1
REVIEW
OF EXCHANGE RATE
TRANSACTIONS AND
INTERNATIONAL PARITIES
2
Parity
conditions
Exchange rates, interest rates, and prices must
be linked
We start with prices...
3
Law of
one
p
rice
In the absence of shipping costs, tariffs, and other
frictions, identical goods should trade for the same real
price in different economies:
P
i
= s P*
i
The Law of One Price holds perfectly for homogeneous
goods with low transaction costs
Why?
Examples: precious metals, wheat, oil
4
Purchasing
power parity (PPP)
Purchasing Power Parity is simply the extension of the Law of
One Price to all products in two economies. It says that the
overall real price levels should be identical:
P = s P*
Example:
Costs $1400 to purchase a certain basket of U.S.
consumption goods
If Swiss Franc trades at 2 ($ per Franc), how many Swiss
Francs will the same basket cost in Geneva?
5
Relative
purchasing
p
ower parity (RPPP)
Because overall economy price levels consist of different
goods in different countries, a more appropriate form of
PPP is the relative form
Relative Purchasing Power Parity asserts that relative
changes in price levels will be offset by changes in
exchange rates:
%
D
P

%
D
P* = %
D
s
Or denoting inflation (%
D
P) as

D
* = %
D
s
RPPP asserts that differences in inflation rates will be
offset by changes in the exchange rate
6
Example:
A year ago, the Brazilian Real traded at $0.917/Real.
For 2011, Brazil’s inflation was 4.1% and the U.S. inflation
was 1.7%.
What should be the value of the Real today?
RPPP
7
Exchange
rates
and
asset
p
rices
Exchange rates are determined by the relative supplies
and demands for currencies.
Since buyers and sellers are ultimately interested in
purchasing something with the currency

goods,
services, or investments

their prices and returns must
indirectly influence the demand for a given currency.
So, prices, exchange rates, and interest rates must be
linked….
8
Forward
market
b
asics
Forward Contract
involves contracting today for the future
purchase or sale of foreign exchange.
9
Forward
market
b
asics
90

day Swiss franc contract
0
S
90
($/SF)
You buy Swiss
Francs (long
position)
10
90

day Swiss franc contract
0
S
90
($/SF)
F
90
($/SF) = .8446
Forward
market
b
asics
11
90

day Swiss franc contract
0
S
90
($/SF)
Profit $
Y

axes measures profits or losses
in $.
X

axes shows the spot price
on maturity date of the forward
contract
Forward price a buyer
will pay in dollars for
Swiss franc in 90 days
Forward
market
b
asics
12
90

day Swiss franc contract
Long Contract
0
F
90
($/SF) = .8446
If price drops to 0
then the buyer will
pay $.8446 while he could pay $0.
His loss then is

.8446
S
90
($/SF)
Profit $
Forward
market
b
asics
13
0
F
90
($/SF) = .8446
If price is .8446
then his profit is then 0.
S
90
($/SF)
Profit $

F
90
($/SF)
Forward
market
b
asics
90

day Swiss franc contract
Long Contract
14
90

day Swiss franc contract
0
F
90
($/SF) = .8446
S
90
($/SF)
Profit $

F
90
($/SF)
Long position
Forward
market
b
asics
15
90

day Swiss franc contract
0
F
90
($/SF) = .8446
S
90
($/SF)
Profit $
Short position
F
90
($/SF)
Forward
market
b
asics
16
Law of One Price for
assets
Absent frictions, identical goods must trade for identical
prices in different countries when converted into a
common currency.
The same condition should hold for assets.
One important difference between goods and assets:
Price is not paid immediately

it is paid over time in the
form of returns.
This introduces the primary friction for exchanging
assets

a friction not found in goods.
Risk.
17
Law of One Price for
assets
Hence, there must exist a corresponding version of LOP for
assets which requires returns to be identical across countries
once this friction has been removed:
Covered Interest
Parity (CIP)
Exactly like the Law of One Price, Covered Interest Parity
requires frictionless markets to offer identical rates of returns for
identical assets.
How do make assets in two countries identical?
Eliminate risk:
1.
Eliminate exchange rate risk with forward contracts.
2.
Compare assets whose other risks are minimal (i.e. default).
18
Arbitrageurs will guarantee that the following two
strategies will generate the exact same common

currency
return:
1.
a.
Purchasing $1 worth of U.S. short

term treasuries
(lend money).
Law of One Price for
assets
19
Arbitrageurs will guarantee that the following two strategies will
generate the exact same common

currency return:
1.
a.
Purchasing $1 worth of U.S. short

term treasuries.
b.
Obtain an n

period return of 1+R
t,t+n
.
Law of One Price for
assets
20
Arbitrageurs will guarantee that the following two strategies will
generate the exact same common

currency return:
1.
a.
Purchasing $1 worth of U.S. short

term treasuries.
b.
Obtain an n

period return of 1+R
t,t+n
.
2. a.
Convert $1 into foreign currency at rate 1/
s
t
(FC/$).
Law of One Price for
assets
21
Arbitrageurs will guarantee that the following two strategies will
generate the exact same common

currency return:
1.
a.
Purchasing $1 worth of U.S. short

term treasuries.
b.
Obtain an n

period return of 1+R
t,t+n
.
2. a.
Convert $1 into foreign currency at rate 1/
s
t
(FC/$).
b.
Purchase corresponding foreign short

term treasuries
(borrow money in foreign currency).
Law of One Price for
assets
22
Arbitrageurs will guarantee that the following two strategies will
generate the exact same common

currency return:
1.
a.
Purchasing $1 worth of U.S. short

term treasuries.
b.
Obtain an n

period return of 1+R
t,t+n
.
2. a.
Convert $1 into foreign currency at rate 1/
s
t
(FC/$).
b.
Purchase corresponding foreign short

term treasuries.
c.
Receive an n

period foreign currency return of 1+R*
t,t+n
.
Law of One Price for
assets
23
Arbitrageurs will guarantee that the following two strategies will
generate the exact same common

currency return:
1.
a.
Purchasing $1 worth of U.S. short

term treasuries.
b.
Obtain an n

period return of 1+R
t,t+n
.
2. a.
Convert $1 into foreign currency at rate 1/
s
t
(FC/$).
b.
Purchase corresponding foreign short

term treasuries.
c.
Receive an n

period foreign currency return of 1+R*
t,t+n
.
d.
Eliminate the currency risk of the foreign return by
locking in an exchange rate of
F
t,t+n
($/FC).
Law of One Price for
assets
24
Arbitrageurs will guarantee that the following two strategies will
generate the exact same common

currency return:
1.
a.
Purchasing $1 worth of U.S. short

term treasuries.
b.
Obtain an n

period return of 1+R
t,t+n
.
2. a.
Convert $1 into foreign currency at rate 1/
s
t
(FC/$).
b.
Purchase corresponding foreign short

term treasuries.
c.
Receive an n

period foreign currency return of 1+R*
t,t+n
.
d.
Eliminate the currency risk of the foreign return by
locking in an exchange rate of
F
t,t+n
($/FC).
e.
Obtain an overall n

period return of:
F
t,t+n
(1+R*
t,t+n
) /
s
t
Law of One Price for
assets
25
Synthetic
forward
c
ontract
Another way to derive the forward price of FC is replicate it
synthetically:
1. Borrow $
2. Convert to FC (at S
t
)
3. Lend the FC.
I now effectively have a forward contract. I have committed to pay a
certain quantity of $ in the future in return for receiving a certain
quantity of FC in the future.
Through exchange rate and money markets, we can synthetically
deposit, lend, exchange currency spot, or exchange currency
forward.
We just need to keep proper track of differences between bid and
ask prices and borrowing and lending rates.
26
Time Dimension
Currency Dimension
$
FC
t
t+n
Borrow at $ loan rate
Lend at FC deposit rate
Buy FC Spot at ask
Sell FC Forward at bid
Spot,
forward
, and
money
m
arket
r
elationships
A
B
C
D
27
Time Dimension
Currency Dimension
$
FC
t
t+n
Borrow at FC loan rate
Lend at $ deposit rate
Sell FC Spot at bid
Buy FC Forward at ask
A
B
C
D
Spot,
forward
, and
money
m
arket
r
elationships
28
Time Dimension
Currency Dimension
$
FC
t
t+n
Borrow at $ loan rate
Borrow at FC loan rate
Lend at FC deposit rate
Lend at $ deposit rate
Sell FC Spot at bid
Buy FC Spot at ask
Sell FC Forward at bid
Buy FC Forward at ask
A
B
C
D
Spot,
forward
, and
money
m
arket
r
elationships
29
F
t,t+n
Time Dimension
Currency Dimension
A
B
C
D
$
FC
t
t+n
1/(1+R
t,t+n
)
1/s
t
L
(1+R*
t,t+n
)
D
A
B
Spot,
forward
, and
money
m
arket
r
elationships
30
Time Dimension
Currency Dimension
A
B
C
D
$
FC
t
t+n
(1+R
t,t+n
)
D
1/(1+R*
t,t+n
)
L
s
t
B
1/F
t,t+n
A
Spot,
forward
, and
money
m
arket
r
elationships
31
F
t,t+n
Time Dimension
Currency Dimension
A
B
C
D
$
FC
t
t+n
1/(1+R
t,t+n
)
1/s
t
L
(1+R
t,t+n
)
D
1/(1+R*
t,t+n
)
(1+R*
t,t+n
)
L
D
A
s
t
B
1/F
t,t+n
A
B
Spot, f
orward
, and
money
m
arket
r
elationships
32
(1)
An arrow from FC to $, can be thought of
as SELLING FC or BUYING $.
(2)
The reverse arrow from $ to FC represents
the reverse transaction, SELLING $ or BUYING FC.
(3)
An arrow from right to left (from the future to the present),
can be thought of as borrowing

taking cash from the future
and bringing it to the present.
(4)
The reverse arrow from left to right (from the present
to the future), can be thought of as investing

taking cash
that you have now and putting it away until the future.
33
Exchange
rate
r
isk
Covered Interest Parity says that if we lock in the forward
rate to eliminate exchange rate risk, the common

currency
return to otherwise riskless deposits in two currencies will
be identical:
1+R
t,t+n
=
F
t,t+n
(1+R*
t,t+n
) /
s
t
What happens if we don’t lock in the forward rate?
How will the returns compare if we use an
unhedged
or
“uncovered” version and just convert returns at the future
spot rate?
1+R
t,t+n
vs.
s
t+n
(1+R*
t,t+n
) /
s
t
34
Exchange
rate
r
isk
If exchange rate risk is not priced (if investors do not require
compensation for bearing exchange rate risk) then expected
returns are equal:
1+R
t,t+n
vs
. E [
s
t+n
] (1+R*
t,t+n
) /
s
t
and, if those expectations are rational,
on average
they are
right:
1+R
t,t+n
=
s
t+n
(1+R*
t,t+n
) /
s
t
Alternatively, this says that
on average
the forward rate
equals the future spot rate:
F
t,t+n
=
s
t+n
.
This is known as the
unbiased forward hypothesis
.
35
Uncovered Interest
Parity (UIP)
Put differently, if exchange rate risk is not priced, an
‘unhedged’ version of covered interest parity should
hold as well.
1+R
t,t+n
= F
t,t+n
(1+R*
t,t+n
)
s
t
36
UIP
Put differently, if exchange rate risk is not priced, an
‘unhedged’ version of covered interest parity should
hold as well.
On average:
1+R
t,t+n
= s
t+n
(1+R*
t,t+n
)
s
t
37
UIP
Put differently, if exchange rate risk is not priced, an
‘unhedged’ version of covered interest parity should
hold as well.
On average
:
1+R
t,t+n
= s
t+n
(1+R*
t,t+n
)
s
t
Which can be closely approximated by the
Uncovered Interest Parity
equation:
R
t,t+n

R*
t,t+n
= %
D
s
t,t+n
.
38
The Intuition of
CIP and UIP
(1)
In CIP, if FC interest rates are low, how can we get US$
based investors to hold FC assets?
The answer is that we offer them a more favorable forward rate
(higher F in terms of $/FC) to offset the low FC interest rate.
So the market is working by pricing F to offset a known low FC
interest rate.
(2)
In UIP, if we expect the US$ to be weaker in the future
(meaning more $ per FC) how would we get investors to
willingly hold US$ assets?
The answer is, we offer them an added bonus in the form of a
higher $ interest rate

just high enough to offset the loss of a
weaker US$. So the market is working by setting a high $
interest rate to offset an expected depreciation of the US$.
39
UIP
High interest rate currencies don’t, on average, depreciate
sufficiently. There are 3 possible explanations:
1.
Risk
Premia
:
The high interest rates of discount
currencies are not only compensating investors for an
expected decline in the exchange rate, but also for the
bearing risks associated with that currency.
2.
Peso Problem:
Remember, UIP holds “on average.”
We
may have difficulty observing the true average in the data.
High interest rate currencies may include the possibility of
extremely large depreciations which have not occurred
during the sample period.
3.
Irrational Expectations:
investors systematically get
the future exchange rate wrong.
40
Key
international
r
elationships
41
Relative
Inflation
Rates
Exchange
Rate
Change
Key
international
r
elationships
42
RPPP:
P

P* = %
D
s
䥮I污l楯渠摩d晥牥湴f慬猠
慲攠潦a獥琠sy 捨c湧敳
楮i獰s琠數捨c湧攠牡瑥r
剥污l楶攠
䥮I污l楯渠
剡瑥t
Exchange
Rate
Change
Key i
nternational
r
elationships
43
Purchasing
Power
Parity
Relative
Inflation
Rates
Exchange
Rate
Change
Key
international
r
elationships
44
Purchasing
Power
Parity
Relative
Interest
Rates
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Key
international
r
elationships
45
CIP:
F
t,t+n
/
s
t
=(1+
R)
/(1+ R*)
Forward differs from
spot by interest rate
differential
Purchasing
Power
Parity
Relative
Interest
Rates
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Key
international
r
elationships
46
Covered
Interest
Parity
Purchasing
Power
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
47
Covered
Interest
Parity
Purchasing
Power
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
48
Unbiased Forward:
F
t,t+n
= E(s
t+n
)
Forward is
expectation of spot
Covered
Interest
Parity
Purchasing
Power
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
49
Unbiased
Forward
Rate
Covered
Interest
Parity
Purchasing
Power
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
50
Unbiased
Forward
Rate
Covered
Interest
Parity
Purchasing
Power
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
51
Fisher Effect:
1+R = (1+r)(1+
⤠
Interest rate equals
real rate plus
expected inflation
Unbiased
Forward
Rate
Covered
Interest
Parity
Purchasing
Power
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
52
1+R = (1+r)(1+E(
⤩)
Unbiased
Forward
Rate
Covered
Interest
Parity
Purchasing
Power
Parity
R

R* =

⨠*楴栠剉RⰠ
interest rates reflect
expected inflation
differential.
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
53
Fisher Effect
and
Real Interest
Parity
Unbiased
Forward
Rate
Covered
Interest
Parity
Purchasing
Power
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
54
F
t,t+n
/ s
t
=(1+
R)
/(1+ R*)
Unbiased
Forward
Rate
Purchasing
Power
Parity
Fisher Effect
and
Real Interest
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
55
F
t,t+n
= E(s
t+n
)
Purchasing
Power
Parity
Fisher Effect
and
Real Interest
Parity
F
t,t+n
/ s
t
=(1+
R)
/(1+ R*)
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
56
Uncovered Interest Parity:
R

R* =
%
D
s
䕸捨慮来E牡r攠捨慮来猠
潦晳f琠t湴敲敳e楦晥f敮e楡汳
Purchasing
Power
Parity
Fisher Effect
and
Real Interest
Parity
F
t,t+n
= E(s
t+n
)
F
t,t+n
/ s
t
=(1+
R)
/(1+ R*)
Key i
nternational
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
57
1+R = (1+r)(1+
)
R

R* =

*
Unbiased
Forward
Rate
Covered
Interest
Parity
Purchasing
Power
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
58

⨠㴠%
D
s
ㄫ删㴠⠱⭲⤨ㄫ
)
R

R* =

*
Unbiased
Forward
Rate
Covered
Interest
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
59
1+R = (1+r)(1+
)
R

R* =

*
Uncovered Interest Parity:
R

R* = %Ds
Exchange rate changes
offset interest differentials

⨠㴠%
D
s
Unbiased
Forward
Rate
Covered
Interest
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
60
Uncovered Interest Parity
Unbiased
Forward
Rate
Covered
Interest
Parity
Purchasing
Power
Parity
Fisher Effect
and
Real Interest
Parity
Key
international
r
elationships
Relative
Inflation
Rates
Exchange
Rate
Change
Forward
Exchange
Rates
Relative
Interest
Rates
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