· Web viewIn short, currency 1 appreciates if E 1/2 falls.Equivalently, currency 1 appreciates if the change of the exchange rate is negative: Δ E 1/2 = E 1/2, later - E 1/2, before

Chapter 2: Introduction to exchange rates and the foreign exchange market

Key words: Exchange rate, interest rate and arbitrage

Goals: Understanding how the market for foreign exchange works

Definition: An exchange rate (E) is the price of some foreign currency.

There are two equivalent formats in which the exchange rate is quoted.

1 EUR = 1.4033 USD

is equivalent to

1 USD = 0.7126 EUR

To avoid confusion, I will state explicitly the format of foreign exchange in lecture notes and exams.

Example 1: The US exchange rate against the euro is US dollars per euro, denoted by E$/€.

Notice that euro is the denominator, and US dollar is the numerator.

Exercise: please find the latest US exchange rate against euro from google finance.

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1 EUR = ___________ USD

In symbol, E$/€ = ____________________.

Example 2: from google finance, find the British Pound exchange rate against US dollar.

In symbol, E£/$ = ____________________.

In general E1/2 denotes the exchange rate in units of country 1 currency per unit of country 2 currency.

The exchange rate of currency 1 is expressed as E1/2

A currency appreciates (or strengthens) if it is worth more other currency.

A currency depreciates (or weakens) if it is worth less other currency.

If E1/2 is going up, then one unit of country 2 currency can be converted to ( more less ) country 1 currency. As a result, the country 2 currency ( appreciates depreciates ); while the country 1 currency ( appreciates depreciates).

In short, currency 1 depreciates if E1/2 rises.

Equivalently, currency 1 depreciates if the change of the exchange rate is positive: Δ E1/2 = E1/2, later - E1/2, before > 0.

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If E1/2 is going down, then one unit of country 2 currency can be converted to ( more less ) country 1 currency. As a result, the country 2 currency ( appreciates depreciates ); while the country 1 currency ( appreciates depreciates).

In short, currency 1 appreciates if E1/2 falls.

Equivalently, currency 1 appreciates if the change of the exchange rate is negative:Δ E1/2 = E1/2, later - E1/2, before < 0.

Fact: if currency 1 appreciates against currency 2, then currency 2 must depreciate against currency 1. The values of the two currencies move in opposite direction.

Exercise: from google finance, on December 31, 2010, E$/€ = _______________on May 4, 2011, E$/€ = _______________During this period, Euro ( appreciates depreciates ); US dollars ( appreciates depreciates ).

Typically, a country is trading with more than one country. The effective exchange rate is the trade-weighted average of exchange rates against a basket of currencies.

Example

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Suppose 40% of Home country trade is with country A and 60% is with country B. Currency H appreciates 10% against currency A but depreciates 30% against currency B. Please calculate the change in Home country’s effective exchange rate.Δ EH/A = ____________________

Δ EH/B = ____________________

Weight for currency A = ___________________

Weight for currency B = ___________________

Δ Eeffective = ____________________

In words, currency H ( appreciates depreciates ) by __________.

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Overall, US dollar ( appreciates depreciates )

We can use exchange rate to compare prices in a common currency

ExampleIn July 2008, a Big Mac was sold at $3.57 in USA and £2.29 in UK. The exchange rate is E£/$=0.5. Please show which country has high price of a Big Mac.

E$/£ = __________

(Answer 1, use $ as the common currency)

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The dollar price of a Big Mac in USA = ____________________

The dollar price of a Big Mac in UK = _____________________

(Answer 2, use £ as the common currency)

The pound price of a Big Mac in USA = ____________________

The pound price of a Big Mac in UK = _____________________

Exercise: suppose the pound price of a Big Mac in UK remains unchanged, but pound depreciates against dollar. Then the dollar price of a Big Mac in UK goes (up down).

Reality Check 1: What happens to US’ imports from China if Chinese Yuan appreciates?

Reality Check 2: What happens to the number of Chinese students at Miami U if Chinese Yuan appreciates?

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Fact: depreciation makes home goods less expensive in foreign countries, and therefore boosts export to foreign countries.

Y = C + I + G + NX(E)

There are two major types of exchange rate regimes.

Fixed (or pegged) exchange rate regimes are those in which a country’s exchange rate fluctuates in a narrow range (or not at all) against some based currency over a sustained period. Government needs to intervene in the market to make the exchange rate rigidly fixed.

Floating (or flexible) exchange rate regimes are those in which a country’s exchange rate fluctuates in a wider range, and the government makes no attempt to fix it against any base currency.

Some groups of countries agree to form a currency union.

Some countries dollarize by adopting the currency of another country as their own.

Check Figures 2-2 and 2-3 in the textbook.

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Foreign exchange (FX) market is the market where the exchange rate is determined by market forces.

Spot exchange rate is the exchange rate for the spot transaction, in which immediate exchange of one currency for another happens between two parties.

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When individuals buy a little foreign currency through a retail channel, the pay a higher price than the midrange quote seen in the press; and when they sell, they are paid a lower price. The difference between the “buy at” and “sell for” prices is spread, an example of transaction cost.

Forward exchange rate is the exchange rate for the forward contract, in which the settlement date for the delivery of the currencies is in the future.

Forward rate tends to track spot rate closely. Check Figure 2-5.

Forward contracts (and more generally, derivatives) allow individuals engage in hedging (risk avoidance) and speculation (risk taking).

Example of hedging:

Suppose a US firm expects to receive payment of €1 million in 90 days. The dollar value of this payment will go down if euro depreciates. To avoid this exchange rate risk, the firm may engage in hedging with a forward contract to deliver (or sell) €1 million in 90 days with a forward rate locked today.

Example of speculation:

Suppose the current forward rate for a 90-day contract is $1.4 per euro. A French investor speculates that dollar will strengthen

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in 90 days. Then he can use the forward contract to exchange 100 euros for 140 dollars in 90 days, and then use the spot contract to sell the 140 dollars and get more than 100 euros. This happens only when dollars actually appreciates.

An important player on FX market is government.

Suppose country A’s economy is worsening, and people expect that currency A will depreciate (or become less valuable). Then people start selling currency A and buying US dollars (why?). For some reasons A’s government wants to avoid currency A’s depreciation. They can intervene in the FX market by selling US dollars and buying currency A. However, this kind of intervention has to stop once the government runs out of its limited dollar reserves. Once a reserve is gone, market forces take over. A rapid deprecation will inevitably follow. For a small country, dollarization is necessary if its currency keeps depreciating.

Check the figures for Argentine Pesos and Ecuadorean sucres in Figure 2-3.

Google “1997 Asian financial crisis”

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Exercise

Discuss how Chinese government intervenes in the FX market to avoid the appreciation of Chinese Yuan. What is the cost for the intervention taken by the Chinese government?

The major pricing theory is no-arbitrage. Exchange rate is the price of a currency, so the no-arbitrage theory applies.

By definition arbitrage means to buy low and sell high.

The market is in equilibrium and price is stabilized if it satisfies no-arbitrage condition.

Example of arbitrage with two currencies at two locations (let’s neglect transaction cost)

E£/$, new york = 0.5E£/$, london = 0.55

The pound is more expensive in (New York or London)

Arbitrage means to buy pound (and sell dollar) in (New York or London) and sell pound (and buy dollar) in (New York or London).

More details of the arbitrage:

In London, you sell 1 dollar for _________ pound.

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In New York, you sell __________ pound for __________ dollars.

Your profit is _________ dollars. This arbitrage profit is riskless.

Now imagine many people are doing the same as you.

The London rate will go (up or down) if everyone buy pounds.

The New York rate will go (up or down) if everyone sells pounds.

In the end, the London and New York rates will converge (i.e., lower rates goes up and higher rate goes down) because of arbitrage. The arbitrage will continue as long as the rates at the two locations differ, and the arbitrage will keep making the two rates converge. Eventually, the market will be at equilibrium and price becomes stable once

E£/$, new york = E£/$, london

The condition above is no-arbitrage condition.

Actually, this is an example of law of one price: the prices of the same goods, in this case, the currency pound, should be the same otherwise there is chance for arbitrage.

Exercise: Question 5 on page 61Arbitrage with three currencies

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In general there is opportunity for arbitrage if

E1/3 ≠ E2/3 E1/2 (or equivalently, E1/3 ≠ E1/2

E3 /2)

E1/3 denotes the direct exchange rate of currency 1 against currency 3.

E2/3 E1/2 denotes the cross exchange rate of currency 1 against currency 3.

Currency 2 is vehicle currency.

So different direct and cross rates can invoke arbitrage.

ExampleSuppose E£/$ = 0.5, E€/£= 1.4 and E€/$ = 0.8

The direct exchange rate of euro against dollar is_______________The cross exchange rate of euro against dollar is________________The vehicle currency is _________________You want to buy euro using (direct or cross) rateYou want to sell euro using (direct or cross) rateThe direct rate will go (up or down)The cross rate will go (up or down)The adjustment of the two rates will continue until they are equalized.

To sum up, the no-arbitrage condition with three currencies is

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E1/3 = E2/3 E1/2

or equivalently

E1/3 = E1/2

E3 /2

In practice if E1 /2 and E3 /2 are known but E1 /3 is unknown, we can use the formula above to calculate E1 /3

Covered Interest Parity (CIP), a theory for determining the forward exchange rate (F)

Suppose the dollar deposit pays interest rate of i$ and the euro deposit pays i€

A US saver has two choices.

Choice one, he can choose dollar deposit, and for one dollar he can earn dollar return of _____________.

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Choice two, if there is no capital control, he can convert one dollar to __________ euro using the spot rate E$/ €

Then he chooses euro deposit and earns euro return of ___________________Finally he converts the euro return to dollar return using the riskless forward rate F$ /€ and get ____________(Read page 48)

The market is in equilibrium if the investor is indifferent between the two choices. That is the case when the two choices yield the same common currency returns, i.e.,

1+i$=(1+i€ )F $/€

E$ /€ (2-1)

Equation (2-1) is called the covered interest parity, from which we can derive a formula for determining the forward rate

F$ /€=E$ /€(1+i$)(1+i€ )

We can rearrange (2-1) and obtain

F$ /€−E$ /€

E$/€=i$−i€

which states that the forward premium (the proportional difference between the forward and spot rates) equals the interest rate differential.

Exercise

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Suppose the euro interest rate is 3%, the dollar interest rate is 5%, and the spot rate is $1.3 per euro. The forward rate would be____________________ ; the forward premium would be __________________.

Exercise

Question 6 part (a, b, c, d) on page 61 of the textbook.

Uncovered Interest Parity (UIP), a theory for determining the spot exchange rate (E)

Suppose the dollar deposit pays interest rate of i$ and the euro deposit pays i€

A US saver has two choices.

Choice one, he can hold dollar deposit, and for one dollar he earns dollar return of _____________.

Choice two, if there is no capital control, he can convert one dollar to __________ euro using the spot rate E$/ €

Then he chooses euro deposit and earns euro return of ___________________Finally he converts the euro return to dollar return using the risky expected future spot rate E$/€

e and get ____________where E$/€

e denotes the expected spot rate that will prevail in the future. (Read page 52)

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The market is in equilibrium if the following no-arbitrage condition holds

1+i$=(1+i€ )E$ /€

e

E$ /€ (2-2)

Equation (2-2) is called the uncovered interest parity (UIP).

Under UIP, returns to holding dollar deposits accruing interest must equal the expected returns from investing in euros.

From (2-2) which we can derive a formula for determining the current spot rate:

E$/€=E$ /€e (1+i€)

(1+i$)

In words we can calculate the current spot rate if we know interest rates and expected future spot rate

Suppose the euro interest rate is 2%, the dollar interest rate is 4% and the expected future spot rate is $1.4 per euro. Then the current spot rate is _______________

In the following chapters we will learn how the expected future spot rate and interest rates are determined.

We can rewrite (2-2) as

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E$ /€e −E$/€

E$ /€=i$−i € ,

which says that under UIP, the expected rate of depreciation of dollars against euro equals the interest rate differential of dollar and euro deposits.

Exercise: suppose the interest rate on euro deposit is 2% and on dollar deposit it is 4%. Then you expect the dollar will (depreciate or appreciate) against euro by _________.

Big picture

i$ , i€ , E$/€e UIP

→E$ /€ CIP

→F$ /€

Discuss figure 2-12 on page 5

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