Exchange Rates
Spot Rate * 1 Month 3 Months 1 YearEuropeEMU (euro) 1.2375 1.2364 1.2346 1.2285Norway (krone) 6.8168 6.8217 6.8292 6.861Sweden (krona) 7.4509 7.4601 7.4738 7.5284Switzerland (franc) 1.2559 1.2549 1.2532 1.2451United Kingdom (pound) 1.8472 1.8421 1.8325 1.7877Americas:Canada (dollar_ 1.3276 1.3289 1.3311 1.3388Mexico (peso) 10.9815 11.0338 11.126 11.5775Pacific/ Africa:Hong Kong (dollar) 7.7928 7.7858 7.774 7.739Japan (yen) 106.83 106.72 106.53 105.505South Africa (rand) 6.4662 6.5107 6.5917 6.9812South Korea (won) 1160.5 1163.8 1169.2 1186
Forward Rate *
* Rates are per $US, other than Euro and UK Pounds
March 22, 2004
Foreign Exchange Markets
Exchange Rate - Amount of one currency needed to purchase one unit of another.
Spot Rate of Exchange - Exchange rate for an immediate transaction.
Forward Exchange Rate - Exchange rate for a forward transaction.
Foreign Exchange Markets
Forward Premiums and Forward DiscountsExample - The Peso spot price is 10.9815 peso per
dollar and the 1 year forward rate is 11.5775 Peso per dollar, what is the premium and discount relationship?
Foreign Exchange MarketsForward Premiums and Forward
DiscountsExample - The Peso spot price is 10.9815 peso per
dollar and the 1 year forward rate is 11.5775 Peso per dollar, what is the premium and discount relationship?
-5.15%=1-11.5775
10.98151
)(-Discountor Premium=1- PriceForward
Spot Price
T
Foreign Exchange Markets
Forward Premiums and Forward DiscountsExample - The Peso spot price is 10.9815 peso per dollar
and the 1 year forward rate is 11.5775 Peso per dollar, what is the premium and discount relationship?
Answer - The dollar is selling at a 5.15% premium, relative to the peso. The peso is selling at a 5.15% discount, relative to the dollar.
Exchange Rate Relationships Basic Relationships
1 + r
1 + rforeign
$
1 + i
1 + iforeign
$
f
Sforeign / $
foreign / $
E(s
Sforeign / $
foreign / $
)
equals
equals
equals equals
Exchange Rate Relationships1) Interest Rate Parity Theory
The ratio between the risk free interest rates in two different countries is equal to the ratio between the forward and spot exchange rates.
1 + r
1 + r=
foreign
$
f
Sforeign / $
foreign / $
Exchange Rate Relationships
Example - You have the opportunity to invest $1,000,000 for one year. All other things being equal, you have the opportunity to obtain a 1 year Mexican bond (in peso) @ 6.7 % or a 1 year US bond (in dollars) @ 1.22%. The spot rate is 10.9815 peso:$1 The 1 year forward rate is 11.5775 peso:$1
Which bond will you prefer and why?
Ignore transaction costs
Value of US bond = $1,000,000 x 1.0122 = $1,012,200
Value of Mexican bond = $1,000,000 x 10.9815 = 10,981,500 peso exchange
10,981,500 peso x 1.067 = 11,717,261 peso bond pmt
11,717,261 peso / 11.5775 = $1,012,072 exchange
Exchange Rate Relationships
Example - You have the opportunity to invest $1,000,000 for one year. All other things being equal, you have the opportunity to obtain a 1 year Mexican bond (in peso) @ 6.7 % or a 1 year US bond (in dollars) @ 1.22%. The spot rate is 10.9815 peso:$1 The 1 year forward rate is 11.5775 peso:$1
Which bond will you prefer and why? Ignore transaction costs
Exchange Rate Relationships2) Expectations Theory of Exchange Rates
Theory that the expected spot exchange rate equals the forward rate.
f
Sforeign / $
foreign / $
=E(s
Sforeign / $
foreign / $
)
Exchange Rate Relationships3) Purchasing Power Parity
The expected change in the spot rate equals the expected difference in inflation between the two countries.
1 + i
1 + i=
foreign
$
E(s
Sforeign / $
foreign / $
)
Exchange Rate Relationships
solve for Es
Es = 11.5225
foreign/$
foreign/$
$
foreign )=
i+1
i+1
S
E(s
Example - If inflation in the US is forecasted at 1.5% this year and Mexico is forecasted at 6.5%, what do we know about the expected spot rate?
Given a spot rate of 10.9815 peso:$1
10.9815
E(s )=
.015+1
.0651 foreign/$
Exchange Rate Relationships4) International Fisher effect
The expected difference in inflation rates equals the difference in current interest rates.
Also called common real interest rates
1 + r
1 + r=
foreign
$
1 + i
1 + iforeign
$
Exchange Rate Relationships4) International Fisher effect
The expected difference in inflation rates equals the difference in current interest rates.
Also called common real interest rates
05.11.015
1.065
1.0122
1.067
Exchange Rate RelationshipsExample - The real interest rate in each country is
about the same
.0019 =1-1.065
1.067=
i+1
r+1)(
foreign
foreignrealr
-.0028=1-1.015
1.0122=
i+1
r+1)(
$
$realr
Forward Rate vs. Actual Spot Rate
-15
-10
-5
0
5
10
154/
1/19
84
4/1/
1986
4/1/
1988
4/1/
1990
4/1/
1992
4/1/
1994
4/1/
1996
4/1/
1998
4/1/
2000
4/1/
2002
4/1/
2004
Per
cen
t er
ror
Percent error in the one month forward rate for Swiss Franc per US $ compared to actual spot rate
International Prices
CountryLocal Price Converted
to U.S. Dollars CountryLocal Price Converted
to U.S. Dollars
Canada 2.33 Philippines 1.23China 1.26 Russia 1.45Denmark 4.46 South Africa 1.86Euro area 3.28 Switzerland 4.9Japan 2.33 United Kingdom 3.37Mexico 2.08 United States 2.9
The Big Mac Index – The price of a Big Mac in different countries (May 29, 2004)
Purchasing Power & Exchange Rates
-100
-80
-60
-40
-20
0
20
40
60
80
100
-100 -50 0 50 100
Relative change in purchasing power, percent
Rel
ativ
e ch
ange
in e
xcha
nge
rate
, per
cent
Exchange Rates
1
10
19
00
19
10
19
20
19
30
19
40
19
49
19
59
19
69
19
79
19
89
19
99
Nominal versus Real Exchange Rates
U.S. Dollar / British Pound (in log scale)
Interest Rates and Inflation
0
5
10
15
20
25
30
35
40
-10 0 10 20 30
Countries with the highest interest rates generally have the highest inflation rates. In this diagram each of the 129 points
represents a different country.
Average inflation rate, percent, latest 5 years to 2003
Ave
rage
mon
ey m
arke
t rat
e, p
erce
nt,
late
st 5
yea
rs to
200
3
Exchange Rate RiskExample - Honda builds a new car in Japan for a cost + profit of 1,715,000 yen. At an exchange rate of 120.700Y:$1 the car sells for $14,209 in Indianapolis. If the dollar rises in value, against the yen, to an exchange rate of 134Y:$1, what will be the price of the car?
1,715,000 = $12,799
134Conversely, if the yen is trading at a forward discount, Japan will experience a decrease in purchasing power.
Exchange Rate RiskExample - Harley Davidson builds a motorcycle for a cost plus profit of $12,000. At an exchange rate of 120.700Y:$1, the motorcycle sells for 1,448,400 yen in Japan. If the dollar rises in value and the exchange rate is 134Y:$1, what will the motorcycle cost in Japan?
$12,000 x 134 = 1,608,000 yen