Foreign Exchange 1

Foreign Exchange

BA 282

Macroeconomics

Class Notes - Part 3

Foreign Exchange 2

Foreign Exchange Rates The exchange rate is the price of one country’s

currency in terms of another country’s currency Quoted exchange rates can be either direct or

indirect, one method is usually the convention Direct: home currency per unit of foreign currency

Examples from US perspective:

1.676 US Dollars (USD) per British Pound (GBP)

1.152 US Dollars (USD) per Euro (EUR)

Indirect: foreign currency per unit of home currency Examples from US perspective:

109.58 Japanese Yen (JPY) per US Dollar (USD)

1.3664 Swiss Francs (CHF) per US Dollar (USD)

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Prices in Foreign Currency

Use the exchange rate in direct terms

Example 1: How much does a €100 sweater cost an American if the exchange rate is 1.15 $/€?

Price in $ = €100 * 1.15 $/€ = $115.00

Example 2: How much does a 100 CHF sweater cost an American if the exchange rate is 1.37 CHF/$?

Price in $ = 100 CHF * (1 / 1.37 CHF/$) = $72.99

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Depreciation and Appreciation

A depreciation of the local currency means that it takes more local currency to buy a unit of foreign currency An appreciation of the local currency is the opposite

Example: If the $/€ exchange rate goes up from 1.10 to 1.20 the

dollar has depreciated against the euro

but, the euro has appreciated against the dollar.

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Depreciation and the Price of Imports

A depreciation of a country’s currency makes its goods cheaper for foreigners and makes foreign goods more expensive.

Example: Consider a bottle of French wine that costs $20 when the $/€ exchange rate is 0.85. Now what is the $ price of the bottle of wine if the dollar depreciates to 0.95 $/€ ?Price in € before depreciation = $20 (1/0.85 $/€ ) = € 23.53

Price in $ after depreciation = € 23.53 (0.95 $/€ ) = $ 22.35

or

Price in $ after depreciation = $20 (0.95/0.85) = $ 22.35

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Foreign Exchange Trading The vast majority of foreign exchange (FX) trading

is done over-the-counter (OTC)

Most transactions have the USD on one side Dollar is called a vehicle currency

Trading is centered at major multinational banks (called dealers) such as Citibank, Bank of America, Deutsche Bank, HSBC, etc.

By volume, it is the largest market in the world Average daily turnover is about 1.5 trillion USD

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Foreign Exchange Trading Trading takes place 24 hours a day during the

business week

Trading moves around the globe:London => New York => Tokyo => London

Other important participants are Corporations Nonbank financial institutions Central banks

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For current rates see: http://online.wsj.com/documents/mktindex.htm?worldval.htm

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Spot vs. Forward rates Spot Rate: the exchange rate that is applicable

today The settlement or value date for a spot transaction (the

date on which the parties actually exchange assets) occurs two business days after the deal is made

Forward Rate: the exchange rate agreed on today for a transaction at a future date. Most commonly quoted 30, 90, or 180 days in the future. The forward exchange rate is set so that no money

changes hands today.

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Forward Example

Boeing plans to deliver a 777 to KLM in six months and receive 110 million Euros. Boeing calls Citibank and enters into a 180-day forward contract at a forward rate of 0.8700 $/€.

This obligates Boeing to deliver €110m to Citibank in 180 days in exchange for

€ 110m * 0.8700 $/€ = $ 95.700m

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Why Use Forwards Suppose that Boeing did not enter into a forward

agreement. What would be the dollar proceeds from the sale if in 6 months the Euro ends up trading at:

USD/EUR USD Proceeds

0.82 0.82 * 110m = $ 90.2m

0.87 0.87 * 110m = $ 95.7m

0.92 0.92 * 110m = $ 101.2m

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Derivative Securities A forward contract is the simplest form of a

derivative security

Definition: A derivative security is a financial contract that derives its value from the price of another underlying asset.

Other common examples: Swaps Put and call options Futures contracts (exchange-traded forwards)

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FX Trading Statistics

Average Daily Volume(USD Billions)

Transaction Type April 2004

Spot Transactions 621

Forwards and Forex Swaps 1,152

Currency Swaps 21

Options 117

Correction for reporting errors -31

Estimated Total 1,880

Source: Bank for International Settlements

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FX Derivative Market StatsThe Global Foreign Exchange Derivatives Markets

Notional Amounts Outstanding in Billions of US Dollars

December 2003

Total contracts 24,475

with other reporting dealers 8,660 with other financial institutions 9,450 with non-financial customers 6,365

up to one year 18,840 between one and five years 3,901 over five years 1,734

Memorandum Item: Exchange-traded Contracts 132

Source: Bank for International Settlements

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JPY/USD

0

50

100

150

200

250

300

350

4001970

1975

1980

1985

1990

1995

2000

2005

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Trade-Weighted USD Exchange Rate

The index is a weighted average of the foreign exchange values of the U.S. dollar against other major currencies. The index weights, which change over time, are derived from U.S. export shares. The index is calculated in indirect terms so higher values imply a stronger USD.

60

80

100

120

140

160

1973

1978

1983

1988

1993

1998

2003

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USD/EUR

0.80

0.90

1.00

1.10

1.20

1.30

1.40Jan-99

Jul-99

Jan-00

Jul-00

Jan-01

Jul-01

Jan-02

Jul-02

Jan-03

Jul-03

Jan-04

Jul-04

Jan-05

Jul-05

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The Law of One Price

In competitive markets free of transportation costs and other barriers to trade, identical goods sold in different countries must sell for the same price (when expressed in the same currency).

Why?

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The Law of One Price We can write an equation for the law of one price

as,

PiLC = Pi

FC * Ewhere

PiLC is the local currency price of good i

PiFC is the foreign currency price of good i

E is the dollar to euro exchange rate

Or we can rearrange the equation to get

E = PiLC / P

iFC

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Purchasing Power Parity (PPP) PPP looks just like the law of one price except the

prices are for a “basket” of goods rather than for a particular good so

E = PLC / PFC

or

PLC = PFC * E

where

PLC is the local currency aggregate price level

PFC is the foreign currency aggregate price

level

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Invented in 1986 as a light-hearted guide to whether currencies are at their “correct” level, burgernomics is based on the theory of purchasing-power parity (PPP). This says that, in the long run, exchange rates should move toward rates that would equalise the prices of an identical basket of goods and services in any two countries. To put it simply: a dollar should buy the same everywhere. Our basket is a McDonald's Big Mac, produced locally to roughly the same recipe in 118 countries. The Big Mac PPP is the exchange rate that would leave burgers costing the same as in America. Comparing the PPP with the actual rate is one test of whether a currency is undervalued or overvalued.

The first column of the table shows local-currency prices of a Big Mac. The second converts them into dollars. The average price of a Big Mac in four American cities is $2.71. The cheapest burgers are in China ($1.20); the dearest are in Switzerland ($4.52). In other words, the yuan is the most undervalued currency, the Swiss franc the most overvalued. The third column calculates Big Mac PPPs. Dividing the local Chinese price by the American price gives a dollar PPP of 3.65 yuan. The actual exchange rate is 8.28 yuan, implying that the Chinese currency is undervalued by 56% against the dollar.

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Purchasing Power Parity (PPP) PPP asserts that all countries’ price levels are

equal when measured in terms of the same currency Note: In practice the basket of goods is the same as the

one used for the CPI

PPP predicts that a decline (increase) in a currency’s domestic purchasing power will be associated with a proportional currency depreciation (appreciation) in the foreign exchange market

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Absolute PPP vs. Relative PPP

Absolute PPP (PLC = PFC * E) represents the

relationship between the level of the exchange rate and the level of prices in the two economies

Relative PPP states that the percentage change in the exchange rate will be equal to the difference in the percentage change in the price levels in the two countries

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Absolute PPP vs. Relative PPP

We can write an equation for Relative PPP as

(Et - Et-1)/ Et-1 = LC,t – FC,t

where i,t is the inflation rate Pi,t - Pi,t-1)/ Pi,t-1 in country i between

time t-1 and t

Et is the exchange rate at time t

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Empirical Evidence on PPP To test absolute PPP, we measure the price level

of a basket of goods in various countries. For example, The Economist’s Big Mac Index

To test relative PPP we can look at the correlation between exchange rates and relative price levels Typically correlations are low

Empirically, PPP theory does poorly in predicting exchange rate movements for developed countries

Why is it hard to test these theories?

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Problems with PPP Transport costs and trade barriers

If it costs a substantial amount to transport goods, then this prevents the ability to do “arbitrage”

In some industries transport costs are effectively infinite (e.g., housing). These are called nontradable goods.

Governments usually have import tariffs, etc.

Monopolistic or oligopolistic practices

Measurement differences

“Sticky” prices

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Demand for Foreign Currency

If we think of foreign currency as a financial asset then the demand for foreign currency will depend on the investment properties of foreign currency

For example, we might consider the following properties Expected Return Risk Liquidity Inflation

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Demand for Foreign Currency For now we are going to concentrate on only one of these

Expected Return

Notation

RLC Interest rate in local currency (e.g., USD)

RFC Interest rate in foreign currency (e.g., EUR)

Et Actual exchange rate at time t in LC/FC

Ee Expected exchange rate in one year

(this is the expectation of a random

variable)

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Demand for Foreign Currency Definition: The annual rate of depreciation of LC

relative to FC is the percentage increase in E over one year,

rate of depreciation = (E1 - E0) / E0

The LC rate of return on FC deposits is approximately RFC plus the rate of depreciation

Today we do not know what E1 will be, only what we expect it to be (Ee). So,

expected rate of return on FC = RFC + (Ee - E0) / E0

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FX Market Equilibrium

Equilibrium in the foreign exchange market is defined as

difference in rate of return = RLC - RFC - (Ee - E0) / E0 = 0

This is also called the interest parity condition and can be written as

RLC = RFC + (Ee - E0) / E0

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Graphing Interest Parity We can rearrange this equation so that

E0 = Ee / (1 + RLC - RFC)

Example: Suppose R€=5.2% and Ee=0.95 $/€, what is the exchange rate today (E0) for the following USD interest rates?

R$ E0

2%

4%

6%

8%

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Plot the Points

Rate of Return ($)

Exchange Rate ($/€)

Expected Return on € Deposits

8%6%4%2%

0.9814

0.9615

0.9425

0.9241

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Graphical Equilibrium

Rate of Return (LC)

Exchange Rate (LC/FC)

RLC

E0*

E0’

E0’’

Expected Return on FC Deposits

1

2

3

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Changing LC Interest Rates and Exchange Rate Equilibrium

Rate of Return (LC)

Exchange Rate (LC/FC)

RLC

E0’

E0

Expected Return on FC Deposits

1

2

R’LC

1’

LC Appreciates

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Changing FC Interest Rates and Exchange Rate Equilibrium

Rate of Return (LC)

Exchange Rate (LC/FC)

E0

E0’

Expected Return on FC Deposits

1

RLC

2

Rise in FC Interest Rate

LC Depreciates

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Money, Interest Rates, & Exchange Rates

We can combine what we learned previously about the demand for money with what we now know about exchange rates

This gives a more integrated picture of how money, interest rates, and exchange rates interact

For convenience let’s rotate the money market graph clockwise 90o and combine it with the FX market graph

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Money Market / Exchange Rate Linkages

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Time path of US economic variables after a permanent increase in the US money supply

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FX & Currency Swaps A swap is an agreement between two parties to

exchange a predefined set of cashflows for a specified period.

A FX swap is the spot sale of a currency combined with a forward repurchase agreement (like a repo)

A simple currency swap is when one counterparty would agree to pay €10 million each year for five years. The other counterparty would agree to pay $8 million each year for five years. Note that this currency swap is just a set of five forward

contracts.

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FX & Currency Swap facts Most currency swaps entail an up-front exchange of

principal (unlike interest rate swaps)

Like FX forwards, most FX swaps have one side in USD

Currency swaps tend to be traded at longer maturities than forwards or options (> 1 year)

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FX Options A call (put) option gives the owner the right but not the

obligation to buy (sell) foreign currency at a prespecified exchange rate (called the strike) at a prespecified date.

An option allow the owner to participate in exchange rate changes in one-direction only

Consequently, options always have an upfront cost (called the premium)

For a US investor, call options payoff when the USD/FCU exchange rate increases put options payoff when the USD/FCU exchange rate decreases

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Calls and PutsCall OptionX = Strike

C0 = Call Premium

Net Payoff = max(E-X,0) - C0

Payoff

USD/FCUat Maturity

X

C0

Put OptionX = Strike

P0 = Put Premium

Net Payoff = max(X-E,0) - P0

Payoff

USD/FCUat MaturityX

P0

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Put Option Example Put options are frequently used to “hedge” foreign

exchange revenues Back to Boeing example,

Recall Boeing expects to receive 110 million Euros in six months. Boeing calls Citibank and buys a 180-day put option with a strike of 0.85 $/€ for a premium of $2 million today.

When does Boeing exercise the put option? Would the put option premium be more or less if the

strike was 0.80 $/€?

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Changes in E0 and Expected Returns

How does a change in E0 (all else held constant)

change the LC expected return of FC deposits? Example:

E0 equals 1.00$/€ and Ee equals 1.05$/€.

Now suppose E0 increases to 1.03$/€

What happens to the dollar return on euros?

In general, a depreciation of the local currency results in a decrease in the local currency return of foreign currency deposits