Chapter 2: Introduction to exchange rates and the foreign
exchange market
Key words: Exchange rate, interest rate and arbitrage
Goals: Understanding how the market for foreign exchange
works
Definition: An exchange rate (E) is the price of some foreign
currency.
There are two equivalent formats in which the exchange rate is
quoted.
1 EUR = 1.4033 USD
is equivalent to
1 USD = 0.7126 EUR
To avoid confusion, I will state explicitly the format of foreign
exchange in lecture notes and exams.
Example 1: The US exchange rate against the euro is US dollars
per euro, denoted by E$/€.
Notice that euro is the denominator, and US dollar is the
numerator.
Exercise: please find the latest US exchange rate against euro
from google finance.
1
1 EUR = ___________ USD
In symbol, E$/€ = ____________________.
Example 2: from google finance, find the British Pound
exchange rate against US dollar.
In symbol, E£/$ = ____________________.
In general E1/2 denotes the exchange rate in units of country 1
currency per unit of country 2 currency.
The exchange rate of currency 1 is expressed as E1/2
A currency appreciates (or strengthens) if it is worth more other
currency.
A currency depreciates (or weakens) if it is worth less other
currency.
If E1/2 is going up, then one unit of country 2 currency can be
converted to ( more less ) country 1 currency. As a result, the
country 2 currency ( appreciates depreciates ); while the
country 1 currency ( appreciates depreciates).
In short, currency 1 depreciates if E1/2 rises.
Equivalently, currency 1 depreciates if the change of the
exchange rate is positive:
Δ E1/2 = E1/2, later - E1/2, before > 0.
2
If E1/2 is going down, then one unit of country 2 currency can be
converted to ( more less ) country 1 currency. As a result, the
country 2 currency ( appreciates depreciates ); while the
country 1 currency ( appreciates depreciates).
In short, currency 1 appreciates if E1/2 falls.
Equivalently, currency 1 appreciates if the change of the
exchange rate is negative:
Δ E1/2 = E1/2, later - E1/2, before < 0.
Fact: if currency 1 appreciates against currency 2, then currency
2 must depreciate against currency 1. The values of the two
currencies move in opposite direction.
Exercise: from google finance,
on December 31, 2010, E$/€ = _______________
on May 4, 2011, E$/€ = _______________
During this period, Euro ( appreciates depreciates ); US dollars
( appreciates depreciates ).
Typically, a country is trading with more than one country. The
effective exchange rate is the trade-weighted average of
exchange rates against a basket of currencies.
Example
3
Suppose 40% of Home country trade is with country A and 60%
is with country B. Currency H appreciates 10% against currency
A but depreciates 30% against currency B. Please calculate the
change in Home country’s effective exchange rate.
Δ EH/A = ____________________
Δ EH/B = ____________________
Weight for currency A = ___________________
Weight for currency B = ___________________
Δ Eeffective = ____________________
In words, currency H ( appreciates
__________.
4
depreciates ) by
Overall, US dollar ( appreciates depreciates )
We can use exchange rate to compare prices in a common
currency
Example
In July 2008, a Big Mac was sold at $3.57 in USA and £2.29 in
UK. The exchange rate is E£/$=0.5. Please show which country
has high price of a Big Mac.
E$/£ = __________
(Answer 1, use $ as the common currency)
5
The dollar price of a Big Mac in USA =
____________________
The dollar price of a Big Mac in UK =
_____________________
(Answer 2, use £ as the common currency)
The pound price of a Big Mac in USA =
____________________
The pound price of a Big Mac in UK =
_____________________
Exercise: suppose the pound price of a Big Mac in UK remains
unchanged, but pound depreciates against dollar. Then the dollar
price of a Big Mac in UK goes (up down).
Reality Check 1: What happens to US’ imports from China if
Chinese Yuan appreciates?
Reality Check 2: What happens to the number of Chinese
students at Miami U if Chinese Yuan appreciates?
6
Fact: depreciation makes home goods less expensive in foreign
countries, and therefore boosts export to foreign countries.
Y = C + I + G + NX(E)
There are two major types of exchange rate regimes.
Fixed (or pegged) exchange rate regimes are those in which a
country’s exchange rate fluctuates in a narrow range (or not at
all) against some based currency over a sustained period.
Government needs to intervene in the market to make the
exchange rate rigidly fixed.
Floating (or flexible) exchange rate regimes are those in which a
country’s exchange rate fluctuates in a wider range, and the
government makes no attempt to fix it against any base currency.
Some groups of countries agree to form a currency union.
Some countries dollarize by adopting the currency of another
country as their own.
Check Figures 2-2 and 2-3 in the textbook.
7
Foreign exchange (FX) market is the market where the exchange
rate is determined by market forces.
Spot exchange rate is the exchange rate for the spot transaction,
in which immediate exchange of one currency for another
happens between two parties.
8
When individuals buy a little foreign currency through a retail
channel, the pay a higher price than the midrange quote seen in
the press; and when they sell, they are paid a lower price. The
difference between the “buy at” and “sell for” prices is spread,
an example of transaction cost.
Forward exchange rate is the exchange rate for the forward
contract, in which the settlement date for the delivery of the
currencies is in the future.
Forward rate tends to track spot rate closely. Check Figure 2-5.
Forward contracts (and more generally, derivatives) allow
individuals engage in hedging (risk avoidance) and speculation
(risk taking).
Example of hedging:
Suppose a US firm expects to receive payment of €1 million in
90 days. The dollar value of this payment will go down if euro
depreciates. To avoid this exchange rate risk, the firm may
engage in hedging with a forward contract to deliver (or sell) €1
million in 90 days with a forward rate locked today.
Example of speculation:
Suppose the current forward rate for a 90-day contract is $1.4
per euro. A French investor speculates that dollar will strengthen
9
in 90 days. Then he can use the forward contract to exchange
100 euros for 140 dollars in 90 days, and then use the spot
contract to sell the 140 dollars and get more than 100 euros. This
happens only when dollars actually appreciates.
An important player on FX market is government.
Suppose country A’s economy is worsening, and people expect
that currency A will depreciate (or become less valuable). Then
people start selling currency A and buying US dollars (why?).
For some reasons A’s government wants to avoid currency A’s
depreciation. They can intervene in the FX market by selling US
dollars and buying currency A. However, this kind of
intervention has to stop once the government runs out of its
limited dollar reserves. Once a reserve is gone, market forces
take over. A rapid deprecation will inevitably follow. For a
small country, dollarization is necessary if its currency keeps
depreciating.
Check the figures for Argentine Pesos and Ecuadorean sucres in
Figure 2-3.
Google “1997 Asian financial crisis”
10
Exercise
Discuss how Chinese government intervenes in the FX market
to avoid the appreciation of Chinese Yuan. What is the cost for
the intervention taken by the Chinese government?
The major pricing theory is no-arbitrage. Exchange rate is the
price of a currency, so the no-arbitrage theory applies.
By definition arbitrage means to buy low and sell high.
The market is in equilibrium and price is stabilized if it satisfies
no-arbitrage condition.
Example of arbitrage with two currencies at two locations (let’s
neglect transaction cost)
E£/$, new york = 0.5
E£/$, london = 0.55
The pound is more expensive in (New York or London)
Arbitrage means to buy pound (and sell dollar) in (New York
or London) and sell pound (and buy dollar) in (New York or
London).
More details of the arbitrage:
In London, you sell 1 dollar for _________ pound.
11
In New York, you sell __________ pound for __________
dollars.
Your profit is _________ dollars. This arbitrage profit is riskless.
Now imagine many people are doing the same as you.
The London rate will go (up or down) if everyone buy pounds.
The New York rate will go (up or down) if everyone sells
pounds.
In the end, the London and New York rates will converge (i.e.,
lower rates goes up and higher rate goes down) because of
arbitrage. The arbitrage will continue as long as the rates at the
two locations differ, and the arbitrage will keep making the two
rates converge. Eventually, the market will be at equilibrium and
price becomes stable once
E£/$, new york = E£/$, london
The condition above is no-arbitrage condition.
Actually, this is an example of law of one price: the prices of the
same goods, in this case, the currency pound, should be the same
otherwise there is chance for arbitrage.
Exercise: Question 5 on page 61
Arbitrage with three currencies
In general there is opportunity for arbitrage if
12
E1/3 ≠ E2/3 E1/2 (or equivalently, E1/3 ≠
𝐸1/2
𝐸3/2
)
E1/3 denotes the direct exchange rate of currency 1 against
currency 3.
E2/3 E1/2 denotes the cross exchange rate of currency 1 against
currency 3.
Currency 2 is vehicle currency.
So different direct and cross rates can invoke arbitrage.
Example
Suppose E£/$ = 0.5, E€/£= 1.4 and E€/$ = 0.8
The direct exchange rate of euro against dollar
is_______________
The cross exchange rate of euro against dollar
is________________
The vehicle currency is _________________
You want to buy euro using (direct or cross) rate
You want to sell euro using (direct or cross) rate
The direct rate will go (up or down)
The cross rate will go (up or down)
The adjustment of the two rates will continue until they are
equalized.
To sum up, the no-arbitrage condition with three currencies is
13
E1/3 = E2/3 E1/2
or equivalently
E1/3 =
𝐸1/2
𝐸3/2
In practice if 𝐸1/2 and 𝐸3/2 are known but 𝐸1/3 is unknown, we
can use the formula above to calculate 𝐸1/3
Covered Interest Parity (CIP), a theory for determining the
forward exchange rate (F)
Suppose the dollar deposit pays interest rate of 𝑖$ and the euro
deposit pays 𝑖€
A US saver has two choices.
Choice one, he can choose dollar deposit, and for one dollar he
can earn dollar return of _____________.
Choice two, if there is no capital control, he can convert one
dollar to __________ euro using the spot rate 𝐸$/€
14
Then he chooses euro deposit and earns euro return of
___________________
Finally he converts the euro return to dollar return using the
riskless forward rate 𝐹$/€ and get ____________
(Read page 48)
The market is in equilibrium if the investor is indifferent
between the two choices. That is the case when the two choices
yield the same common currency returns, i.e.,
𝐹$/€
1 + 𝑖$ = (1 + 𝑖€ ) 𝐸
(2-1)
$/€
Equation (2-1) is called the covered interest parity, from which
we can derive a formula for determining the forward rate
𝐹$/€ = 𝐸$/€
(1 + 𝑖$ )
(1 + 𝑖€ )
We can rearrange (2-1) and obtain
𝐹$/€ − 𝐸$/€
= 𝑖$ − 𝑖€
𝐸$/€
which states that the forward premium (the proportional
difference between the forward and spot rates) equals the
interest rate differential.
Exercise
15
Suppose the euro interest rate is 3%, the dollar interest rate is
5%, and the spot rate is $1.3 per euro. The forward rate would
be____________________ ; the forward premium would be
__________________.
Exercise
Question 6 part (a, b, c, d) on page 61 of the textbook.
Uncovered Interest Parity (UIP), a theory for determining the
spot exchange rate (E)
Suppose the dollar deposit pays interest rate of 𝑖$ and the euro
deposit pays 𝑖€
A US saver has two choices.
Choice one, he can hold dollar deposit, and for one dollar he
earns dollar return of _____________.
Choice two, if there is no capital control, he can convert one
dollar to __________ euro using the spot rate 𝐸$/€
Then he chooses euro deposit and earns euro return of
___________________
Finally he converts the euro return to dollar return using the
𝑒
risky expected future spot rate 𝐸$/€
and get ____________
𝑒
where 𝐸$/€
denotes the expected spot rate that will prevail in the
future.
(Read page 52)
16
The market is in equilibrium if the following no-arbitrage
condition holds
𝑒
𝐸$/€
1 + 𝑖$ = (1 + 𝑖€ ) 𝐸
(2-2)
$/€
Equation (2-2) is called the uncovered interest parity (UIP).
Under UIP, returns to holding dollar deposits accruing interest
must equal the expected returns from investing in euros.
From (2-2) which we can derive a formula for determining the
current spot rate:
𝑒
𝐸$/€ = 𝐸$/€
(1 + 𝑖€ )
(1 + 𝑖$ )
In words we can calculate the current spot rate if we know
interest rates and expected future spot rate
Suppose the euro interest rate is 2%, the dollar interest rate is 4%
and the expected future spot rate is $1.4 per euro. Then the
current spot rate is _______________
In the following chapters we will learn how the expected future
spot rate and interest rates are determined.
We can rewrite (2-2) as
17
𝑒
𝐸$/€
− 𝐸$/€
= 𝑖$ − 𝑖€ ,
𝐸$/€
which says that under UIP, the expected rate of depreciation of
dollars against euro equals the interest rate differential of dollar
and euro deposits.
Exercise: suppose the interest rate on euro deposit is 2% and on
dollar deposit it is 4%. Then you expect the dollar will
(depreciate or appreciate) against euro by _________.
Big picture
𝑒 𝑈𝐼𝑃
𝑖$ , 𝑖€ , 𝐸$/€ →
𝐶𝐼𝑃
𝐸$/€ → 𝐹$/€
Discuss figure 2-12 on page 5
18
19