Exchange rate

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. 3,9



Changes in exchange rates:



Fixed exchange rate: devaluation and revaluation



Flexible exchange rates: depreciation and appreciation.

 JJ Michalek

Echange rate changes:

Exchange rate regime

Flexible Stable

Increase of

exchange rate Depreciation Devaluation Decrease of

exchange rate Appreciation Revaluation



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

Major exchange regimes and their characteristics

 JJ Michalek

Exchange regimes in Poland

Exchange rate regimes in Central and Eastern European countries (IMF report 2014)

Jan J. Michałek



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

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 ,

2

ENY EL2,20 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

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.

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



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

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).

Figure 13-2: Interest Rates on Dollar and Deutschemark Deposits, 1975-1998

The Demand for

Foreign Currency Assets

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 E_PLN/€

S^€

D^€

Foreign exchange in €

) , , , (

) )(

)(

)(

(

*EeEf

R R D D^ ^









 JJ Michalek

Equilibrium under stable exchange rate regime:

Exchange rate is too high

Intervention of CB 0

EPLN/€=4.2

EPLN/€ S^€

D^€

Foreign deposits In € BOP=0 BOP>0

 JJ Michalek

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

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

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:

 ^{1 }

 ^{ }  ^{1 }

 ^{  1}

E R E E

E R

E^{e e}

where:

E: spot exchange rate, and E^e 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

E R E

E R E R E

E R E E

E R E

E R R E E

E^e * ^e 1 * * ^e * ^e 1 * ^E * * ^e

And the product: R^*





So a proxy for foreign deposits expected rate of return can be written as:

 

E E R^* E^e

So a proxy for equality between domestic and foreign deposits can be written as:

which is uncovered interest parity:

E E R E

R

e



 ^*

 JJ Michalek

The Demand for Currency Deposits (cont.)



The difference in the rate of return on dollar deposits and euro deposits is



R

- (R

+ (E

- E

)/E

) =

R

- R

- (E

- 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

Rule for efficient investment

The rule for efficient investment is:

==> the interest party holds Example:

R= 15%; R*=5%; EPLN/E =2.00 a E^ePLN/E =2.21 -->

0.15 - 0.05 -(2.21-2.0)/2.0=0.1-0.105<0 ==> invest abroad.

And if E^e =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)

e at invest E

E R E

R

E

hom

*  0



abroad invest E

E R E

R ^* ^E 0



 



 ^* 0

E E R E

R ^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

 JJ Michalek

Covered interest parity

If instead of E^e we apply E^f (forward exchange rate) We get a condition for equality of covered rates :

The element:

E E p E

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 E R E

R

f







Illustration of covered interest parity

Illustration of covered IP (with neutral bands)

R-R*<(E^f-E)/E

45^o

Inflow of capital

Outflow of capital CIP

R-R^* (E^f-E)/E

R-R*>(E^f-E)/E

 JJ Michalek

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

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^*)

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 (E^e_PLN/€) --> 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

Money market equilibrium

MS/P=L(R,Y)

3 2

1

Q³ Q² M^s/P=Q¹

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'

M^S1 1 E1

R1

L(RPL,YPL) M^SPL/PPL

Expected Euro return Return from

Polish deposits (PLN) EPLN/€

R

Domestic Money market Foreign exchange rate market

 JJ Michalek

Money and exchange rate: increase of domestic money supply

R2

2'

2 E2

M^S2

Present Euro return 1'

M^S1 1 E1

R1

L(RPL,YPL) M^SPL/PPL

Returun from Polish deposits (PLN) EPLN/€

Polish real Money supply

R

Domestic Money market Foreign exchange market

Money and exchange rate expectations: overshooting

R2

E2

3' 2'

M^S2 2

Present euro return 1'

M^S1 1 E1

R1

L(RPL,YPL) M^SPL/PPL

New expected Euro reurn

Income from domestic deposits (PLN)

EPLN/€

Real Polish Money supply

R

Domestic money market Foreign Exchange market

 JJ Michalek

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.

 M^s = P x L(R,Y)

 P = M^s/L(R,Y)











The inflation rate equals growth rate in money supply

minus the growth rate for money demand.

Money and exchange rate

expectations: long run adaptation

M^S2

3' 4' 2'

R2

E3

E2

2

Previous income from Euro deposits 1'

M^S1 1 E1

R1

L(RPL,YPL) M^SPL/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

Long run adaptation: Money supply and prices (change at t _o )

Money supply: Domestic interest rate:

The increase of money supply from M¹PL to M²PL will cause abrupt fall in interest rate R¹S do R²S 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 t _o )

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