International Parity Conditions

(or chapter 4)

2

Agenda

• What is PPP & law of one price?

• What is exchange rate pass-through?

• How do interest rates & exchange rates link?

• Interest rate parity?

• What is covered interest arbitrage?

• What is uncovered interest arbitrage?

3

Prices and Exchange Rates

Law of one price: product’s price same in all markets

P$ S = P¥

where spot exchange rate is S, yen per dollar.

P

PS

¥

$

4

Purchasing Power Parity & Law of One Price

Absolute purchasing power parity: spot exchange rate is determined by relative prices of

similar basket of goods.

Relative purchasing power parity: Relative change in prices b/n countries determines

change in forex rate.

5

Absolute PPP: Big Mac Index

Economist’s Big Mac PPP:• Big Mac in China costs Yuan 9.90.

• Big Mac in US costs $2.71.

• Implied PPP exchange rate

Yuan3.7/$ $2.71

Yuan9.90

6

$Sfr2.4803/ $2.54

Sfr6.30

Economist,

4/ 2003

7

Relative PPP

% change spot rate foreign currency US$/ yen

InfJAPAN- InfUS

2

4

-5

-4

-1

-3 -1-4 -2 2 41 3 5

3

1

-2

-3

-6 6

PPP line

P

8

But:

PPP is not very accurate predictor…• Why?

PPP holds well over very long term… PPP holds better for countries w/ high inflation &

underdeveloped capital markets…• Why?

9

Is forex under-/over- valued? Use forex indices: trade-weighted bilateral exchange

rates b/n the home country & trading partners

Nominal exchange rate index : use actual exchange rates.

Real effective exchange rate index indicates how the weighted average purchasing power of the currency has changed relative to some arbitrarily selected base period.

FC

$$N

$R C

C x E E

10

Q:

• Can you tell when a currency is overvalued?

• Why the real exchange rate deviates from 100?

11

0

20

40

60

80

100

120

140

160

180

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999

United States Japan

United States & Japan (1995 = 100)

Real Effective Exchange Rate Indices

12

Exchange Rate Pass-Through

Pass-through: change in prices of imported/exported goods when exchange rate changes

• BMW made in Germany cost @ spot rate US$ 35,000.

• where P$ is the price in US$, P€ is price in euros, S is spot rate

• Euro appreciates by 20%. But BMW is now only $40,000.

• Pass-through:

• Degree of pass-through: 14.29 % / 20 % = 0.71 or 71 %

S x PP BMW$BMW € €/$

14.29%or ,1429.1000,35$

000,40$

P

P$

1 BMW,

$2 BMW,

13

Interest Rates & Exchange Rates? What is a fair nominal interest rate?

– Well, can ask a banker … or read Irvin Fisher…

• Fisher Effect: nominal interest rates in each country are equal to the required real rate of return plus compensation for expected inflation.

i = r + + r

• i is nominal rate, r is real rate, is expected rate of inflation.

• FE good for short maturity bonds, NOT long maturity ones.– Why?

14

International Fisher effect International Fisher effect (Fisher-open):

spot exchange rate change equals opposite of interest rate differential.

where S is indirect quote. Direct Quotes: US$/ Foreign Currency. Indirect Quotes: Foreign Currency / US$. Fisher-open not precise in short-term.

• Why?

Should include forex risk premium.

i i 100 x S

S S $

2

21 FC

15

Forward Rate Forward Rate

• A forward rate: exchange rate quoted today for settlement @ future date

36090

x i 1

36090

x i 1

x S F$

FC

FC/$FC/$90

16

Forward Rate Spot rate SF 1.48/$ 90-day euro Swiss franc deposit rate 4% p.a. 90-day euro-dollar deposit rate 8% p.a.

$Sfr1.4655/ 1.02

1.01 x SF1.48

360

90 x 0.08 1

360

90 x 0.04 1

SF1.48x SF/$90F

17

Premium or discount? Forward premium or discount : % difference b/n spot &

forward rates in annual percentage terms.• For indirect quotes (FC per home currency, FC/$) then

• Swiss franc sells forward @ premium 3.96% p. a.

(takes 3.96% more US$ to get franc at 90-day forward rate)

• For direct quotes ($/FC), use (F-S)/S.

100 x days

360 x

Foward

Foward -Spot f FC

p.a. 3.96% 100 x 90

360 x

SF1.4655

SF1.4655 - SF1.48 f SF

18

Currency Yield Curve & Forwards

Eurodollaryield curve

Euro yield curve

Months

Interestyield

2 41 3 5 6

1.0 %

3.0 %

4.0 %

5.0 %

6.0 %

2.0 %

Forward premium onlow interest rate currrency

19

Interest Rate Parity (IRP)

Interest rate parity:difference in national interest rates for securities of similar risk & maturity should be equal to opposite of forward rate discount/ premium for foreign currency.

or

US$

FC

FC/US$

FC/US$

i1

i1

S

F

FC/US$

FCFC/US$US$

F

1i1S i1

20

90 daysS = SF 1.4800/$

SF 1,480,000

Dollar money market

$1,000,000 $1,020,000 1.02

Start End

i $ = 8 % per annum(2 % 90 days)

Swiss franc money market

SF 1,494,800 1.01

i SF = 4 % per annum(1 % 90 days)

Interest Rate Parity (IRP)

F90 = SF 1.4655/$

$1,019,993

21

Covered Interest Arbitrage (CIA)

Because spot & forward markets are not in equilibrium, arbitrage exists.

Covered interest arbitrage (CIA): invests in currency that offers higher return on covered basis.

22

180 daysS =¥ 106.00/$

¥ 106,000,000

Eurodollar rate = 8.00 % per annum

Dollar money market

$1,000,000 $1,040,000 1.04

Start End

Yen money market

¥ 108,120,000 1.02

Euroyen rate = 4.00 % per annum

Covered Interest Arbitrage (CIA)

F180 = ¥ 103.50/$

ArbitragePotential$1,044,638

23

Uncovered Interest Arbitrage (UIA)

Uncovered interest arbitrage (UIA): investors borrow in currencies w/ low interest rates & convert proceeds into currencies w/ high interest rates.

“Uncovered” because investor does not sell the currency forward.

24

Uncovered Interest Arbitrage (UIA): The Yen Carry Trade

360 daysS =¥ 120.00/$

$ 83,333,333

Investors borrow yen at 0.40% per annum

Japanese yen money market

¥ 10,000,000 ¥ 10,040,000 Repay 1.004

Start End

US dollar money market

$ 87,500,000 1.05

Invest dollars at 5.00% per annum

S360 = ¥ 120.00/$

¥ 10,500,000 Earn¥ 460,000 ProfitThen exchanges

the yen proceeds

for US dollars,

investing in US

dollar money

markets for

one year

25

Interest Rate Parity (IRP) & Equilibrium

2

4

-5

-4

-1

-3 -1-4 -2 2 41 3 5

3

1

-2

-3

-6 6

Percent difference betweenforeign (¥) and domestic ($)interest rates

Percentage premium onforeign currency (¥)

X U

ZY

4.83

26

Forward Rate - Unbiased Predictor?

S1

Exchange rate

Time

t 2 t 3 t 4 t 1

S2

S3

S4

Error

F2

F1

Error F3

Error