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 arbitrageQ: The pound is priced at $1.50 in NY and $1.45 in

London. What would you do as a currency arbitrageur?

b. Triangular arbitrageQ: 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 now3-month forward rate = .9188Pay $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 rateE = 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/€

Current exchange rate

Interest rate on euro deposits

Expected rate of dollar

depreciationExpected 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

Expected dollar return on dollar deposits, R$

Current exchange rate, E$/€

1.02

1.03

1.05

1.07

0.031 0.050 0.069 0.079 0.100

1.00

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 depreciationof the euro isan appreciationof 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