Lecture 2

Lecture 2: Exchange Rates and the Foreign Exchange MarketTopics: Exchange Rates Foreign exchange market Asset approach to exchange rates

Interest Rate Parity Conditions

1 Definitions a) Define Exchange Rates: Def of exchange rate: price of one currency in terms

of another. The conventional way of reporting this in economics i

s home currency per foreign. In the U.S. this is $ per foreign currency.(direct or American terms)

For example, currently it would take about $1.50 to buy one European euro (E$/euro) This is the convention in economics and will be used in this class.

Sometimes you will hear quoted the other way around, often called European terms. ie: 0.9 euro/$.

b) Exchange rates are important for trade because they allow you to compare the cost of imports to that of domestic goods in common terms. There was a period when Americans were going to Germany to buy Mercedes and bring them home, rather than buying them in the U.S.

Example: Consider the Mercedes: suppose the going price is 50 thousand euros in Germany and 80 thousand dollars in the US. Would people flock to Germany? Depends on the exchange rate - comparing $ and euro is like comparing apples and oranges.

Suppose the $/euro exchange rate is 1.5. So the 50 thousand euros equals: 50 thousand euros * (1.50$/euro) = 75 thous

and $ At this exchange rate, looks like its cheaper

to buy the car in Germany.

How know using the rate not upside down? Look at units: have euro, want dollars, so multiply by $/euro and euro cancels out, and you left with units in dollars.

c) Note: the way we conventionally define the exchange rate can also make it confusing to talk about changes in the exchange rate, which we call appreciations and depreciations.

Appreciation: increase in value of the given currency relative to another.

Say the $/euro rate changed from 1.5 to 1.4, we say the dollar appreciated relative to the euro. Or we could say the euro depreciated relative to the dollar.

Note that Note that this can be confusing. Given how

we define the exchange rate as home currency per foreign, if this gets lower, it means that it takes less home currency units to buy a foreign currency unit, and this means the home currency is worth more. Hence a appreciation of the home currency.

2 Features of foreign exchange market.

a) Actors 1) commercial banks: Commercial

banks are at the center of the foreign exchange market because almost every sizable international transaction involves the debiting and crediting of accounts at commercial banks in various financial centers.

Interbank trading

Banks routinely enter the foreign exchange market to meet the needs of their customers—primarily corporations. In addition, a bank will also quote to other banks exchange rates at which it is willing to buy currencies from them and sell currencies to them. Foreign currency trading among banks—called interbank trading—accounts for most of the activity in the foreign exchange market.

The rates available to corporate customers, called "retail" rates, are usually less favorable than the "wholesale“ interbank rates. The difference between the retail and wholesale rates is the bank's compensation for doing the business.

2) Corporations: Corporations with operations in several countries frequently make or receive payments in currencies other than that of the country in which they are headquartered.

3) Nonbank financial institutions: Over the years, deregulation of financial markets in the United States, Japan, and other countries has encouraged nonbank financial institutions to offer their customers a broader range of services, many of them indistinguishable from those offered by banks. Among these have been services involving foreign exchange transactions. Institutional investors, such as pension funds, often trade foreign currencies.

4) Central banks. Learned in BOP accounts that central banks sometimes intervene in the foreign exchange market. While the volume of central bank transactions is typically not large, the impact of these transactions may be great.（Why）

b) Characteristics

Volume is enormous: over a trillion dollars a day.

Banks dealing in e market tend to be concentrated in certain key financial cities: know which biggest? London largest, but also NY, Tokyo, Frankfurt and Singapore.

Highly integrated globally: when one major market is closed usually another is open, so people can trade around the clock, moving from one center to another.

Integration means exchange rate quotes in different centers must be the same. Is guaranteed by arbitrage, defined as making a riskless profit on a financial trade？

If NY offer more euros for a $ (lower price of euros, higher price of $, E$/euro is low) than Frankfurt, then people will take their $, sell in NY for bunch of euros, then sell these in Frankfurt for dollars again and end up with more dollars than they started.

Possibility for you to make riskless profit? No ， because of short-lived.

The increased demand for euros in NY would drive up the price of euros in terms of $ - this is an exchange rate depreciation for the $.

There are computers monitoring such openings and ready to take advantage of them.

So gaps close up very quickly.

Vehicle currency. Most foreign exchange transactions are betwee

n banks and take place in $, even if want to change Swedish Kroner for Polish zloty, not dollars.

Easier to change Kroner first to $ and then $ to zlotys. Since US is so important in world economy, there are many people willing to trade dollars for Kroner and zloty for dollars, to take the opposite sides of your trade, rather than the opposite side of a direct Kroner for zloty trade.

Euro and Yen are also used as vehicles, but less so at current time.

c) Spot and forward rates

The exchange transactions talked about so far take place on the spot.

Spot rates are exchange rates for currency exchanges “on the spot”, or when trading is executed in the present.

In practice it can’t be right away because it typically takes two days for the checks to clear used to make the payments.

Forward rates are exchange rates for currency exchanges that will occur at a future (“forward”) date. forward dates are typically 30, 90, 180 or 360

days in the future.

rates are negotiated between individual institutions in the present, but the exchange occurs in the future.

Suppose Best Buy electronics is expecting a shipment of Sony TVs in a month, for which it needs to pay yen.

Could wait until the shipment to buy the yen to pay Sony, but not know what will happen to value of that yen in meantime.

If yen appreciates a lot, the $ price that the store has to pay to get the TVs could change a lot.

To avoid this risk, the store can arrange for currency trade ahead of time to be executed later at a set exchange rate. This rate is the forward rate.

Spot and Forward Rates

D） Other methods of currency exchange

Foreign exchange swaps: a combination of a spot sale with a forward repurchase, both negotiated between individual institutions. swaps often result in lower fees or

transactions costs because they combine two transactions.

Why do this? Say our electronics store sold some computers in Japan and got yen, know will need them again in a month to buy Sony TVs, but not want to hang on the money in yen over the month, want to hold it in dollars for domestic expenses.

Might be lower brokers fees if arrange both transactions at one time.

Futures contracts: a contract designed by a third party for a standard amount of foreign currency delivered/received on a standard date. contracts can be bought and sold in markets, an

d only the current owner is obliged to fulfill the contract.

Some people just trade these contracts to make a profit, because expect the value of the contract to change as expectations for exchange rate movements change. This is an example of currency speculation.

i.e. if suddenly looks like $ will appreciate, a contract specifying dollars be delivered for a given amount of yen looks more profitable, and price of contact will go up.

Options contracts: a contract designed by a third party for a standard amount of foreign currency delivered/received on or before a standard date.

contracts can be bought and sold in markets.

a contract gives the owner the option, but not obligation, of buying or selling currency if the need arises.

Call option: have the right to buy an amount of currency at a specified e rate any time before a specified date.

Put option: right to sell. Like futures, options can themselves be

bought and sold.

3 Asset approach to exchange rates:

Preview: Theories of exchange rate determination

Now we come to the question of how does the foreign exchange market determine what the exchange rate will be. There two main theories we will study here:

The asset approach – which is based upon “interest rate parity”

The monetary approach – which is based upon “purchasing power parity”

Each of these tells a logical but somewhat different story of how the e rate is determined.

A general theme in the next couple lectures will be to discuss these stories, the empirical evidence on how well each explains e rate movements, and how the two theories perhaps could be integrated together.

Asset Approach: First we discuss the asset approach. Recall that most foreign exchange holdings are in form of bank deposits, which is a type of asset, and these can be analyzed as any other asset.

The Demand for Currency Deposits

What influences the demand for (willingness to buy) deposits denominated in domestic or foreign currency?

Factors that influence the return on assets determine the demand for those assets.

The Demand for Currency Deposits (cont.)

Rate of return: the percentage change in value that an asset offers during a time period. The annual return for $100 savings account with an interest rate of

2% is $100 x 1.02 = $102, so that the rate of return = ($102 - $100)/$100 = 2%

Real rate of return: inflation-adjusted rate of return. stated in terms of real purchasing power: the amount of real goods

& services that can be purchased with the asset.

the real rate of return for the above savings account when inflation is 1.5%: 2% – 1.5% = 0.5%. The asset can purchase 0.5% more goods and services after 1 year.


If prices are given at some level, inflation is 0% and (nominal) rates of return = real rates of return.

For bank deposits in different currencies, we often assume that prices are given at some level. (A good short run assumption.)


Risk of holding assets also influences decisions about whether to buy them.

Liquidity of an asset, or ease of using the asset to buy goods and services, also influences the willingness to buy assets.

But we assume that risk and liquidity of bank deposits in the foreign exchange market are the same, regardless of their currency denomination. risk and liquidity are only of secondary importance when deciding to

buy or sell currency.

importers and exporters may be concerned about risk and liquidity, but they make up a small fraction of the market.


We assume that investors are primarily concerned about the rates of return on bank deposits. Rates of return are determined by

interest rates that the assets earn

expectations about appreciation or depreciation


A currency’s interest rate is the amount of a currency an individual can earn by lending a unit of the currency for a year.

The rate of return for a deposit in domestic currency is the interest rate that the bank deposit earns.

To compare the rate of return on a deposit in domestic currency with one in foreign currency, consider the interest rate for the foreign currency deposit the expected rate of appreciation or depreciation of the foreign

currency relative to the domestic currency.


Suppose the interest rate on a dollar deposit is 2%.

Suppose the interest rate on a euro deposit is 4%.

Does a euro deposit yield a higher expected rate of return? Suppose today the exchange rate is $1/€1, and the expected rate 1

year in the future is $0.97/€1.

$100 can be exchanged today for €100.

These €100 will yield €104 after 1 year.

These €104 are expected to be worth $0.97/€1 x €104 = $100.88.


The rate of return in terms of dollars from investing in euro deposits is ($100.88-$100)/$100 = 0.88%.

Let’s compare this rate of return with the rate of return from a dollar deposit. rate of return is simply the interest rate After 1 year the $100 is expected to yield $102:

($102-$100)/$100 = 2%

The euro deposit has a lower expected rate of return: all investors will prefer dollar deposits and none are willing to hold euro deposits.


Note that the expected rate of appreciation of the euro is ($0.97- $1)/$1 = -0.03 = -3%.

We simplify the analysis by saying that the dollar rate of return on euro deposits approximately equals the interest rate on euro deposits plus the expected rate of appreciation on

euro deposits 4% + -3% = 1% ≈ 0.88%

R€ + (Ee$/€ - E$/€)/E$/€


The difference in the rate of return on dollar deposits and euro deposits is

R$ - (R€ + (Ee$/€ - E$/€)/E$/€ ) =

R$ - R€ - (Ee$/€ - E$/€)/E$/€

expected rate of return = interest rate on dollar deposits

interest rateon euro deposits

expected rate of return on euro deposits

expected exchange rate

currentexchange rate

expected rate of appreciation of the euro

The Demand for Currency Assets

The Market for Foreign Exchange

We use the demand for (rate of return on) dollar denominated

deposits and the demand for (rate of return on) foreign currency

denominated deposits to construct a model of the foreign exchange market.

The foreign exchange market is in equilibrium when deposits of all currencies offer the same expected rate of return: interest parity. interest parity implies that deposits in all currencies are

deemed equally desirable assets.

The Market for Foreign Exchange (cont.)

Interest parity says:

R$ = R€ + (Ee$/€ - E$/€)/E$/€

Why should this condition hold? Suppose it didn’t. Suppose R$ > R€ + (Ee

$/€ - E$/€)/E$/€ . Then no investor would want to hold euro deposits, driving down th

e demand and price of euros. Then all investors would want to hold dollar deposits, driving up the

demand and price of dollars. The dollar would appreciate and the euro would depreciate, increasi

ng the right side until equality was achieved.


How do changes in the current exchange rate affect expected returns in foreign currency?


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.

Appreciation of the domestic currency today raises the expected return of deposits in foreign currency. A current appreciation of the domestic currency will lower the initial

cost of investing in foreign currency, thereby raising the expected return in foreign currency.

Expected Returns on Euro Deposits when Ee

$/€ = $1.05 Per Euro

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$

Determination of the Equilibrium Exchange Rate

No one is willing to hold euro deposits

No one is willing to hold dollar deposits

The Market for Foreign Exchange

The effects of changing interest rates:

an increase in the interest rate paid on deposits denominated in a particular currency will increase the rate of return on those deposits.

This leads to an appreciation of the currency.

A rise in dollar interest rates causes the dollar to appreciate.

A rise in euro interest rates causes the dollar to depreciate.

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

The Effect of an Expected Appreciation of the Euro (cont.) If people expect the euro to appreciate in the

future, then investment will pay off in a valuable (“strong”) euro, so that these future euros will be able to buy many dollars and many dollar denominated goods. the expected return on euros therefore increases. an expected appreciation of a currency leads to an

actual appreciation (a self-fulfilling prophecy) an expected depreciation of a currency leads to an

actual depreciation (a self-fulfilling prophecy)

Empirical tests on interest parity.

It is difficult to test the interest rate parity condition, because it is difficult to get a measure of people’s expectations.

Some economists have used the actual future exchange rate as a proxy for expectations in the past, assuming that people correctly predict the future rate.

Some economists have used survey data on expectations – they call people who take part in the foreign exchange market and ask them what rates they expect.

Both sets of tests tend to find the interest parity condition does not hold well. But this may simply reflect the fact that the expected future exchange rate component of the equation was measured with error, not that the theory was wrong.

Another reason why the tests may reject the interest parity condition is the role of risk.

There is some risk involved because you do not know ahead of time what the future exchange rate will be; if your expectations turn out to be wrong, the payoff from your investment scheme may be different from what you expected. This may make people require an extra expected return on EURO deposits as compensation for uncertainty. In this case there would be an extra term in the interest parity equation: RP representing the risk premium:

R$ = REURO + (Ee $/EURO - E$/EURO)/ E$/EURO - RP (Note: RP can in principle be either positive or neg

ative, depending on how the risk is perceived both by people trading EURO for $ and those trading $ for EURO, since both groups are exposed to risks of different types).

Covered Interest Parity

Covered interest parity relates interest rates across countries and the rate of change between forward exchange rates and the spot exchange rate:

R$ = R€ + (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 make easy, risk-free money in the foreign exchange

markets if covered interest parity did not hold? Covered positions using the forward rate involve little risk.

Summary

1. Exchange rates are prices of foreign currencies in terms of domestic currencies, or vice versa.

2. Depreciation of a country’s currency means that it is less expensive (valuable) and goods denominated in it are less expensive: exports are cheaper and imports more expensive. A depreciation will hurt consumers of imports but help

producers of exports.

Summary (cont.)

3. Appreciation of a country’s currency means that it is more expensive (valuable) and goods denominated in it are more expensive: exports are more expensive and imports cheaper. An appreciation will help consumers of imports but hurt producers

of exports.

4. Commercial banks that invest in deposits of different currencies dominate the foreign exchange market. Expected rates of return are most important in determining the

willingness to hold these deposits.

Summary (cont.)5. Returns on bank deposits in the foreign

exchange market are influenced by interest rates and expected exchange rates.

6. Equilibrium in the foreign exchange market occurs when returns on deposits in domestic currency and in foreign currency are equal: interest rate parity.

7. An increase in the interest rate on a currency’s deposit leads to an increase in the rate of return and to an appreciation of the currency.

Summary (cont.)

8. An expected appreciation of a currency leads to an increase in the expected rate of return for that currency, and leads to an actual appreciation.

9. Covered interest parity says that rates of return on domestic currency deposits and “covered” foreign currency deposits using the forward exchange rate are the same.

Case 1

In Munich a bratwurst costs 2 euros; a hot dog costs $1 at Boston’s Fenway Park. At an exchange rate of $1.5/per euro, what is the price of a bratwurst in terms of hot dogs? All else equal, how dose this relative price change if the dollar appreciates to $1.25 per euro? Compared with the initial situation, has a hot dog become more or less expensive relative to a bratwurst?

Answer 1

At an exchange rate of $1.50 per euro, the price of a bratwurst in terms of hot dogs is 3 hot dogs per bratwurst.

After a dollar appreciation to $1.25 per euro, the relative price of a bratwurst falls to 2.5 hot dogs per bratwurst.

Case 2

A U.S. dollar costs 7.5 Norwegian kroner, but the same dollar can be purchased for 1.25 Swiss Francs. What is the Norwegian krone/Swiss francs exchange rate?

Case 3 Calculate the dollar rates of return on the following assets:

a. A painting whose price rises from $200,000 to $250,000 in a year.

b. A bottle of rare Burgundy, whose price rises from $180 to $216 between 2006 and 2007.

Case 3

c. A 10,000 pounds deposit in a London bank in a year when the interest rate on pounds is 10%,and $/pound exchange rate moves from $1.50 per pound to $1.38 per pound.

Case 4

What would be the real rates of return on the assets in the case 3 if the price changes described were accompanied by a simultaneous 10 percent increase in all dollar prices?

Case 5 Suppose the dollar interest rate and the

pound sterling interest rate are the same,5 percent per year. What is the relation between the current equilibrium $/£ exchange rate and its expected future level? Suppose the expected future $/£ exchange rate, $1.52 per pound, Britain’s interest rate rises to 10 percent per year. If the U.S. interest rate also remains constant, what is the new equilibrium $/£ exchange rate?

Question 1 Suppose you have $50,000 you wish to invest.

For each of the following scenarios explain whether you would be better off putting your money in the foreign or domestic alternative presented. Assume that the level of risk is same for the two alternatives in each case.

a. You don’t anticipate needing your money for 10 years. Historically the US stock market has a long run return of about 15% per year. You expect that trend to continue. The stock market in Taiwan has historically yielded a return of 22% per year, though you expect only half that return over the next ten years due to the financial turmoil in Asia. A US dollar is currently worth 33 Taiwanese dollars. You expect the exchange rate to hold steady over the next ten years.

Answera. Since there is no anticipated change in the

exchange rate, all that you need to do is compare the expected return of 15% in the US to the expected return of 11% in Taiwan. Since the US return is higher, you do better by keeping your money in the US. The historical return of 22% in Taiwan is irrelevant here.

b. You know you will need your money in 2 years. The interest rate on corporate bonds in the US is 5% while corporate bonds in Peru carry an interest rate of 14%. The current exchange rate is 3.34 New Sol per dollar. You expect that in two years the exchange rate will be 4.8 New Sol per dollar.

b. Keeping your money in the US for the two years yields a gross return of $50,000 x (1.05)2 = $55,125. Putting your money in the Peruvian bond yields a gross return of $50,000 x (1.14)2 x 3.34 x (1/4.8) = $45,215. Thus you should keep your money in the US because the expected depreciation of the New Sol more than cancels out the higher interest rate in Peru.

c. You only want to invest for four months. The interest rate on bank deposits on Euros is 4.5% while that on dollar deposits is 3.5%. The current exchange rate is 0.92 Euros per dollar. You expect the exchange rate to be 0.93 Euros per dollar four months from now.

c. Again you should keep your money in the US. Using a similar method to that in part b, we see that in the US, the gross bank account return is approximately $50,580, while the return on the Euro account is only about $50,200.

Question 2 a. Suppose that the South African interest rate is 4% and

the US interest rate is 6%. If the expected future spot exchange rate one year from now is 6.05 Rand per dollar, what must the current spot exchange rate be in order to clear the foreign exchange market?

b. Suppose that the expected future spot rate is 6.25 rather than 6.05. How does that alter the equilibrium exchange rate you calculated in part a?

c. Using the expected exchange rate from part b, explain what would happen if the South African interest rate happened to be 6.7%. Can your answer to part b also be the answer to this question? Explain.

d. Ignoring your expectations about the future spot rate, what would be the equilibrium forward exchange rate using the information given in part c if there is no risk premium and if covered interest rate parity holds?

Lecture 2

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