International Parity Conditions
(or chapter 4)
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?
2
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
S $
P
3
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.
4
Absolute PPP: Big Mac Index
 Economist’s Big Mac PPP:
• Big Mac in China costs Yuan 9.90.
• Big Mac in US costs $2.71.
• Implied PPP exchange rate
Yuan9.90
 Yuan3.7/$
$2.71
5
Economist,
4/ 2003
Sfr6.30
 Sfr2.4803/ $
$2.54
6
Relative PPP
4
P
% change spot rate foreign currency
US$/ yen
3
2
1
-6
-5
-4
-3
-2
-1
1
-1
2
3
4
5
6
InfJAPAN- InfUS
-2
-3
-4
7
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?
8
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.
$
C
E  E x FC
C
$
R
$
N
9
Q:
• Can you tell when a currency is overvalued?
• Why the real exchange rate deviates from 100?
10
Real Effective Exchange Rate Indices
United States & Japan (1995 = 100)
180
160
United States
Japan
140
120
100
80
60
40
20
0
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
11
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.
$
BMW
P
€
 PBMW
x S €/$
• 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:
$
PBMW,
2
$
PBMW,
1
$40,000

 1.1429, or  14.29%
$35,000
• Degree of pass-through: 14.29 % / 20 % = 0.71 or 71 %
12
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?
13
International Fisher effect

International Fisher effect (Fisher-open):
spot exchange rate change equals opposite of interest rate
differential.
S1  S2
$
x 100  i  i FC
S2
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.
14
Forward Rate
 Forward Rate
• A forward rate: exchange rate quoted today for
settlement @ future date
F90FC/$  SFC/$

 FC 90 
 1   i x 360 



x

 $ 90 
 1   i x 360 



15
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.
SF/$
F90
90 
 
 1   0.04 x 360 


 SF1.48x
90 
 
 1   0.08 x 360 


 SF1.48 x
1.01
 Sfr1.4655/$
1.02
16
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/$) then
f
f
SF
FC
Spot - Foward 360

x
x 100
Foward
days
SF1.48 - SF1.4655 360

x
x 100   3.96% p.a.
SF1.4655
90
• Swiss franc sells forward @ premium 3.96% p. a.
(takes 3.96% more US$ to get franc at 90-day forward rate)
• For direct quotes ($/FC), use (F-S)/S.
17
Currency Yield Curve & Forwards
Interest
yield
6.0 %
Euro yield curve
5.0 %
4.0 %
Forward premium on
low interest rate currrency
3.0 %
Eurodollar
yield curve
2.0 %
1.0 %
1
2
3
4
Months
5
6
18
Interest Rate Parity (IRP)
 Interest rate parity:difference in national interest
rates for securities of similar risk & maturity should
be equal to opposite of forward rate discount/
premium for foreign currency.
1  i   S
US$
FC/US$
1  i  F
FC
1
FC/US$
or
FFC/US$ 1  i FC

FC/US$
S
1  i US$
19
Interest Rate Parity (IRP)
i $ = 8 % per annum
(2 % 90 days)
Start
$1,000,000
S = SF 1.4800/$
End
 1.02
$1,020,000
Dollar money market
$1,019,993
90 days
F90 = SF 1.4655/$
Swiss franc money market
SF 1,480,000
 1.01
SF 1,494,800
i SF = 4 % per annum
(1 % 90 days)
20
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.
21
Covered Interest Arbitrage (CIA)
Eurodollar rate = 8.00 % per annum
Start
$1,000,000
End
 1.04
$1,040,000
$1,044,638
Arbitrage
Potential
Dollar money market
S =¥ 106.00/$
180 days
F180 = ¥ 103.50/$
Yen money market
¥ 106,000,000
 1.02
¥ 108,120,000
Euroyen rate = 4.00 % per annum
22
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.
23
Uncovered Interest Arbitrage (UIA):
The Yen Carry Trade
Investors borrow yen at 0.40% per annum
Start
¥ 10,000,000
Then exchanges
End
 1.004
Japanese yen money market
¥ 10,040,000 Repay
¥ 10,500,000 Earn
¥
460,000 Profit
the yen proceeds
for US dollars,
S =¥ 120.00/$
investing in US
360 days
S360 = ¥ 120.00/$
dollar money
US dollar money market
markets for
one year
$ 83,333,333
 1.05
$ 87,500,000
Invest dollars at 5.00% per annum
24
Interest Rate Parity (IRP) & Equilibrium
4
3
Percentage premium on
foreign currency (¥)
2
1
4.83
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
-1
-2
-3
Percent difference between
foreign (¥) and domestic ($)
interest rates
-4
X
U
Y
Z
25
Forward Rate - Unbiased Predictor?
Exchange rate
F2
S2
Error
Error
S1
F1
F3
Error
S3
S4
Time
t1
t2
t3
t4
26