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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