Chapter 13Section II

Equilibrium in the Foreign Exchange Market

2

Factors affecting the demand for FX

• To construct the model, we use two factors:1. demand for (rate of return on) dollar denominated

deposits R$2. demand for (rate of return on) foreign currency

denominated deposits to construct a model of the foreign exchange market = R*+x

• The FX market is in equilibrium when deposits of all currencies offer the same expected rate of return: uncovered interest parity: R$=R*+x.– interest parity implies that deposits in all currencies

are deemed equally desirable assets.

3

• Uncovered Interest parity (UIRP) says:

R$ = R€ + (Ee$/€ - E$/€)/E$/€

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

$/€ - E$/€)/E$/€ .

• no investor would want to hold euro deposits, driving down the demand and price of euros.

• 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, increasing the right side until equality was achieved.

4

UIRP (continued)

Note: UIRP assumes investors only care for expected returns: they don’t need to be compensated for bearing currency risk.

To determine the equilibrium exchange rate, we assume that:

– Exchange rates always adjust to maintain interest parity.

– Interest rates, R$ and R€, and the expected future dollar/euro exchange rate, Ee

$/€, are all given.

Mathematically, we want to solve the UIRP condition for E$/€ . That is the same as asking how the RHS and the LHS of the UIRP condition change with E$/€ , and then looking for an ‘intersection.’

5

How do changes in the spot e.r affect expected returns in foreign currency?

• Depreciation of the domestic currency today (E↑) lowers the expected return on deposits in foreign currency (expected RoR*↓). Why?– E↑ will ↑ the initial cost of investing in foreign currency, thereby ↓

the expected return in foreign currency. • E↑ then x ↓ hence R*+x ↓

• Appreciation of the domestic currency today (E ↓) raises the expected return of deposits in foreign currency (expected Ror* ↑).Why? – E ↓ wil lower the initial cost of investing in foreign currency,

thereby ↑ expected return in foreign currency.• E ↓ then x ↑, hence R*+x ↑

6

Expected Returns on € Deposits when Ee

$/€ = $1.05 Per €

Current exchange rate

Interest rate on € deposits

Expected rate of $ depreciation

Expected dollar return on € 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

7

The spot e.r. and Exp Return on $ Deposits

E ExpRor*

1.07 0.031

1.05 0.050

1.03 0.069

1.02 0.079

1.00 0.100

8

The spot e.r and the Exp Return on $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$

9

Determination of the Equilibrium e.r.

No one is willing to hold euro deposits

No one is willing to hold dollar deposits

10

The effects of changing interest rates

• An increase in the interest rate paid on deposits denominated in a particular currency will increase the RoR on those deposits to an appreciation of the currency.

– A rise in $ interest rates causes the $ to appreciate: ↑ in R$ then ↓E($/€)

– A rise in € interest rates causes the $ to depreciate: ↑ in R€ then ↑E($/€)

• A change in the expected future exchange rate has the same effect as a change in interest rate on foreign deposits:

11

A Rise in the $ Interest Rate

• See slide 3 for intuition

A depreciationof the euro isan appreciationof the dollar.

12

A Rise in the € Interest Rate

• R$ < R€ + (Ee - E)/E

The expected return from holding € assets is > than $assets.

Investors get out of $ assets into € assets, sell $ to buy €, the $ depreciates or € appreciates. This creates an expected appreciation of the dollar (x↓), thus a fall in the expected return from holding € assets

13

14

An Expected Appreciation of the Euro

People now expect the euro to appreciate

15

An Expected Appreciation of the Euro ↑Ee

• If people expect the € to appreciate in the future, then investment will pay off in a valuable (“strong”) €, so that these future euros will be able to buy many $ and many $ denominated goods.

• The expected return on €s therefore increases: ↑ROR€. – ↓Ee (expected appreciation of a currency) leads to an

actual appreciation: a self-fulfilling prophecy.– ↑Ee (expected depreciation of a currency) leads to an

actual depreciation: a self-fulfilling prophecy.

16

Covered Interest Parity and Forward Rates

17

Covered InvestmentSuppose that when investing $1 in a deposit in euros, instead of planning to convert euros back into dollars at an exchange rate of Ee

$/ € one year from now, I enter now a contract to sell euros forward at the rate F$/€.

My return from such investment then is:

R€ + (F$/€ -E$/€ )/E$/€

So, you buy the € deposit with $ To avoid exchange rate risk by buying the € with $, at the same time sell the proceeds of your investment (principal+interest) forward for $ → you have covered yourself.

18

CIRP• Since I could invest the same $1 domestically at R$ , the

forward market is in equilibrium when the Covered Parity Condition (CIRP) holds:

R$ = R€ + (F$/€ -E$/€ )/E$/€

where F$/€ = the forward exchange rate. This is called “covered” parity because it involves no risk-taking by investors: unlike UIRP, CIRP is a true arbitrage relationship.

• Covered interest parity relates interest rates across countries and the rate of change between forward exchange rates,F and the spot exchange rate, E. It says that ROR on $ deposits and “covered” foreign currency deposits are the same.

19

Remarks:

• Unlike UIRP, CIRP holds well among major exchange rates quoted in the same location at the same time, and even across different locations in integrated capital markets.

• CIRP fails when comparing markets segmented by current or expected capital controls: investors in a country subject to “political risk” require higher interest rates as compensation.

• For UIRP = CIRP , F$/€ should = Ee$/€ (the spot rate

expected one year from now).

• In fact, empirically, the forward rate moves closely with the current spot rate, rather than the expected future spot rate:

20

• f = (F$/€ -E$/€ )/E$/€ is called the “forward premium” (on euros against dollars). – f>0 the dollar is sold at discount (euro at premium)– f<0 the dollar is sold at premium (euroa at discount)– f=0 domestic and foreign currency interest rates are equal.

• Exemple: Data from Financial Times, February 9, 2006– E($/€)=1.195, F($/€)=1.22 (1-year from now)

– i$=5.03%, i€=2.9%. i$-i€=2.13% expected depreciation of the $US a year from now.

– f = (F$/€ -E$/€ )/E$/€ = (1.22/1.195)-1=2.1%. The dollar is sold at 2.1% discount in the forward market.

21

Expected exchange rates and the term structure (TS)of interest rates

• There is no such a thing as “the” interest rate for a country. Rates vary with investment opportunities and maturity dates.

• In bond market, there are 3-month, 6-month, 1-year, 3-year, 10-year, 30-year bonds.

• Term structure is described by the slope of a line connecting the points in time when we observe interest rates.– R rises with term to maturity→a rising TS– R same with all maturities →flat TS– R falls with term to maturity → inverse TS

22

Different types of term structure

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 3 6 12 36

months

%

TS1TS2TS3

• TS1: rising term structure• TS2: flat term structure• TS3: inverted term

structure.

In International finance we can use the TS on different currencies to infer the expected change in the exchange rate.

23

Remarks

• Usually, the forward rate, F, is considered a market forecast of the future spot rate Ee (even though empirically F moves more closely with the spot exchange rate, E).

• Even if there is not a forward exchange

market in a currency, at each point on the TS, the interest differential i-i* allows us to infer the directions of the expected change in E for the two currencies by the markets.

24

Differentials between term structures

0

1

2

3

4

5

6

3 6 12 36

months

%

TS-high

TS-low

• Constant differential: x=(Ee-E)/E=0. Currencies will appreciate or depreciate against each other at a constant rate.

• Diverging: x>0 or f>0. High interest currency expected to depreciate at an increasing rate.

• Converging: x>0, f>0 but decreasing. High interest currency expected to depreciate at a decreasing rate.

0

1

2

3

4

5

6

7

8

3 6 12 36

months

%

TS-high

TS-low

0

1

2

3

4

5

6

3 6 12 36

months

%

TS-high

TS-low

25

Practical application: wwww.bloomberg.com/markets/index.html:

Rates and Bonds

2

2.5

3

3.5

4

4.5

5

3m 6m 1y 2y 5y 10y

TSUS TSG TSUK

2/22

06US Germ UK i-iG i-iUK

3-m 4.56 2.52 4.45 2.04 0.11

6-m 4.71 2.63 4.43 2.08 0.28

1-y 4.70 2.76 4.29 1.94 0.41

2-y 4.69 2.93 4.26 1.76 0.43

5-y 4.58 3.18 4.23 1.4 0.35

10-y 4.54 3.43 4.12 1.11 0.42

Forward discount of $ on £ is increasing but on € decreasing.