INTERNATIONAL FINANCE

2.3. Models of
exchange rate
determination
GROUP 2
 INTRODUCTION

Supply and Demand of Money

EXCHANGE RATE
an assumption: “Domestic and Foreign
MODELS
bonds are perfect substitutes”
Asset prices
Buying Selling Rate of
Asset
price price return
An investor has 2 investment options:
asset A or asset B, the decision based
mostly on expected rate of return. A 100 120 20%

Case 1
Case 1: He will be indifferent between B 200 240 20%
investing in asset A or asset B
Asset prices
Case 2: The investor expects the price
Buying Selling Rate of
of asset A will be $132 in the future. Asset
price price return
-> Invest in asset A
-> Demand for A ↑ A 100 132 32%
↑
-> Price of A
Case 2
-> The price of A will be bid up until the
B 200 240 20%
expected rate of return on A is the same
as the return on B.
Clearly what people expect to happen
to future prices of assets will be crucial
in determining their current prices.
 Buy AUS bonds or US bonds?
Assume both are same in risk and maturity,
people will take these 2 factors into accounts:
Uncovered + Their currency in denomination
+ Interest rate attached to the bonds

interest rate UIP (uncovered interest parity) condition:

parity (UIP) Es = r(AUS) – r(US)

Es: the expected rate of depreciation of the
exchange rate of the AUD
R(AUS): the AUS interest rate
UIP condition implies that R(US): the US interest rate
the expected rate of
return on domestic and -> The expected rate of depreciation of the AUD
against the USD is equal to the interest rate
foreign bonds are equal.
differential between AUS and US bonds.
 AUD at 4%
AUD 100 AUD
104

Convert at USD 70*1.485 = AUD 103.95

spot rate of
AUD1,5/USD1

Expected
conversion rate of
AUD 1,485/USD 1
USD 66,7 USD 70
US at 5%

Under UIP condition, AUS and US bonds are said to be perfect substitutes.
This is a crucial assumption in this chapter.
A change in future expected conversion rate from AUD 1,485/$1 to AUD 1,8/$1
AUD at 4%
AUD 100 AUD 104

Convert at USD 57,75*1,8 = AUD 103,95

spot rate of
AUD1,81/USD 1

Expected
conversion rate of
AUD 1,8/USD1
USD 55 USD
US at 5%
57.75

AUS and US bonds are said to be perfect substitutes

Changes in expectations about the future are potentially powerful

forces in determining the spot exchange rate.
TEAM 2

Table of Content

MONETARY MODELS

FLEXIBLE-PRICE MODEL

STICKY-PRICE MODEL

REAL INTEREST RATE DIFFERENTIAL MODEL

PORTFOLIO BALANCE MODEL

 Conventional Demand Function:

The flexible-price
m: log price of the domestic money
monetary model stock
p: log of the domestic price level
y: log of domestic real income
r: nominal domestic interest rate
 Foreign Money Demand Function:

The flexible-price
monetary model
m*: log price of the foreign money
stock
p*: log of the foreign price level
y*: log of foreign real income
r*: foreign interest rate
The flexible-price
monetary model
It is assumed that purchasing power parity holds continously
s = p = p*
where s is the log of the exchange rate defined as
domestic currency per unit of domestic currency

It is assumed that domestic and foreign bonds are perfect

subtitutes and UIP holds on a continuous basis.
Expected rate of depreciation of the domestic currency is
equal to the interest-rate differential between domestic and
foreign bonds.
The flexible-price
monetary model

Spot Exchange rate is determined by:

Relative money supplies
Relative levels of real national income
Relative interest rates
The flexible-price
monetary model
The spot exchange can be writeen in another way related to
expected inflation rate.
Nominal interest rate is made up of two components, the real
interest rate and expected inflation rate.

r = i + Pe r* = i* + Pe*
s = (m - m*) - n(y-y*) + (Pe - Pe*)
The flexbile price monetary model is based on the premise that:
All prices in an economy are flexbile
Domestic and foreign bonds are perfect subtitutes.
The demand for money in relation to the supply of money is
important in the exchange rate determination.
 This model is the phenomenon that
The Dornbusch
a currency may appreciate or
Sticky - Price depreciate following a economic
shock in the short run by a greater
Monetarist Model percentage that required in the
long run. Therefore, it overshoots
its long-run value.
 Assumptions of the model:

PPP does not hold continously it

holds in the long run only
The Dornbusch UIP on the other hand holds on a
continuous basis
Sticky - Price Prices of goods and wages are
Monetarist Model sticky
The financial markets that is the
money markets and the foreign
exchange rate is flexible both
upward and downwards in the short
and long run.
 According to model, prices in the
The Dornbusch
goods market and wages in the
Sticky - Price labor market are determined in
sticky-price markets. They only
Monetarist Model tend to change slowly over time in
response to various shocks such as
changes in the money supply.
The simple explanation of the
Dornbusch model

In the model the UIP condition

is assumed to hold
continuously, we have sticky
price
Initial equilibrium:
Domestic and world
interest rates (r1)
Initial money supply (M1),
price level (P1)
Exchange rate (S1).
The simple explanation of the
Dornbusch model
Suppose at time t1 the
authorities unexpectedly
expand the domestic money
supply by 20% to M2.

-> Leading to a long-run

equilibrium with UIP and a
20% rise in domestic price
level.
The simple explanation of the
Dornbusch model

Short-run effects: Sticky

prices maintain P1, causing
excess money supply and a
drop in interest rates to r2,
resulting in currency
depreciation (S2)
The simple explanation of the
Dornbusch model

Short-run depreciation
overshoots equilibrium (S2),
gradually appreciating to
long-run equilibrium (Sbar) as
prices adjust.
The simple explanation of the
Dornbusch model

Long-run: Exchange rate

stabilizes at Sbar, interest
rates return to original levels,
and economy reaches new
equilibrium
The demand for to hold domestic money is given
by a conventional money demand function

We assume again that UIP holds, given international bond

market equilibrium for
Long run exchange rate determined by PPP:

As the model allows for deviations from its long-run equilibrium

value, we specify expected change of the exchange rate, the
regressive expectation is given by:
 Long-run steady state equilibrium
The Frankel real exchange rate:

interest rate
differential
model Short-run exchange rate:
The Frankel real interest rate
differential model
If there is a disequilibrium set of real interest rates, then the real
interest exchange rate will deviate from its long-run equilibrium value.
If the real domestic interest rate is below the real foreign interest rate,
the real exchange rate of the domestic currency will be undervalued in
relation to its long-run equilibriumvalue. Hence there is an expected
appreciation of the real exchange rate of the domestic currency to
compensate.
Short-run exchange rate overshoots its long-run equilibrium value,
depreciating proportionately more than the increase in the money stock.
Hence there are expectations of a future real appreciation of the
currency to compensate for the lower real rate of return on domestic
bonds.
Implications of the monetary views of
exchange rate determination
Whichever model is adopted, it is clear that monetary policy is
the only predictable and effective means of influencing the
exchange rate.
In the flexible-price model authorities cannot influence the
real exchange rate. In the sticky-price model however,
authorities can exploit the finite speeds of adjustment of
domestic markets to influence the real exchange rate in the
short run, provided that output is fixed.
The most clear implantation is that monetary policy is the
most effective means of managing the exchange rate.
A money supply
expansion and
exchange rate
“overshooting”

Figure 12.14 describes the effects of an x% increase in

the money supply in the context of the Dornbusch
model.
 A money supply expansion and
exchange rate “overshooting”
Long-term effects
Initially the economy is in full equilibrium at
point A where G1G1 schedule intersects M1M1
schedule.
Money supply is expanded x% by the authorities
unexpectedly.
In the long-run, domestic prices will rise by the
same percentage as the rise in the money stock.
Long run price is x % above p1.
As PPP holds in the long run, a rise in the
domestic price level of x% requires depreciation
of the exchange rate by x%, that gives a long run
equilibrium rate.
A money supply expansion and
exchange rate “overshooting”
Short-term effects

x% increase in the money supply results in a

rightward shift of the M1M1 schedule to M2M2.

Domestic prices are sticky in the short-run.

Domestic prices initially does not change. The price

level remains at p1 with a jump in the exchange rate
from s1 to s2 on the money market schedule M2M2.

As the short-run equilibrium exchange rate s2

exceeds the long-run equilibrium rate, this is the
phenomenon of exchange rate "overshooting"
 It emphasizes capital-market rather than goods-market
arbitrage being the major determinant of exchange rates
in the short run.

It provides an Intuitively appealing explanation of why

Importance of exchange rate movements have been large relative to
movements in International prices and changes In
the sticky-price International money stocks.

monetary model Furthermore, it explains such movements as the outcome

of a rational foreign exchange market that produces an
exchange rate that deviates from PPP based on
economic fundamentals, not in isolation from them.

It helps explain why observed exchange rates are usually

even more volatile than supposed determinants such as
the money supply.
Portfolio
Balance Model
A model of exchange rate
determination pioneered by
Branson (1976) and Kouri (1976),
analyzes the intricate links
between asset portfolios and
currency values. Branson's
contributions laid the foundation
for further researches on
exchange rate determination.
Difference to monetary approach
Only money supply (in relation to money demand) matters for the exchange rate
→ ignore source of money creation

In portfolio balance model, the UIP condition will not be hold due to risk
premium.

Risk premium
Interest rate difference
 Introduction
The portfolio balance model will base on the
weight of bonds in the agent's portfolio to
determine the change of exchange rate.

Situation 1: An increase in the perceived

riskiness of foreign bonds compared to
domestic bonds can lead to both a fall in the
domestic interest rate and an appreciation of
the domestic currency as private agents
rebalance their portfolios. On the other hand, an
increase in the perceived riskiness of domestic
bonds can lead to a depreciation of the
domestic currency and/or a rise in the domestic
interest rate.
 Introduction
The portfolio balance model will base on the
weight of bonds in the agent's portfolio to
determine the change of exchange rate.

Situation 2: A higher proportion of domestic

bonds in agents’ portfolios will lead to an
increase in the demand for foreign bonds, the
higher domestic interest rate will lead to a fall in
the demand for foreign bonds. If the former
effect is greater than the latter, the exchange
rate depreciates; but if the reverse is true, the
exchange rate appreciates.
RISK PREMIUM
This additional expected
return on the relatively
risky as compared to the
less risky bond, resulting
from currency risks and
country risks.
 3 conditions of risk premium
Difference in risks Investors are risk-aversion Difference between portfolios
There must be different Investors are risk - aversion to consider There must be a difference between the risk-
in risk of domestic bonds which bonds is better with their risk minimizing portfolio and the actual portfolio,
and foreign bonds to and expected return. forced at market clearing prices into
create risk premium. investors’ portfolios
 Operation of PBM

→
A disturbance in asset-holders’ portfolios a change in the exchange rate and
domestic interest rate→ effects on output and the current account.
A current account surplus/deficit→ an accumulation/decumulation of foreign assets →
further changes in assets-holders’ portfolios
...and so on until the model is restored to long-run equilibrium
The model
There are assumed to be three
assets that are held in the
portfolios of private agents and
the authorities:
1. Domestic monetary base, M;
2. Domestic bonds denominated
only in the domestic currency, B;
3. Foreign bonds denominated
only in the foreign currency, F
 3 schedules
Money market (MM)
Positive slope: a depreciation of S
leads to a rise in r to offset increased M.
Rightward shift: an increase in money
supply requires a fall in r.

Bond market (BB)

Negative slope: a depreciation of S
leads to a fall in r to offset increased B.
Rightward shift: an increase in bond
supply requires a rise in r.

Foreign bond (FF)

Negative slope: a rise in r leads to an
appreciation in S to offset increased F.
Leftward shift: an increase in foreign
bond supply requires a fall in r.
FXO
OPERATION
An exchange of domestic money for
foreign assets
Leads to a rightward shift of FF and
MM schedule
Since agents hold fewer foreign assets
than before the operation:
The exchange rate will have
depreciated to S2
The domestic interest rate must
have fallen to r2
Reasons:
The FXO creates a shortage of
foreign assets in agents’ portfolios
OMO
OPERATION
In contrast to an FXO, an OMO leaves the FF
schedule unchanged while leading to a
rightward shift of the money supply
schedule from M1 to M2 and a leftward shift
of the BB schedule from B1 to B2. This
means that there is a depreciation of the
exchange rate and a fall in the domestic
interest rate. This is because the OMO
creates an excess supply of money in
agents’ portfolios which leads to an
increased demand for both domestic and
foreign bonds; this results in a fall in the
domestic interest rate and a depreciation of
the currency which raises the value of
foreign bond holdings.
SFXO
OPERATION
The SFXO has the effect of increasing the
supply of domestic bonds, shifting the BB
schedule to the right from B1 to B2, whilst
decreasing agents’ holdings of foreign assets,
shifting the FF schedule to the right from F1
to F2; the MM schedule remains unchanged
because the domestic money base is left
unaffected. The net effect of the operation is
a depreciation of the exchange rate and a
rise in the rate of interest. The exchange rate
depreciates because the SFXO causes a
shortage of foreign assets in agents’
portfolios requiring an exchange rate
depreciation to achieve the desired holdings.
The interest rate rises because the excess
supply of domestic bonds in agents’
portfolios depresses domestic bond prices.
 CONCLUSION
FXO (expansionary) OMO (expansionary) SFXO = ex FXO + contract OMO

Purchase back
Purchase foreign bonds from domestic bonds to Purchase foreign assets with domestic
Authorities’
private agents with newly create increase private monetary base + offset the increase M by
action
money stock sector holdings of selling domestic bonds
money

Equation
dM=-SdFp=SdR: rightward shift of
MM and FF
dM = -dBp = dBa: MM
right/BB left
dM=-SdFp-dM=dBp → -SdFp=dBp
Exchange rate
depreciation: raises
Exchange rate depreciation:
→
shortages of F in portfolios
the value of foreign
bond
Exchange rate depreciation: raises the value
increasing domestic currency value of remaining holdings.Interest rate rise:
Effects holdingsInterest rate
of remaining holdings of F.Interest excess B supply depresses domestic bond
rate fall: encourage agents to hold
fall: excess M supply
→
in portfolios
prices→ offset
dM.
increase demand for
both bonds
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