assets in USD = liabilities in US;≠– Uncovered position, ex.assets in USD ≠ liabilities in USD;

• Long position, ex.assets in USD > liabilities in USD;• Short position, ex.assets in USD < liabilities in USD.

• Hedging: transactions aimed at offsetting foreign exchange risk– Ex.Airbus is to receive $60M in 6 months. It can cover its long position by

transacting with a bank:• Selling $60M on the forward market, or• Swapping its position (buying $60M today and selling $60M in six months), or• Buying a put option for $60M

– Unless the bank has an underlying FX position, it will hedge itself or sell its exposure on Airbus on the market

– Etc. (‘hot potato’ chain of transactions)5


International currencies: theory

Function Private sector Public sector

Means of payment Vehicle Intervention

6

Adapted from Paul Krugman, “The International Role of the Dollar: Theory and Prospects,” 1991.

Unit of account Denomination Anchor

Store of value Investment Reserve


International currencies: factsFunction Dollar Yen Euro Other

Trade with non-€ partners, 01 (1)

- Exports- Imports

--

--

45.444.4

--

Forex turnover, April 01 (2) 90.3 22.7 37.6 49.4

Outstanding amount of international bonds (extensive definition). end 99 (3)

Outstanding amount of international bonds (restrictive definition). end 99 (4)

45.9

48.9

18.7

16.0

21.2

20.7

14.1

14.4

Outstanding amount of cross-border bank loans (extensive definition). end 08 (5)

59.5 11.6 14.0 14.9

Function Dollar Yen Euro Other

Trade with non-€ partners, 07 (1)

- Exports- Imports

--

--

56.946.7

--

Forex turnover, April 07 (2) 86.3 16.5 37.0 60.2

Outstanding amount of international bonds (extensive definition). end 08 (3)

Outstanding amount of international bonds (restrictive definition). end 08 (4)

39.8

44.7

14.2

6.8

29.5

32.2

16.6

16.3

Outstanding amount of cross-border bank loans (extensive definition). end 08 (5)

51.6

54.3

3.2

5.9

22.2

17.6

23.0

22.21999

2008

7

Source: A. Bénassy-Quéré and B. Cœuré , Economie de l’euro, 2nd edition, 2010.

Notes: (1) Unweighted average for eight countries; (2) Out of 200%; (3) Including domestic issues (e.g. bonds in Euro area); (4) Excluding domestic emissions; (5) Including loans/deposits to/from banks located in the USA. the UK. Switzerland and the Eurozone and denominated in their own currencies; excluding interbank loans/deposits; (6) ) Excluding loans/deposits to/from banks located in the USA. the UK. Switzerland and the Eurozoneand denominated in their own currencies; excluding interbank loans/deposits; (7) Excluding unallocated reserves; (9) Share of currencies that are hardly or softly pegged. excluding the Euro area. Sources: BIS, ECB, IMF.

Outstanding amount of cross-border bank loans (restrictive definition). end 99 (6)

61.1 7.8 7.4 23.7

Cross-border bank deposits (extensive definition), end 99 (5)

Cross-border bank deposits (restrictive definition). end 99 (6)

60.0

66.5

4.7

6.2

20.8

13.9

14.6

13.4

Forex reserves. end 99(7) 71.0 6.4 17.9 4.7

Forex pegs, June 03(9) 31.3 0.0 13.6 -

Outstanding amount of cross-border bank loans (restrictive definition). end 08 (6)

54.3 5.9 17.6 22.2

Cross-border bank deposits (extensive definition), end 08 (5)

Cross-border bank deposits (restrictive definition). end 08 (6)

59.3

52.3

2.1

3.2

22.4

21.7

16.2

22.8

Forex reserves. end 08(7) 64.0 3.3 26.5 6.2

Forex pegs, April 08 (9) 45.4 0.0 18.6 -

1999

2008

Exchange rate: definitions

Different exchange rates:

• 1€ = x$ versus 1$ = x€

• Spot/ forward

Euro/dollar, 1970-2009

iPSQ =• Nominal / real

• Bilateral / effective

8

j

iijij P

PSQ =

∏=j

ijijQQ

α

Sources: Banque de France and IMF.


A reactive and volatile price

The euro/dollar on November 3rd 2006

1,275

1,28

Revision of non-farm payrolls

9

1,265

1,27

11:

00:0

0

11:0

8:00

11:1

6:0

0

11:2

4:0

0

11:

32:0

0

11:

40:0

0

11:4

8:00

11:5

6:0

0

12:0

4:0

0

12:

12:0

0

12:

20:

00

12:2

8:0

0

12:3

6:0

0

12:

44:0

0

12:

52:0

0

13:0

0:0

0

13:0

8:0

0

13:

16:0

0

13:

24:0

0

13:3

2:00

13:4

0:0

0

13:4

8:00

13:

56:0

0

14:0

4:00

14:1

2:0

0

14:2

0:00

14:

28:0

0

14:3

6:00

14:4

4:00

14:5

2:0

0

15:0

0:00

15:

08:

00

15:1

6:00

15:2

4:0

0

15:3

2:00

15:

40:0

0

15:4

8:00

15:5

6:0

0

Source: Reuters

Note: At 1:30 PM GMT, the U.S. Bureau of Labor Statistics disclosed an upward revision of Augustand September non-farm payroll increases from 188,000 to 230,000 and from 51,000 to 148,000.


2. The monetary approach and purchasing power paritypurchasing power parity



Money and external adjustment in a fixed exchange-rate regime

The deflation of the 1930sDavid Hume, 1711-1776

David Hume,Political Discourses, 1752

11

Trade deficit

Fall in reserves

Money contraction

Deflation

Domestic price > World price


Purchasing power parity

Gustav Cassel, “Abnormal Deviations in

The Brazilian currency, 1991-1994Gustav Cassel, 1866-1945

Gustav Cassel, “Abnormal Deviations in International Exchanges,” The Economic

Journal, 1918

12

Fall in money demand

Deflation

Domestic price> World price

PPP

Source: IMF.


The monetary approach of the balance of payments

(Frenkel, 1976; Mussa, 1976; Bilson, 1978)

The model

p = m ; m = r ; b = β(p*-p-s), β > 0

Fixed exchange rate: s = 0, dr = b

dp= dm = dr = b = β(p*-p) > 0 as long as p < p*

p: domestic price

p*: world price

s: nominal exchange rate dp= dm = dr = b = β(p*-p) > 0 as long as p < p*

Long-run equilibrium: p* = p

Flexible exchange rate: dr = 0

dp = dm= dr = 0

b = dr = 0 ⇒ s= p* - p

Quicker adjustment than with a fixed exchange rate

s: nominal exchange rate

m: money

r: official reserves

b: current account



PPP in practice

Big Mac index (July 2009)Nominal and real effective exchange rate of the euro

Country Big Mac price in

USD

ImpliedPPP

againstUSD

Under (-)/over (+) valuationagainst USD

USA 3.57 - -

Eurozone 4.62 1.08 +29%

14

Source : The Economist, July 18th 2009.

Against 52 countries, CPI-deflated. Source: ECB.

4.62 1.08 +29%

Japan 3.46 89.6 -3%

UK 3.69 1.56 +3%

Switz. 5.98 1.82 +68%

China 1.83 3.50 -49%


PPP as a long-run relationship

Unit-root test:

H0: ρ = 0 against H1: ρ < 0

• H0 rejected → the real exchange rate does not follow a random walk but reverts to its mean value after a shock.

t

p

kkttt QQQ ερ +∆+=∆ ∑

=−−

11 lnlnln

• Half-life of adjustment = date T when half of the adjustment is completed

Ex. ln Qt = (1+ρ)ln Qt-1 = (1+ρ)2ln Qt-2 =… = (1+ρ)Τln Qt-T

ln QT =(1+ρ)Τ ln Q0

(1+ρ)T = ½ ⇒ T = - ln 2 / ln (1+ρ)Empirically, ρ ≈ -0.15 i.e. T≈ 4 to 5 years for advanced economies



Ln Q0

Ln QT

Ln Qt

T t

Developing economies: the Balassa-Samuelson effect (1964)

Intuition

Wages < world levelProductivity <

world level

Tradables

Law of one price

General price level < world level



Price < world level

world level

Productivity = world level

Non-tradablesUndervalued currency

relative to PPP

Productivity catch-up

(tradables)Wage increase

Rise in non-tradable prices

Real exchange-rate appreciation

Dynamics

Developing economies: the Balassa-Samuelson effect (1964)

The model

• Two sectors:– Tradables: YT = πT LT; PT = PT*/S (law of

one price) ;

– Non-tradables: YN = πN LN; PN. PN*

– Y . L . π . P = production. employment.

• Tradables

• Non-tradables

***; TTTT PWPW ππ ==

*

**;

NN

NN

WP

WP

ππ==

– Y i. Li. πi. Pi = production. employment. productivity. price (i=T.N)

• Nominal exchange rate S

• Inter-industry labor mobility– Same wage in the two sectors. W

• Perfect competition– Price = marginal cost → Pi = W/πi

• Same abroad (*)

17

NN ππHence:

*

***;

N

TTN

N

TTN

PP

PP

ππ

ππ ==

• Law of one price

*

*

* /

/

/ NN

TT

N

N

SP

P

ππππ=1

/*=

SP

P

T

T and


The Balassa-Samuelson effect (cont’d)

Real exchange rate:

−−

−−=

*

*

*

*

)1(N

N

N

N

T

T

T

T dddd

Q

dQ

ππ

ππ

ππ

ππα

( ) ( )( ) ( )

αα

αα

αα

ππππ

−−

−

−

=

===

1

*

*1

*1**

1

* /

/

//// NN

TT

N

N

NT

NT

SP

P

SPSP

PP

SP

PQ

18

Developing country:

πT < πT*

πN ≈ πN*Q < 1

*

*

T

T

T

T dd

ππ

ππ >

0*

*

≈≈N

N

N

N dd

ππ

ππ

0>Q

dQ Real appreciation due to rise in non-traded

prices

Undervaluedcurrency

compared to PPP


The Balassa-Samuelson effect in practice

PPP GDP per capita and real exchange rates in 2006

China: insufficient appreciation against the US dollar

19

Source: IMF, World Economic Outlook, Sept. 2008. Source: Cheung, Chinn and Fuji (2007).


3. Interest-rate parities



Covered interest parity

How to invest X euro over n years without any foreign-exchange risk?

Two strategies:

If one strategy dominates the other, there is a window for making riskless profit

At market equilibrium, both strategies should be equivalent:

Fn/S = (1+i*)n/(1+i)n or in log,Two strategies:1) Invest in euro at domestic interest rate i

– Value in n years: X (1+i)n euro2) Convert X in dollars at spot rate S,

invest on US market at US interest rate i* and sell the proceeds on the forward market at rate Fn

– Value in one year: X (1+i*)n Sdollar– Once converted back to euro:

X (1+i*) n S / Fn euro

Covered interest rate parity

If n = 1, then:

21

Fn/S = (1+i*) /(1+i) or in log,

i* - i = (1/n)(f – s)

F1/S = (1+i*)/(1+i) or in log,

i* - i = f – s


Covered interest parity (cont’d)

• Valid if:– Free capital movements– Negligible transaction costs– No country risk

• January 8th 2008– Euro/yen

• 161.1 spot• 155.7 1-year forward

22

– No country risk • 155.7 1-year forward

– 1-year money market interest rate• i = 4.60% in euro• i* = 0.91% in yen

– (1+i)/(1+i*) = 1.03657– S/F = 1.03468

0.18% spread, explained by transaction cost


Assuming risk neutrality,a higher return under the second strategy induces investors to borrow in euro and invest in dollar, which raises the spot price of the dollar against the euro until both strategies yield the same expected return:

Uncovered interest parity

Again, consider investing X euros during nyears, but assume that the investor is willing to bear foreign exchange risk

Two strategies:1) Invest in euro at domestic interest rate i

(1+i)n = (1+i*)n S/Sne or in log,

i - i* = (1/n)(s - sne)

Uncovered interest rate parity

If n = 1, then:

23

1) Invest in euro at domestic interest rate i– Value in n years: X (1+i)n euro

2) Convert X in dollars at the spot rate S,invest on US market at US interest rate i* and convert the proceeds in n years at the expectedspot rate Sn

e

– Value in n years: X (1+i*)n Sdollar– Expectedvalue in euro:

X (1+i*)n S/Sneeuro

i - i* = (1/n)(s - sne)

(1+i) = (1+i*) S/S1e or in log,

i - i* = s – se


Assume n = 1:• Covered interest parity: Arbitrage condition (no risk)

• Uncovered interest parity: Speculation condition (forex risk)

Because Se cannot be observed, UIP cannot be tested directly

Indirect test• If both CIP and UIP apply, then: F = Se: the forward rate is an unbiased proxy of the

Empirical evidence

i

i

S

F

++=

1

*1

i

i

S

Se

++=

1

*1

• If both CIP and UIP apply, then: F = S : the forward rate is an unbiased proxy of the expected rate

• Assuming rational expectations, Se = E(S) (mathematical expectation).• Under CIP, UIP and rational expectations, we thus have: F = E(S): the forward rate is an

unbiased predictor of the future spot rate, which at each time t writes:St = Ft-1.t + ut with Et-1(ut) = 0

Empirical test st - st-1 = a + b (ft-1.t - st-1) + ut Empirical result: b < 0 !

Possible explanations: variable risk premium; non-rational expectations; ‘peso problem’; market inefficiency



Implications for exchange-rate dynamics

• Flexible exchange rate:

The spot exchange rate reflects market expectations of monetary policies and the long-run value of the exchange rate;

If i is expected to fall relative to i* by 1 percentage point during 3 years, then the exchange rate immediately depreciates by 3% relative to its long-run value, i.e. the exchange rate is more volatile than the interest-rate differential

∑∞

=++∞++ −+==−+=

0

*,

*1, )(...)(

k

ekt

ekt

etttt

ettt iisiiss

25

exchange rate is more volatile than the interest-rate differential

• Fixed exchange rate:

Suppose the exchange rate is expected to depreciate by 10% within 1 month. To maintain the peg. monetary authorities must raise the interest rate by 120% (=10%/nwith n=1/12). Defending a peg can be very costly … and market operators know it

Ex.Sweden, 1992.

( )te

nttntnt ssn

ii −−= +,*,,

1


4. Exchange-rate determination



Simplified BoP equilibriumSmall economy under free float

Net financial inflows ∆Fin - ∆out > 0

Financial outflows

Financial inflows∆Fin

ExportsX

ImportsM

Current account balanceB = X-M < 0

27

Note: the capital account is neglected.

Financial outflows∆Fout


The portfolio-choice model(Branson, Halttunen and Masson, 1979)

Two countries, two currencies(euro, dollar)• Domestic country: net foreign asset position ΩΩΩΩ = A + F/S (in euro)

A: net assets in the domestic currency (in euro)

F: net assets in the foreign currency (in dollar)

S: number of dollars in one euro (rises when the euro appreciates).

• Foreign country: ΩΩΩΩ* = A*/S + F* (in euro)A*: net assets in the domestic currency (in dollar)

F*:net assets in the foreign currency (in euro)

• Two-country model: ΩΩΩΩ + ΩΩΩΩ* = 0Euro market equilibrium: A = -F*

Dollar market equilibrium: A* = -F

Hence: Ω = -F* + F/S = -Ω*

• Small-economy assumption: the domestic currency (the euro) is not used internationally: A = -F* = 0



Assumptions• Domestic real wealth:

D Gross wealth in the domestic currency

F/S Net assets in foreign currency

P Consumer price index

f = F/PSW

• Household’s utility function: u(w)with w = ln W u’>0, u’’<0

P

SFDW

/+=

• Household’s utility function: u(w)with w = ln W u’>0, u’’<0

Risk aversion:

• Only two sources of risk: exchange rate, domestic price

29

0/

²/² >∂∂∂∂−=wu

wua

idtD

dD =

dtiF

dF*=

SSS dzdtmS

dS σ+= E(dzS) = E(dzP) = 0

with: V(dzS) = V(dzP) = dt

‘Wiener process’PPP dzdtmP

dP σ+=


Solving the model

• f is chosen so as to maximize the variation of expected utility:

• Order-two expansion:

• Hence:

22

2

2

1)()( dw

w

udw

w

uwudwwu

∂∂+

∂∂+=+

( ) ( )221

)( dwEu

dwEu

duE∂+∂=

dt

EduMax

f

• Hence:

• Normalize by ∂u/∂w around initial wealth. The program simplifies as:

30

( ) ( )222

1)( dwE

w

udwE

w

uduE

∂∂+

∂∂=

dt

Vdwa

dt

Edw

dt

EduMax

f 2−=


• Differentiate domestic wealth:

22

)/(

P

dPSFD

PS

FdS

SP

dF

P

dDdW

+−−+=P

dP

S

dSf

F

dFf

D

dDf

W

dWdw −−+−== )1(

Solving the model (cont’d)

• Introduce return and exchange-rate processes:

• Which yields the expectation and the variance of wealth variation:

31

[ ] PPSSPS dzdzfdtmfmfiifdw σσ −−−−+−= *)1(

)*( imifmidt

EdwSP −−+−= SPPS ff

dt

Vdw σσσ 2222 ++=


• FOC:

• mS is the expected exchange-rate variation:

• Denotef0 = - σSP/σS² (‘share of minimum risk’) yields:

( ) ⇒=+−−−=∂∂

0)*( 2SPSS faimi

f

u σσ 22

*

S

S

S

SP

a

imif

σσσ −−+−=

sssdt

EdS

Sm ee

S −=∆== 1

Model solution

0 SP S

• Balance of payment equilibrium:fPW= Ω. Replacingf by its value:

32

20

*

S

a

a

isiff

σ−∆−+=

Ω−+∆−=PW

fasii Se

02* σ

Risk premium

−Ω+−+= 02*)( f

PWaiiss S

e σor


If a = 0, UIP holds.

Application to the euro/dollar

33Sources: ECB and US Bureau of Economic Analysis.

1999 2000 2001 2002 2003 2004 2005 2006 2007

EUR/USD (USD for 1 EUR) 1.07 0.92 0.89 0.95 1.13 1.24 1.24 1.26 1.37

US current account. USD bn -299.8 -415.2 -389.0 -472.4 -527.5 -665.3 -791.5 -869.1 -731.3

Euro area current account. EUR bn -23.9 -88.8 -22.1 57.0 32.4 55.6 18.1 -1.3 26.6

Net FDI flows from the Euro area to the United

States. USD bn62.3 126.2 2.2 -41.0 -10.0 -67.0 -44.4 40.2 -21.1

3-month interest-rate differential (EUR-USD) -2.5 % -2.1 % +0.5 % +1.2 % +1.1% +0.5% -1.4% -2.1% -1.0%


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