Chapter 13
Section II
Equilibrium in the Foreign
Exchange Market
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$=R*+x.
– interest parity implies that deposits in all currencies
are deemed equally desirable assets.
2
• Uncovered Interest parity (UIRP) says:
R$ = R€ + (Ee$/€ - E$/€)/E$/€
• Why should this condition hold? Suppose it didn’t.
– Suppose R$ > R€ + (Ee$/€ - E$/€)/E$/€ .
• no investor would want to hold euro deposits, driving down the
demand and price of euros.
• all investors would want to hold dollar deposits, driving up the
demand and price of dollars.
• The dollar would appreciate and the euro would depreciate,
increasing the right side until equality was achieved.
3
UIRP (continued)
Note: UIRP assumes investors only care for expected
returns: they don’t need to be compensated for bearing
currency risk.
To determine the equilibrium exchange rate, we assume
that:
– Exchange rates always adjust to maintain interest parity.
– Interest rates, R$ 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$/€ , and then
looking for an ‘intersection.’
4
How do changes in the spot e.r affect
expected returns in foreign currency?
• Depreciation of the domestic currency today (E↑) lowers
the expected return on deposits in foreign currency
(expected RoR*↓).
Why?
– E↑ will ↑ the initial cost of investing in foreign currency, thereby ↓
the expected return in foreign currency.
• E↑ then x ↓ hence R*+x ↓
• Appreciation of the domestic currency today (E ↓) raises
the expected return of deposits in foreign currency
(expected Ror* ↑).
Why?
– E ↓ wil lower the initial cost of investing in foreign currency,
thereby ↑ expected return in foreign currency.
• E ↓ then x ↑, hence R*+x ↑
5
Expected Returns on € Deposits when
Ee$/€ = $1.05 Per €
Current
Interest rate on Expected rate of
exchange rate
$ depreciation
€ deposits
E$/€
R€
(1.05 - E$/€)/E$/€
Expected dollar return
on € deposits
R€ + (1.05 - E$/€)/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
6
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
7
The spot e.r and the Exp Return on $Deposits
Current exchange
rate, E$/€
1.07
1.05
1.03
1.02
1.00
0.031
0.050
R$
0.069
0.079 0.100
Expected dollar return
on dollar deposits, R$
8
Determination of the Equilibrium e.r.
No one is willing to
hold euro deposits
No one is willing to
hold dollar deposits
9
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:
10
A Rise in the $ Interest Rate
A depreciation
of the euro is
an appreciation
of the dollar.
• See slide 3 for intuition
11
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
12
13
An Expected Appreciation of the Euro
People now
expect the
euro to
appreciate
14
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.
15
Covered Interest Parity and
Forward Rates
16
Covered Investment
Suppose 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.
17
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.
18
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:
19
• 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.
20
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, 3year, 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
21
Different types of term structure
%
4.5
4
3.5
TS1
TS2
TS3
3
2.5
2
• TS1: rising term structure
• TS2: flat term structure
• TS3: inverted term
structure.
1.5
1
0.5
months
0
1
3
6 12 36
 In International finance
we can use the TS on
different currencies to
infer the expected change
in the exchange rate.
22
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.
23
Differentials between term structures
6 %
5
4
TS-high
TS-low
3
2
• Constant differential:
x=(Ee-E)/E=0. Currencies will
appreciate or depreciate
against each other at a
constant rate.
1
months
0
3
8
6
12
36
%
7
6
5
TS-high
4
TS-low
3
• Diverging: x>0 or f>0. High
interest currency expected to
depreciate at an increasing
rate.
2
1
months
0
3
6
12
36
6 %
5
4
TS-high
TS-low
3
2
• Converging: x>0, f>0 but
decreasing. High interest
currency expected to
depreciate at a decreasing
rate.
1
months
0
3
6
12
36
24
Practical application:
wwww.bloomberg.com/markets/index.html:
Rates and Bonds
2/22
06
US
Germ
UK
i-iG
i-iUK
5
4.5
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
3
5-y
4.58
3.18
4.23
1.4
0.35
2.5
10-y
4.54
3.43
4.12
1.11
0.42
4
3.5
2
3m 6m
Forward discount of $ on £ is increasing
but on € decreasing.
TSUS
1y
2y
TSG
5y 10y
TSUK
25