Chapter 13
Supplementary Notes
Exchange rate
• The price of a currency in terms of another
currency
• DC = $, FC = €
• The exchange rate can be quoted as
– DC / FC ($ per unit of €)
– FC / DC (€ per unit of $)
• We agree to express the exchange rate as
E = DC / FC.
Appreciation and Depreciation
•
•
•
•
Appreciation: increase in value
Depreciation: decrease in value
An increase in E = depreciation of DC
A decrease in E = appreciation of DC
Cross rates
$1 = C$1.3538; $1 = ¥120.00
• Then the yen price of C$1?
= (¥ /$)/(C$/$)
=120.00/1.3538 = 88.64
• What is the C$ price of a yen?
Effective exchange rates: the average of
several exchange rates
Trade Weighted Index of the US dollar
• Top: A weighted average of the
foreign exchange value of the
U.S. dollar against the
currencies of a broad group of
major U.S. trading partners.
• Bottom: … against a subset of
the broad index currencies that
circulate widely outside the
country of issue. (major
currencies)
Participants
•
•
•
•
Private firms (exporters and importers)
Commercial banks
(Other financial institutions)
Central banks
Main characteristics of the market
• Major trading centers: London, New York,
Tokyo, Frankfurt, Singapore.
• The volume of foreign exchange has
grown:
– in 1989 the daily volume of trading was $600
billion, in 2001 the daily volume of trading was
$1.2 trillion.
• About 90% of transactions in 2001
involved US dollars.
Exchange rate and prices
• Depreciation of DC makes
– Foreign goods more/less expensive to
domestic consumers
– Domestic goods more/less expensive to
foreign consumers
• Appreciation has the opposite effects
Example
• A US dollar costs 7.5 Norwegian kroner,
but the same dollar can be purchased for
1.25 Swiss franc. What is the Norwegian
kroner/Swiss franc exchange rate?
• Currency codes: USD($), CHF, NOK(kr)
• NOK/CHF = (NOK/USD)/(CHF/USD) = __
Foreign exchange markets
a. Spot market (for immediate delivery and
payment)
b. Forward market (for future delivery and
payment)
Forward contract: A fixed-price contract
made today for delivery of a certain
amount of a currency at a specified
future date (settlement date).
c. Swaps
A currency swap combines both a spot and a forward
transaction into one deal.
d. Futures
A FX futures contract: A standardized agreement with
an organized exchange to buy or sell a currency at a
fixed price at a certain date in the future.
e. Options
A FX option is a contract for future delivery of a specific
currency, in which the holder of the option has the right
to buy (or sell) the currency at an agreed price, the
strike or exercise price, but is not required to do so.
Call and put options
Activities in the FX market
a. Arbitrage
Simultaneous buying and selling (of a currency)
to take profit from price differential
b. Hedging
Covering from exchange risk due to open
positions in FX
c. Speculation
Holding an open position to profit from the
difference in one’s expectation and market’s
valuation
Examples
a. Spatial arbitrage
Q: The pound is priced at $1.50 in NY and $1.45 in
London. What would you do as a currency arbitrageur?
b. Triangular arbitrage
Q: In FX market (in the same or different locations), the
foreign exchange rates are quoted as follows:
the $/£ rate is 1.5, the €/$ rate is 1.1, and the €/£ rate
is 1.55.
Start with a pound, and see how much profit can be
made if you make a complete 3-way trip to the pound?
Hedging: Dealing with foreign exchange risk
An importer with a payable of €1 million in 3 months.
What options are available?
(i) Do nothing. Wait 3 months and buy euros spot when the
payment is due
There is foreign exchange risk.
(ii) Buy euros 3-month forward now
3-month forward rate = .9188
Pay $1 mil * (.9188) in 3 months.
(iii) Exchange risk can be covered with futures or options.
Demand for
foreign currency assets
• Demand for assets depends on
– Rate of return: The percentage increase in
value an asset offers over some time period.
– Risk: The variability it contributes to savers’
wealth
– Liquidity: The ease with which it can be sold
or exchanged for goods
Rate of return
Defining Asset Returns
• The percentage increase in value an asset offers
over some time period.
• Interest (or Dividend) + valuation change
The Real Rate of Return
• The rate of return computed by measuring asset
values in terms of some broad representative
basket of products that savers regularly purchase.
• Equals the nominal rate of return minus the rate of
inflation
Rate of return for foreign assets
• Suppose
– Today’s exchange rate = $1.10/€
– Next year’s expected exchange rate = $1.165/€
• [The expected depreciation of the dollar = 5.9%]
– The interest rate on dollar deposits = 10%
– The interest rate on euro deposits = 5%
• Which deposit, dollar or euro, offers the higher
return?
A Simple Rule
– The dollar rate of return on euro deposits is
approximately the euro interest rate plus the
rate of depreciation of the dollar against the
euro.
• The rate of depreciation of the dollar against the
euro is the percentage increase in the dollar/euro
exchange rate over a year.
– In symbol, R* + (Ee - E)/E
where:
R* = foreign interest rate
E = today’s exchange rate (remember DC per FC!)
Ee = the exchange rate expected a year from today
R* + (Ee - E)/E
• The above equals R* + Ee /E – 1.
• Depreciation of the domestic currency today
lowers the expected return on deposits in foreign
currency.
– A current depreciation of domestic currency will raise
the initial cost of investing in foreign currency, thereby
lowering the expected return in foreign currency.
– In the case of appreciation, change the direction of
the underlined words.
Expected Returns on Euro Deposits
when Ee$/€ = $1.05/€
Expected rate of
Current
Interest rate on
dollar
exchange rate euro deposits
depreciation
Expected dollar return
on euro deposits
E$/€
R€
(1.05 - E$/€)/E$/€
R€ + (1.05 - E$/€)/E$/€
1.07
0.05
-0.019
0.031
1.05
0.05
0.000
0.050
1.03
0.05
0.019
0.069
1.02
0.05
0.029
0.079
1.00
0.05
0.050
0.100
The Current
Exchange
Rate and
the Expected
Return on
Dollar
Deposits
The Current Exchange Rate and the
Expected Return on Dollar Deposits
Current exchange
rate, E$/€
1.07
1.05
1.03
1.02
1.00
0.031
0.050
R$
0.069
0.079 0.100
Expected dollar return
on dollar deposits, R$
Equilibrium Exchange Rate
• Equilibrium in the FX market obtains
when:
R = R* + (Ee - E)/E
• (Uncovered) Interest Parity condition
– If R > R* + (Ee - E)/E  DC assets are more
attractive and the DC appreciates.
– If R < R* + (Ee - E)/E  FC assets are more
attractive and the DC depreciates.
Determination of the Equilibrium
Exchange Rate
No one is willing to
hold euro deposits
No one is willing to
hold dollar deposits
Changes in R, R*, and Ee
The domestic currency
• Appreciates (E) if the domestic interest
rate rises (R ).
• _____ (E__) if the foreign interest rate
rises (R* ).
• _____ (E__) if the domestic currency is
expected to depreciate (Ee ).
The Effect of a Rise in the
Dollar Interest Rate
A depreciation
of the euro is
an appreciation
of the dollar.
The Effect of a Rise in the
Euro Interest Rate
The Effect of an Expected
Appreciation of the Euro
People now
expect the
euro to
appreciate