REVIEW OF EXCHANGE RATE

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10 Νοε 2013 (πριν από 3 χρόνια και 5 μήνες)

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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