International Macroeconomics
Chapter 2
Introduction to Exchange Rates and
the Foreign Exchange Market
1
Chapter Outline
• The basics of exchange rates
• Foreign exchange market
• Arbitrage in foreign exchange market
2
The Basics of Exchange Rates
• An exchange rate of a currency is the price of the
currency expressed in terms of another currency.
• Exchange rates quotations
– Direct/Indirect
• Pick a home currency (US$, for instance)
• Direct quote – $1.1291/€1
• Indirect quote – €0.8857/$1
– American/European
• American quote - $0.1567/ ¥1
• European quote – ¥6.3815/$1
– Yahoo Finance, oanda.com, etc.
3
The Basics of Exchange Rates (cont.)
• Depreciation and Appreciation of Currencies
– Depreciation (appreciation) is a decrease (increase) in
the value of a currency relative to another currency.
– $1.3124/€1  $1.2568/€1  $1.1291/€1
– Percentage change:
 E$/€ = 1.1291-1.2568 = -0.1277
%  E$/€ = -0.1277/1.2568 = -0.1016 = -10.16%
– Thus, the euro depreciated against the dollar by
10.16%.
4
The Basics of Exchange Rates (cont.)
• Depreciation and Appreciation of Currencies
– A depreciated (appreciated) currency means that
imports are more (less) expensive and domestically
produced goods and exports are less (more) expensive.
– A depreciated (appreciated) currency lowers (raises)
the price of exports relative to the price of imports.
5
The Basics of Exchange Rates (cont.)
Exchange rate ($/£)
1.25
1.50
1.75
Price of sweater in $
62.50
75.00
87.50
Price of a pair of jeans in $
45.00
45.00
45.00
Relative price (Sweater/pair of jeans)
1.39
1.67
1.94
Note: The above calculations assume unchanged money prices of $45
per pair of jeans and £50 per sweater
The Basics of Exchange Rates (cont.)
• Effective exchange rates
– Calculated based on the weighted-average of changes in a group
of exchange rates of a currency (say ‘Home’ currency, typically the
US dollar).
– For a exchange rate, the weight is usually determined by the trade
volume between two countries.
– For example, 60% of US trade is with country 1 and 40% is with
country 2. US$ appreciates 10% against 1 and depreciates 15%
against 2. Hence, the change in the effective exchange rate of US$
is calculated as: 10%*60%+(-15%)*40% = 0%. Thus, effectively,
US$ remains the same.
– Check the Major Currency Index (MCI) at St. Louis Fed.
7
The Basics of Exchange Rates (cont.)
Effective Exchange Rates
In general, suppose there are N currencies in the basket,
and Home’s trade with all N partners is:
Trade = Trade1 + Trade2 + . . . + TradeN.
Applying trade weights to the change of each bilateral
exchange rate, the home country’s effective exchange
rate (Eeffective) will change according to the following
weighted average:
Eeffective E1 Trade 1 E2 Trade 2
EN Trade N



Eeffective
E Trade
E Trade
E Trade
12N
Trade - weighted average of bilateral nominal exchange rate changes
8
The Basics of Exchange Rates (cont.)
Effective Exchange Rates
9
The Basics of Exchange Rates (cont.)
There are two major types of exchange rate regimes—
• Fixed (or pegged) exchange rates fluctuate in a narrow range (or
not at all) against some base currency over a sustained period.
Revaluations and devaluations may occur when the government
intervenes in the foreign exchange market.
• Floating (or flexible) exchange rates fluctuate as a result of
market forces (demand/supply), and the government makes no
attempt to fix it. Appreciations and depreciations occur
continuously in real time trading.
Terms: managed float, crawling peg, currency band, and dollarization.
10
The Basics of Exchange Rates (cont.)
A Spectrum of Effective Rate Regimes
This figure shows IMF classification of exchange rate regimes around the world for
covers 192 economies in 2010. Regimes are ordered from the most rigidly fixed to the
most freely floating. Seven countries use an ultrahard peg called a currency board,
while 35 others have a hard peg.
11
The Basics of Exchange Rates (cont.)
A Spectrum of Exchange Rate Regimes (continued)
An additional 43 counties have bands, crawling pegs or bands, while 46 countries have
exchange rates that either float freely, are managed floats are allowed to float within
wide bands.
12
Foreign Exchange Market
• The set of markets where foreign currencies and
other assets are exchanged for domestic ones.
– Institutions buy and sell deposits of currencies or other
assets for investment purposes.
• Recently, the daily volume of foreign exchange
transactions has been more than $5 trillion – up
from $500 billion in 1989.
• Participants include commercial banks(other
depository institutions), non-bank financial
institutions, non-financial businesses, and central
banks.
13
Foreign Exchange Market (cont.)
Spot rates vs. Forward rates
– Spot rates are the exchange rates at which currencies
are traded immediately at the present.
– Forward rates are the exchange rates agreed upon
between two parties to trade currencies at a certain
future time.
14
Dollar/Pound Spot and Forward Exchange Rates
1983–2011
Source: Datastream. Rates shown are 90-day forward exchange rates and spot exchange rates, at end of month.
15
Foreign Exchange Market (cont.)
Other derivatives –
• Foreign exchange swaps
– Exchanges of loan principals and interest payments in
different currencies
• Futures contracts
– a standardized contract to buy or sell a specified
currency of standardized quality at a certain date in the
future, at a specified price.
– Forward contracts vs. Futures contracts
• Options contracts (Call/Put)
– A right given to the buyer to buy or sell a currency at a
specified price for a standard amount on or before a
specified future date .
16
Foreign Exchange Market (cont.)
Derivatives allow investors to engage in hedging
(risk avoiding) and speculation (risk taking) –
• Hedging
– Disney would like to hedge the exchange rate risk on its ¥10billion
expected to be earned in Shanghai in one year. What would you
suggest on how Disney should conduct the hedge?
• Speculation
– The current exchange rate between Chinese yuan and US$ is
¥6.4/$. If you expect that yuan is going to depreciate further in 3
months and wish to make a bet, you would sell yuan futures now. If
your expectation bears out, you will make a profit; if not, your
investment will be a total loss.
17
Foreign Exchange Market (cont.)
• Factors that influence the return on assets
determine the demand of those assets, including
currency deposits.
• Rate of return: the percentage change in value
that an asset offers during a time period.
– Real rate of return: inflation-adjusted rate of return
• Risk and return
– Inflation risk
– Liquidity risk
– Default risk
– Maturity risk
18
Foreign Exchange Market (cont.)
• We assume that risks of currency deposits in
foreign exchange markets are the same,
regardless of their currency denomination.
• Rates of return that investors expect to earn are
determined by
- Interest rates that the assets will earn
- Expectations about appreciation or depreciation
19
Foreign Exchange Market (cont.)
• Suppose the interest rate on a dollar deposit is 2%.
• Suppose the interest rate on a euro deposit is 4%
• Is investment in a euro deposit more attractive than that
in a dollar deposit?
 Suppose today the exchange rate is $1/€1, and the expected
rate one year in the future is $0.97/€1.
 $100 can be exchanged today for €100.
 These €100 will yield €104 after one year.
 These €104 are expected to be worth $0.97/€1 x €104 =
$100.88 in one year.
 The rate of return in terms of dollars from investing in euro
deposits is ($100.88-$100)/$100 = 0.88%.
20
Foreign Exchange Market (cont.)
• Analyze the dollar rate of return on euro deposits:
[($100 / $1/€1) x (1+4%) x $0.97/€1]/100 – 1
= (1+4%) x (0.97-1)/1 + 4%
= 4% + (-3%) + 4% x (-3%)
= 0.88%
• Considering the even smaller value of the multiplication of
two small percentages, we decompose the dollar rate of
return on euro deposits into two components:
– The interest rate on euro deposits
– The expected rate of appreciation of euro deposits
 R€ + (Ee$/€ - E$/€)/E$/€ = 4% + (-3%) = 1%  0.88%
21
Foreign Exchange Market (cont.)
• Compare the rate of return on dollar deposits with
that on euro deposits
R$ - [R€ + (Ee$/€ - E$/€)/E$/€ ] = 2% - 1% = 1%
• The investment in dollar deposits is more
attractive.
22
Arbitrage in Foreign Exchange Market
• Arbitrage: buying at a lower price and
selling at a higher price for a profit.
• Active trading and the increasing degree of
integration in forex market imply that there
are no significant arbitrage opportunities on
currencies.
23
Arbitrage in Foreign Exchange Market (cont.)
Arbitrage with three currencies:
E£/$=0.6; E£/€=0.7; E€/$=1.0
No-arbitrage condition requires E£/$=E£/€*E€/$. In this example, however,
E£/$=0.6 < E£/€*E€/$ =0.7*1.0=0.7. Thus, an arbitrage opportunity exists.
Now, how to take advantage of it? Suppose you have one US$ and
ignore transaction cost:
1. First, buy euro with your one US$: $1* E€/$=1*1= €1;
2. Next, sell the euro for pound: €1*E£/€=1*0.7=£0.7;
3. Lastly, sell the pound for US$: £0.7/E£/$=0.7/0.6=$1.17.
Your arbitrage profit is 1.17-1=$0.17 or 0.17/1=17%.
24
Arbitrage in Foreign Exchange Market (cont.)
• Interest Rate Parity (IRP) –
the relationship between interest rates on currency
deposits and foreign exchange rates.
• If the US federal reserve raises interest rates relative to
those of European Central Bank (ECB), US dollar would
appreciate against the euro. Reversely, changes in the
exchange rate between US dollar and euro may indicate
market expectations of a change in interest rate policies.
25
Arbitrage in Foreign Exchange Market (cont.)
• Covered Interest Parity (CIP) relates interest rates
across countries and the rate of change between
forward exchange rates and the spot exchange rate:
i$ = i€ + (F$/€ - E$/€)/E$/€
where F$/€ is the forward exchange rate.
• It says that rates of return on dollar deposits and
“covered” foreign currency deposits are the same.
– How could you earn a risk-free return in the foreign exchange
markets if covered interest parity did not hold?
– Covered positions using the forward rate involve little risk.
Arbitrage in Foreign Exchange Market (cont.)
Consider alternative one-year investments for $100,000:
1.
Invest in the U.S. at i$. Future value = $100,000 × (1 + i$)
2.
Trade your $ for £ at the spot rate, invest $100,000/E$/£ in Britain at
i£ while eliminating any exchange rate risk by selling the future
value of the British investment forward.
F$/£
Future value = $100,000(1 + i£)×
E$/£
Assuming these investments have the same risk (they probably do if
they are short-term bank deposits), they must have the same future
value (otherwise an arbitrage would exist).
F$/£
(1 + i£) ×
= (1 + i$)
E$/£
27
Arbitrage in Foreign Exchange Market (cont.)
F$/€
(1 + i€) ×
= (1 + i$)
E$/€
Take natural logs on both sides of the above equation
and rearrange, we get
i$ = i€ + f$/€ - e$/€
- where f$/£ and e$/£ are the natural log terms of
forward rate and spot rate, respectively.
When forward premium (discount), i.e. (F$/€ - E$/€)/E$/€ is
small, it is very close to (f$/€ - e$/€). In that case,
i$ = i€ + (F$/€ - E$/€)/E$/€
Arbitrage in Foreign Exchange Market (cont.)
• Uncovered Interest Parity (UIP) relates interest rates
across countries and the expected rate of change in
the spot exchange rate:
E$e/ €

1  i$   1  i€ 

E$ / €
Dollar return on

dollar deposits
Expected dollar return
on euro deposits
𝑒
where 𝐸$/€
is the expected exchange rate. Since it is
expected not determined, traders face exchange rate
risk under UIP.
Arbitrage in Foreign Exchange Market (cont.)
• Uncovered Interest Parity (UIP) is a no-arbitrage
condition that describes an equilibrium in which
investors are indifferent between the returns on
unhedged interest-bearing bank deposits in two
currencies.
• If both CIP and UIP hold, the forward rate must equal
𝑒
the expected future spot rate, i.e. 𝐹$/€ = 𝐸$/€
.
Consequently, investors are indifferent towards
exchange rate risk, which makes them risk neutral.
But, is it true?
Arbitrage in Foreign Exchange Market (cont.)
• Empirically, UIP doesn’t hold, especially in the short
run, which means
𝑒
𝐸$/€
𝐹$/€
−1≠
−1
𝐸$/€
𝐸$/€
• Explanations
 Are investors rational?
 Are investors risk neutral?
 Are empirical tests appropriate? (endogeniety, non-stationary
variables, time horizon, etc.)