Download S - FBE Moodle

Lecture 2
Exchange Rate Determination
Some basic questions
• Why aren’t FX rates all equal to one?
• Why do FX rates change over time?
• Why don’t all FX rates change in the same
direction?
• What drives forward rates – the rates at which
you can trade currencies at some future date?
2
Definitions
• r$ : dollar rate of interest (r¥, rHK$,…)
• i$ : expected dollar inflation rate
• f€/$ : forward rate of exchange
• s€/$ : spot rate of exchange
– “Indirect quote”:
s€/$ = 0.83215
– “Direct quote”:
s$/€ = 1.2017
 1 $ buys 0.83215 €
 1 € buys $1.2017
3
3. Four theories
.
Difference in
interest rates
1 + r€
1 + r$
Fisher
Theory
Interest
Rate
parity
Exp. difference in
inflation rates
1 + iSFr
1 + i$
Relative PPP
Difference between
forward & spot rates
F€/$
Exp. Theory
s€/$
of forward
rates
Expected change
in spot rate
E(s€/$)
S€/$
4
Theory #1: Purchasing power parity
Law of One Price
Versions of
PURCHASING
POWER
PARITY
Absolute PPP
Relative PPP
5
The Law of One Price
• A commodity will have the same price in
terms of common currency in every country
– In the absence of frictions (e.g. shipping costs,
tariffs,..)
– Example
Price of wheat in France (per bushel): P€
Price of wheat in U.S. (per bushel): P$
S€/$ = spot exchange rate
P€ = s€/$  P$
6
The Law of One Price, continued
• Example:
Price of wheat in France per bushel (p€) = 3.45 €
Price of wheat in U.S. per bushel (p$) = $4.15
S€/$ = 0.83215 (s$/€ = 1.2017)
Dollar equivalent price
of wheat in France= s$/€ x p€
= 1.2017 $/€ x 3.45 € = $4.15
 When law of one price does not hold, supply
and demand forces help restore the equality
7
Absolute PPP
• Extension of law of one price to a basket of goods
• Absolute PPP examines price levels
– Apply the law of one price to a basket of goods with
price P€ and PUS (use upper-case P for the price of the
basket):
S€/$ = P€ / PUS
where P€ = i (wFR,i  p€,i )
PUS = i (wUS,i  pUS,i )
8
Absolute PPP
• If the price of the basket in the U.S. rises
relative to the price in Euros, the U.S. dollar
depreciates:
May 21 :
s€/$ = P€ / PUS
= 1235.75 € / $1482.07 = 0.8338 €/$
May 24:
s€/$ = 1235.75 € / $1485.01 = 0.83215 €/$
9
Relative PPP
Absolute PPP:
P€ = s€/$  P$
For PPP to hold in one year:
P€ (1 + i€) = E(s€/$)  P$ (1 + i$),
or:
P€ (1 + i€) = s€/$ [E(s€/$)/s€/$ )]  P$ (1 + i$)
Using absolute PPP to cancel terms and rearranging:
Relative PPP:
1 + i€ = E(s€/$)
1 + i$
s€/$
10
Relative PPP
• Main idea – The difference between
(expected) inflation rates equals the
(expected) rate of change in exchange rates:
1 + i€ = E(s€/$)
1 + i$
s€/$
11
The
Purchasing
Power
Parity
TheoryGustav
(PPP)
The PPP
theory
was developed
by Swedish
economists
Cassel in 1920 to
determine the exchange rate between countries on inconvertible paper currencies.
This theory states that, the rate of exchange between two countries is determined
by purchasing power in two different countries
PPP have two versions:
1. The absolute purchasing power parity theory
2. The relative purchasing power parity theory
12
1) Absolute Purchasing power parity
The absolute version states that the exchange rates
between two countries is equal to the ratio of the
price level in the two countries. The formula is,
R AB = PA /PB
where RAB is the exchange rate between two
countries A and B and PA and PB refers to general
price level in two countries
13
Absolute Purchasing power parity (cont..)
For example if price of one bushel of wheat is $1 in U.S and £1 in U.K then exchange
rate between $ and £ is equal to 1
According to the law of one price, a given commodity should have same price
So purchasing power of two currencies is at parity in both countries
If the price of one bushel of wheat in term of $ were $0.50 in U.S and £1.50 in U.K
…firm would purchase wheat in U.S and resell it in U.K at profit
14
Absolute Purchasing power parity (cont..)
This commodity arbitrage would cause the price of wheat to fall in U.K and
rise in U.S until the prices were equal to $1per bushel in both economies
Criticisms
This version is not used because it ignore the transportation cost and other
factors.
15
2) The Second Version ( Relative purchasing parity)
According to this version the change in the exchange rate over a specific period of
time should be proportional to the relative change in price level in the two nations
over the same period of time
The formula used for determination of exchange rate is
R1 =P1a/P0 . R0
where R1 shows exchange rate in period 1, and R0 shows exchange rate in base period
for example if general price level does not change in foreign nation from the base
period to period 1
Where as general price level in the home nation increase by 50%
P1b/P0
16
The Second Version ( Relative purchasing parity)
So according to PPP theory the exchange rate (price of a unit of foreign currency in
term of domestic currency) should be 50% higher in period 1 as compared to the
base period (home currency depreciated by 50%)
This theory can be explain with the help of other example.
Suppose India and England are on inconvertible paper standard and by spending
Rs.60, the bundle of goods can be purchased in India as can be bought by
spending £ 1 in England. Thus, according to PPP, the rate of exchange will be Rs.
60= £ 1
Suppose domestic price index increase by 300 and foreign price index rises to 200
the new exchange rate will be Rs 60 =£1.5
17
Explanation (PPP)
The exchange rate would be a proper reflection of the purchasing power
in each country if the relative values bought the same amount of
goods in each country.
18
BOP theory for Determination of exchange rate
According to this theory ,exchange rate of a currency depends on its BOP position
A favorable BOP raise the exchange rate
And unfavorable BOP reduces the exchange rate
Thus according to this theory exchange rate is determined by the demand and
supply of foreign exchange
Demand for foreign exchange arises from the debit side of the balance sheet
Supply of foreign exchange arises from credit side of balance sheet
19
BOP theory for Determination of exchange rate
(Cont…)
•
•
•
•
•
•
•
When BOP is unfavorable it means that demand for foreign currency is more than
its supply
It means that external value of domestic currency in relation to foreign currency
fall
Consequently exchange rate to fall…..how ?
Suppose RS 60=$1 , external value of domestic currency is .017
Due to unfavorable BOP Rs90=$1 so external value of domestic currency is ………
.011
On other hand if BOP is favorable it means that supply of foreign is greater than
demand
It means that external value of domestic currency in relation to foreign currency
rise
20
BOP theory for Determination of exchange rate
(Cont…)
•
•
•
•
Consequently exchange rate to rise
Suppose RS 60=$1 , so external value of domestic currency is .017
Due to favorable BOP Rs 40=$1 so external value of domestic currency is ………
.025
In conclusion, in foreign exchange determination BOP is important
21
BOP theory for Determination of exchange rate
(Cont…)
price of $ in Rupee
S
R2
R
R1
S
0
D
Q
Dollars
22
What is the evidence?
• The Law of One Price frequently does not hold.
• Absolute PPP does not hold, at least in the short run.
– See The Economist’s Big McCurrencies
• Homework: Use The Economist Big Mac Index: July 2013
1.
Identify whether Euro, Japanese Yen, Great British Pound, Chinese
Yuan, Swiss Frank and your own countries currency s are overvalued
or undervalued against USA$.
2.
Compare today's exchanage rates with July rates and discuss
whether the big mac index gives right directions or not.
• The data largely are consistent with Relative PPP, at least
over longer periods.
23
Deviations from PPP
Simplistic model
Why does
PPP
not
hold?
Imperfect Markets
Statistical difficulties
24
Deviations from PPP
Simplistic model
Imperfect Markets
Statistical difficulties
Transportation costs
Tariffs and taxes
Consumption patterns differ
Non-traded goods & services
Sticky prices
Markets don’t work well
Construction of price indexes
- Different goods
- Goods of different qualities
25
Summary of theory #1:
.
Exp. difference in
inflation rates
1 + i€
1 + i$
Relative PPP
Expected change
in spot rate
E(s€/$)
S€/$
26
Theory #2: Interest rate parity
• Main idea: There is no fundamental advantage to
borrowing or lending in one currency over
another
• This establishes a relation between interest rates,
spot exchange rates, and forward exchange rates
– Forward market: Transaction occurs at some point in future
– BUY: Agree to purchase the underlying currency at a predetermined
exchange rate at a specific time in the future
– SELL: Agree to deliver the underlying currency at a predetermined
exchange rate at a specific time in the future
27
PART IV.
INTEREST RATE PARITY THEORY
I. INTRODUCTION
A. The Theory states:
the forward rate (F) differs
from
the spot rate (S) at
equilibrium
by an amount
equal to the interest
differential (rh - rf) between
two countries.
28
INTEREST RATE PARITY THEORY
2.
The forward premium or
discount equals the interest
rate differential.
(F - S)/S = (rh - rf)
where
rh = the home rate
rf = the foreign rate
29
INTEREST RATE PARITY THEORY
3. In equilibrium, returns on
currencies will be the same
i. e. No profit will be realized
and interest parity exists
which can be written
(1 + rh) = F
(1 + rf) S
30
INTEREST RATE PARITY THEORY
B. Covered Interest Arbitrage
1. Conditions required:
interest rate differential does
not equal the forward
or discount.
premium
2. Funds will move to a country
with a more attractive rate.
31
INTEREST RATE PARITY THEORY
3. Market pressures develop:
a.
As one currency is more
demanded spot and sold
forward.
b. Inflow of fund depresses
interest rates.
c.
Parity eventually
reached.
32
INTEREST RATE PARITY THEORY
C. Summary:
Interest Rate Parity states:
1.
Higher interest rates on a
currency offset by
forward
discounts.
2.
Lower interest rates are
offset by forward
premiums.
33
Example of a forward market transaction
• Suppose you will need 100,000€ in one year
• Through a forward contract, you can commit to
lock in the exchange rate
• f$/€ : forward rate of exchange
Currently, f$/€ = 1.19854
 1 € buys $1.19854
 1 $ buys 0.83435 €
• At this forward rate, you need to provide
$119,854 in 12 months.
34
Interest Rate Parity
START (today)
$117,228
END (in one year)
r$=2.24%
(Invest in $)
s€/$=0.83215
$117,228  0.83215 = 97,551€
One year
(Invest in €)
$117,228  1.0224 = $119,854
f€/$=0.83435
97,551€  1.0251 = 100,000€
r€=2.51%
35
Interest rate parity
• Main idea: Either strategy gets you the
100,000€ when you need it.
• This implies that the difference in interest
rates must reflect the difference between
forward and spot exchange rates
Interest
Rate Parity:
1 + r€ = f€/$
1 + r$
s€/$
36
Interest rate parity example
• Suppose the following were true:
12 month interest
rate
U.S Dollar
Euro
2.24%
2.70%
Spot rate
1.2017 € / $
Forward rate
1.19854 € / $
– Does interest rate parity hold?
– Which way will funds flow?
– How will this affect exchange rates?
37
Evidence on interest rate parity
• Generally, it holds
• Why would interest rate parity hold better
than PPP?
– Lower transactions costs in moving currencies
than real goods
– Financial markets are more efficient that real
goods markets
38
Summary of theories #1 and #2:
.
Difference in
interest rates
1 + r€
1 + r$
Interest
Rate
parity
Difference between
forward & spot rates
f€r/$
s€/$
Exp. difference in
inflation rates
1 + i€
1 + i$
Relative PPP
Expected change
in spot rate
E(s€/$)
s€/$
39
Theory #3: The Fisher condition
• Main idea: Market forces tend to allocate
resources to their most productive uses
• So all countries should have equal real rates of
interest
• Relation between real and nominal interest rates:
(1 + rNominal) = (1 + rReal)(1 + i )
(1 + rReal) = (1 + rNominal) / (1 + i )
40
Example of capital market equilibrium
• Fisher condition in U.S. and France:
(1 + r$(Real)) = (1 + r$) / (1 + i$)
(1 + r€(Real)) = (1 + r€) / (1 + i€)
• If real rates are equal, then the Fisher condition
implies:
1 + r€ =
1 + r$
1 + i€
1 + i$
• The difference in interest rates is equal to the
expected difference in inflation rates
41
Summary of theories 1-3:
.
Difference in
interest rates
1 + r€
1 + r$
Interest
Rate
parity
Difference between
forward & spot rates
f€/$
s€/$
Fisher
Theory
Exp. difference in
inflation rates
1 + i€
1 + i$
Relative PPP
Expected change
in spot rate
E(s€/$)
s€/$
42
Theory #4: Expectations theory of forward
rates
• Main idea:
– The forward rate equals expected spot exchange
rate
f€/$ = E(s€/$)
Expectations theory
of forward rates:
f€/$ = E(s€/$ )
s€/$
s€/$
43
Expectations theory of forward rates
• With risk, the forward rate may not equal the spot rate
Group 1: Receive €
in six months, want $
Group 2: Contracted to
pay out € in six months
• Wait six months and
convert € to $
• Wait six months and
convert $ to €
• Sell € forward
• Buy € forward
or
or
• If Group 1 predominates, then E(s€/$) < f€/$
• If Group 2 predominates, then E(s€/$) > f€/$
44
Takeaway: Summary of all four theories
.
Difference in
interest rates
1 + r€
1 + r$
Fisher
Theory
Interest
Rate
parity
Exp. difference in
inflation rates
1 + i€
1 + i$
Relative PPP
Difference between
forward & spot rates
f€/$
Exp. Theory
s€/$
of forward
rates
Expected change
in spot rate
E(s€/$)
s€/$
45