1
Exchange rate
and interest parity
Jan J. Michalek
Exchange rate
Exchange rate: the price of one currency expressed in another currency
Definition: how many units of domestic currency are needed to buy one unit of foreign currency: e.g. 3,9PLN/$
Changes in exchange rates:
Fixed exchange rate: devaluation and revaluation
Flexible exchange rates: depreciation and appreciation.
JJ Michalek
2
Echange rate changes:
Exchange rate
regime
Flexible Stable
Increase of
exchange rate
Depreciation Devaluation
Decrease of
exchange rate
Appreciation Revaluation
JJ Michalek
Two types of changes in exchange rates:
Depreciation of home country’s currency
A rise in the home currency prices of a foreign currency
It makes home goods cheaper for foreigners and foreign
goods more expensive for domestic residents.
Appreciation of home country’s currency
A fall in the home price of a foreign currency
It makes home goods more expensive for foreigners and
foreign goods cheaper for domestic residents.
Exchange Rates and
International Transactions
3
Major exchange regimes and their
characteristics
JJ Michalek
Exchange regimes in Poland
4
Exchange rate regimes in Central and
Eastern European countries (IMF report
2014)
Jan J. Michałek
5
Domestic and Foreign Prices
If we know the exchange rate between two
countries’ currencies, we can compute the price of
one country’s exports in terms of the other
country’s money.
Example: The dollar price of a £50 sweater with a
dollar exchange rate of $1.50 per pound is (1.50 $/£) x
(£50) = $75.
Exchange Rates and
International Transactions
Exchange rate: major world
actors
Size of the market:
For example: 1999:$1,7 trillion per day: $637 billion in London, $350 in New York, $150 billion in Tokyo.
Major actors and foreign exchange markets:
Commercial banks (interbank trading: retail operations less than $1 million, wholesale: above $1 million: more favorable rates: 90 percent of all foreign exchange rate transactions)
Multinational corporations;
Non bank financial institutions;
Central banks
Foreign exchange brokers.
JJ Michalek
6
Foreign exchange arbitrage
When banks or economic agents seek to earn benefit from discrepancies among exchange
rates prevailing simultaneously in different markets.
Example: the Exchange rate of dollar to pound sterling ES/Ł equals:
00,2NYE 20,2LE
With 100$
We can buy 50Ł in NY in exchange for $100
And sell 50Ł In London for: 50*2,20= $110
Immediate profit of 10 $ or 10% (very profitable)
Many transactions of this sort are done
Price of Ł raises (increased demand) in NY e.g. to 2,09
Price of Ł decreases (increased supply) In London e.g. to 2,11
A very small difference In Exchange rates between different foreign exchange markets
JJ Michalek
Spot Rates and Forward Rates
Spot rates are exchange rates for currency exchanges “on the spot”, or when trading is executed in the present.
Forward rates are exchange rates for currency exchanges that will occur at a future (“forward”) date.
forward dates are typically 30, 90, 180 or 360 days in the future.
rates are negotiated between individual institutions in the present, but the exchange occurs in the future.
7
Spot and Forward Rates
Hedging: covering against the risk of
exchange rate fluctuations:
If we have to pay 1000 € in three months and we have 4000 PLN & E=4,00PLN/€
We can exchange today: 4000 PLN-> 1000€ (so called balanced or closed position)
If zloty appreciates (e.g.. E=3,9) ---> we gain 100 PLN (in one month it would be possible to buy 1000 € in exchange for 3900 PLN)
If zloty depreciates (e.g. E=4,1) --> we loose 100 PLN
Another option: to keep 4000 PLN as a bank deposit and exchange PLN against Euro after 3 months. Risk of depreciation short position (short of Euro).
JJ Michalek
8
Speculation: the opposite of hedging
Making transactions on spot foreign exchange market;
Deliberately willing to profit from exchange rate changes;
- Long position: buying deposit denominated in foreign currency in the hope that currency price will raise (depreciation of domestic currency)
- Short position: promising to sell foreign currency deposit in the future (in the hope that its price will fall: expectation of appreciation of the domestic currency).
JJ Michalek
Figure 13-2: Interest Rates on Dollar and Deutschemark Deposits,
1975-1998
The Demand for
Foreign Currency Assets
9
Exchange rate equilibrium under flexible exchange
rate system
S€: supply of foreign deposits (denominated in €) expressed in PLN
D€: demand for foreign deposits (depending on real rate of return)
EPLN/€=3.8
EPLN/€=4.2
EPLN/€=4.0
EPLN/€
S€
D€
Foreign exchange in €
),,,(
))()()((
* fe EERRDD
JJ Michalek
Equilibrium under stable exchange rate regime:
Exchange rate is too high
If Exchange rate is fixed (e.g. EPLN/€=4.20) --> agents are not buying sufficient amount of €-->
excess supply of €--> BOP surplus---> Central Bank purchases € in exchange for PLN (foreign
exchange reserves increase) --> domestic money supply raises.
Intervention of CB 0
EPLN/€=4.2
EPLN/€ S€
D€
Foreign deposits In €
BOP=0
BOP>0
JJ Michalek
10
Equilibrium under stable exchange rate regime:
Exchange rate is too low
If Exchange rate is fixed to low (e.g. EPLN/€=3.80) --> agents are buying large amount of €-->
excess demand for €--> BOP deficit---> Central Bank sells € and buys PLN (foreign
exchange reserves decrease) --> domestic money supply decrease.
Intervention
EPLN/€=3.8
EPLN/€
S€
D€
Foreign deposits In €
BOP=0 BOP<0
JJ Michalek
Income from domestic and foreign deposits Income from deposits E=4,00 PLN/€
in PLN in €
R=0,10 R*=0,05 E=4,00 Ee=4,20
200 PLN= 50Euro
Income from deposits 50*(1,05)
200*(1,10) 52,5
220 = 220,5
R=0,10 R*=0,05 E=4,00 Ee=4,30
200 PLN= 50Euro
Income from deposits 50*(1,05)
200*(1,10) 52,5
220 < 225,75
R=0,10 R*=0,05 E=4,00 Ee=4,10
200 PLN= 50Euro
Income from deposits 50*(1,05)
200*(1,10) 52,5
220 > 215,25
R=0,8 R*=0,05 E=4,00 Ee=4,20
200 PLN= 50Euro
Income from deposits 50*(1,05)
200*(1,08) 52,5
216 < 220,5
R=0,10 R*=0,03 E=4,00 Ee=4,20
200 PLN= 50Euro
Income from deposits 50*(1,03)
200*(1,10) 51,5
220 > 216,3
R=0,08 R*=0,03 E=4,00 Ee=4,20
200 PLN= 50Euro
Income from deposits 50*(1,03)
200*(1,08) 51,5
216 = 216,3
JJ Michalek
11
Expected income from foreign
deposits
Uncovered interest parity:
The foreign exchange market is in equilibrium when deposits of all currencies
offer the same expected rate of return
The expected rate of return from foreign deposits equals:
111 *
*
E
ER
E
ERE ee
where:
E: spot exchange rate, and Ee expected exchange rate after period t (1 year)
While domestic rate of return equals R .
JJ Michalek
Uncovered interest parity
Precisely calculated income in foreign exchange (after adding and subtracting R*) can be written as:
E
EERR
E
EER
E
ER
E
EERR
E
ER
E
E eEeeee******* 11
And the product: EEER e * is close to 0 for small R*
and (Ee-E)/E is the expected rate of depreciation
So a proxy for foreign deposits expected rate of return can be written as:
E
EERe *
So a proxy for equality between domestic and foreign deposits can be written as:
which is uncovered interest parity:
E
EERR
e *
JJ Michalek
12
The Demand for Currency
Deposits (cont.)
The difference in the rate of return on dollar deposits
and euro deposits is
R$ - (R€ + (Ee$/€ - E$/€)/E$/€ ) =
R$ - R€ - (Ee$/€ - E$/€)/E$/€
expected rate
of return =
interest rate
on dollar
deposits
interest rate
on euro
deposits
expected rate of return on euro deposits
expected
exchange rate
current
exchange rate
expected rate of appreciation
of the euro
Uncovered interest parity: word of
caution about simplified formula
One should be careful however. The approximate version
would not be a good approximation when interest rates in
a country are high.
For example in 1997 short term interest rates in Russia
were 60% per year, in Turkey they were 75% per year.
With these interest rates the approximate formula would
not give an accurate representation of rates of return.
JJ Michalek
13
Rule for efficient investment The rule for efficient investment is:
==> the interest party holds
Example:
R= 15%; R*=5%; EPLN/E =2.00 a EePLN/E =2.21 -->
0.15 - 0.05 -(2.21-2.0)/2.0=0.1-0.105<0 ==> invest abroad.
And if Ee =2.20 ==>
0.15 - 0.05 -(2.20-2.0)/2.0=0.1-0.1=0 ==> interest party holds (the same
rate of return)
eatinvestE
EERR
E
hom0*
abroadinvestE
EERR
E
0*
0*
E
EERR
E
JJ Michalek
Uncovered interest parity: simple examples
Income from deposits E=4,00 PLN/€ R-R*-(Ee-E)/E=
in PLN in €
R=0,10 R*=0,05 E=4,00 Ee=4,20 0
200 PLN= 50Euro
Income from deposits 50*(1,05)
200*(1,10) 52,5
220 = 220,5
R=0,10 R*=0,05 E=4,00 Ee=4,30 -0,025
200 PLN= 50Euro
Income from deposits 50*(1,05)
200*(1,10) 52,5
220 < 225,75
R=0,10 R*=0,05 E=4,00 Ee=4,10 0,025
200 PLN= 50Euro
Income from deposits 50*(1,05)
200*(1,10) 52,5
220 > 215,25
R=0,8 R*=0,05 E=4,00 Ee=4,20 -0,02
200 PLN= 50Euro
Income from deposits 50*(1,05)
200*(1,08) 52,5
216 < 220,5
R=0,10 R*=0,03 E=4,00 Ee=4,20 0,02
200 PLN= 50Euro
Income from deposits 50*(1,03)
200*(1,10) 51,5
220 > 216,3
R=0,08 R*=0,03 E=4,00 Ee=4,20 0
200 PLN= 50Euro
Income from deposits 50*(1,03)
200*(1,08) 51,5
216 = 216,3
JJ Michalek
14
Covered interest parity
If instead of Ee we apply E
f (forward exchange rate)
We get a condition for equality of covered rates :
The element: E
EEp
f
is called (Forward premium)
Forward premium for depreciation of the domestic currency „ cost of covering”.
I.e. if: R>R* p>0 (expected depreciation of the home currency)
And if (R<R*) p<0 forward discount (expected appreciation)
Covered interest party usually holds continuously
E
EERR
f *
JJ Michalek
Illustration of covered interest
parity Illustration of covered IP (with neutral bands)
R-R*<(Ef-E)/E
45o
Inflow of capital
Outflow of capital CIP
R-R*
(Ef-E)/E
R-R*>(Ef-E)/E
JJ Michalek
15
The Market for Foreign Exchange
Depreciation of the domestic currency today lowers the expected
return on deposits in foreign currency.
A current depreciation of domestic currency will raise the initial
cost of investing in foreign currency, thereby lowering the
expected return in foreign currency.
Appreciation of the domestic currency today raises the expected
return of deposits in foreign currency.
A current appreciation of the domestic currency will lower the
initial cost of investing in foreign currency, thereby raising the
expected return in foreign currency.
Determination of the Equilibrium
Exchange Rate
No one is willing to
hold euro deposits
No one is willing to
hold dollar deposits
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Flexible exchange rate: impact of
domestic interest rate increase
Increase of domestic interest rate appreciation of the exchange rate
E2PLN/€
Income from
domestic deposits R
R2PL 0
E1PLN/€
EPLN/€
R1PL
Income from foreign
deposits (R*)
JJ Michalek
Flexible exrate: impact of foreign interest rate
increase (or expected exchange rate)
1. Increase of foreign interest rate --> increase In income from foreign deposits (income curve shifts
up) --> demand for € raises --> depreciation of the exchange rate;
2. Increase of expected exchange rate (EePLN/€) --> expected depreciation --> increase of expected
income from deposits denominated in € --> demand for € raises --> increase of exchange rate -->
i.e. depreciation.
Income from domestic
deposits in PLN RPL
E2PLN/€
E1PLN/€
EPLN/€
Income from deposits
denominated In €
JJ Michalek
17
Money market equilibrium
MS/P=L(R,Y)
3
2
1
Q3 Q2 Ms/P=Q
1
R3
R2
R1
Real money
holdings
Real aggregated money
demand: L(R,Y)
R Real money
supply
JJ Michalek
Money and exchange rate: short run
equilibrium
1'
1 MS
1
E1
R1
L(RPL,YPL)
MSPL/PPL
Expected Euro return
Return from Polish deposits
(PLN)
EPLN/€
Real Polish
Money supply
R
Domestic
Money
market
Foreign exchange
rate market
JJ Michalek
18
Money and exchange rate: increase of
domestic money supply
R2
2'
2
E2
MS2
Present Euro return
1'
1 MS
1
E1
R1
L(RPL,YPL)
MSPL/PPL
Returun from Polish deposits
(PLN)
EPLN/€
Polish real
Money supply
R
Domestic
Money
market
Foreign exchange
market
JJ Michalek
Money and exchange rate
expectations: overshooting
R2
E2
3'
2'
MS2 2
Present euro return
1'
1 MS
1
E1
R1
L(RPL,YPL)
MSPL/PPL
New expected Euro
reurn
Income from domestic deposits
(PLN)
EPLN/€
Real Polish
Money supply
R
Domestic
money
market
Foreign Exchange
market
JJ Michalek
19
Exchange Rate Overshooting
The exchange rate is said to overshoot when its immediate response to a change is greater than its long run response.
We assume that changes in the money supply have immediate effects on interest rates and exchange rates.
We assume that people change their expectations about inflation immediately after a change in the money supply.
Overshooting helps explain why exchange rates are so volatile.
Overshooting occurs in the model because prices do not adjust quickly, but expectations about prices do.
Long Run and Short Run
(cont.)
In the long run, there is a direct relationship between
the inflation rate and changes in the money supply.
Ms = P x L(R,Y)
P = Ms/L(R,Y)
P/P = Ms/Ms - L/L
The inflation rate equals growth rate in money supply
minus the growth rate for money demand.
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Money and exchange rate
expectations: long run adaptation
MS2
4' 3'
2'
R2
E3
E2
2
Previous income from
Euro deposits
1'
1 MS
1
E1
R1
L(RPL,YPL)
MSPL/PPL
New expected income
from Euro deposits
Income from domestic deposits
(PLN)
EPLN/euro
Real Polish
money supply
R
Domestic
Money
market
Foreign
exchange
market
JJ Michalek
21
Long run adaptation: Money
supply and prices (change at to)
Money supply: Domestic interest rate:
The increase of money supply from M1
PL to M2
PL will cause abrupt fall in interest rate R1
S do
R2
S a then gradual increase of domestic interst rate
R2S
R1S
time time
M2PL
M1PL
t0 to
Long run adaptation: Prices and
exchange rate (change at to)
Level of prices: PPL Exchange rate:
to:overshooting; in the long run: appreciation of the domestic interest rate: Fisher effect
time time
E3PLN/DM
E2PLN/DM
E1PLN/DM
P2PLN
P1PLN
t0 to
