DerivativesLecture 14

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 MarketsExchange 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 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?

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%=1-11.577510.98151

)(-Discountor Premium=1- PriceForward

Spot Price

T

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?

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 + r1 + r

foreign

$

1 + i1 + i

foreign

$

fS

foreign / $

foreign / $

E(sS

foreign / $

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 + r1 + r

=foreign

$

fS

foreign / $

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.

fS

foreign / $

foreign / $

= E(sS

foreign / $

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 + i1 + i

=foreign

$

E(sS

foreign / $

foreign / $

)

Exchange Rate Relationships

solve for Es

Es = 11.5225

foreign/$

foreign/$

$

foreign )=

i+1i+1

SE(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

10.9815E(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 + r1 + r

=foreign

$

1 + i1 + i

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

05.11.0151.065

1.01221.067

Exchange Rate RelationshipsExample - The real interest rate in each country is

about the same

.0019 =1-1.0651.067=

i+1r+1

)(foreign

foreignrealr

-.0028=1-1.015

1.0122=i+1r+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

Perc

ent e

rror

Percent error in the one month forward rate for Swiss Franc per US $ compared to actual spot rate

International PricesThe Big Mac Index

– The price of a Big Mac in

different countries (Jan 22, 2015)

Purchasing Power & Exchange Rates

-100-80-60-40-20

020406080

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

1900

1910

1920

1930

1940

1949

1959

1969

1979

1989

1999

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

Exchange Rate Risk Currency Risk can be reduced by using

various financial instruments

Currency forward contracts, futures contracts, and even options on these contracts are available to control the risk