theories of foreign exchange

7/30/2019 Theories of Foreign Exchange

1/19

THEORIES OF

FOREIGN EXCHANGE

International Parity Conditions


2/19

Exchange Rate Determination

What determines equilibrium relationships amongexchange rates?

International arbitrageur and the "Law of One-price"insure that risk adjusted expected rates of returnsare approximately equal across countries.

There are five key relationships between: Spot rate

Forward rate

Inflation rate Interest rate

Exchange rate


3/19

Purchasing Power Parity

A unit of domestic currency should purchasethe same amount of goods in the homecountry as it would of identical goods in a

foreign country. Absolute form of PPP:

law of one price: price of similar products to

two countries should be equal whenmeasured in a common currency.


4/19

PPP Example

A bottle of wine costs8 in Paris and $10 in NewYork. The exchange rate must reflect this pricerelationship:

e0 = Pd/Pf= $10/8 = $1.25 per(e0 = $ per FC; direct or American quote)

Equivalent to0.80 per $ in indirect quote,European terms.

The strictest version of PPP is not supportedempirically, but changes in relative inflation rates arerelated to changes in exchange rates.


5/19

Relative form of PPP

Acknowledges market imperfections such as:

transport costs

tariffs and quotas.

Rate of change in the prices of products shouldbe similar when measured in a commoncurrency.


6/19

Relative PPP - Example

Example:Suppose the price of wine in Paris increases to 9 in one year implying an inflation of 12.5%, while inthe U.S. the price of wine increases to $10.50 indicatingan inflation rate of 5%. The new exchange rate:

e1 = Pd,1/Pf,1 = $10.5/9 = $1.1667 per

or0.8571 per $

What is the depreciation in the value of?

1.1667/1.2500 -1 = -6.67%


7/19

PPP

Relative PPP:

OR

OR

Approximately: %e0= d - f

)+(1

)+(1xe=e

f

d01

)+(1

)+(1x

P

P=

P

P=e

f

d

f

d

f

d

1

0,

0,

1,

1,

)+(1

)+(1=

e

e

f

d

0

1


8/19

PPP Implication

According to PPP, the currency of countries withhigh inflation rates should devalue relative tocountries with low inflations rates.

Rationale:if d> f, then:

domestic imports increase; domestic exports decrease

foreign imports decrease; foreign exports increase

demand for FC increases; supply decreases demand for LC decreases; supply increases

FC appreciates; LC depreciates


9/19

Relative PPP Example

Suppose the U.S. inflation rate is expected tobe 3 percent for the coming year, while theBritain's expected rate of inflation is 5

percent. The current exchange rate is $1.50 per .

What should be the spot rate in one year?

1.50 1.03/1.05 = $1.47 per


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II: Fisher Effect Recall the relationship between nominal and

real rates of interest, as expressed in theFisher theorem:

1 + i = (1 + r*) (1 + )

Or

Approximately:

i = r* + and r* = i -

)+(1

i)+(1=r+1

*


11/19

Generalized Fisher Effect

Real rates of interest are equalized acrosscountries through arbitrage.

Otherwise funds would flows from countries

with low expected real rates of interest tocountries with high expected real rates ofinterests (in the absence of segmented

markets) Therefore: r*f= r*d OR if- f= id - d


12/19

Generalized Fisher Effect

More precisely:

OR

Approximately:

)+(1

)i+(1=

)+(1

)i+(1

f

f

d

d

)+(1

)+(1=

)i+(1

)i+(1

f

d

f

d

fdfd ii


13/19

III. International Fisher Effect

Combines the generalized Fisher effect to show therelationship between nominal interest rates and currencyexchange rates.

From PPP:

From GFE:

Therefore:

)+(1)+(1=

ee

f

d

0

1

)+(1

)+(1=

)i

+(1

)i+(1

f

d

f

d

)i+(1

)i+(1=

e

e

f

d

0

1


14/19

IFE Implications

Currencies with low interest rates would appreciatewith respect to currencies with high interest rates.

A long-run tendency for interest rates differentials tooffset exchange rate changes has been

demonstrated empirically. Example:Interest rate in U.S. is 4%, while interest

rate in Switzerland is 10%. If the current SF spotrate is $0.80, what should be the SF spot rate one

year from now?$0.80 1.04/1.10 = $0.7564 per SF

Or SF depreciates about 5.5%


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IV. Forward Rates and Expected

Future Spot Rates Early studies indicated forward exchange rates to be

unbiased predictor of future spot exchange rates.f1 = E[e1]

Then the forward rate premium or discount

unbiasedly reflects potential gains to be realizedfrom the purchase or sale of forward currencies. This equality captures the relationship between

forward and spot rates. Recent work has demonstrated the existence of a

slight risk premium. The premium, however,changes signs. Therefore, it is fair to assume thatthe future spot rates would equal forwards rates.


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V. Interest Rate Parity Substituting f1 = E[e1] in the IFE equation:

)i+(1

)i+(1

=e

f

f

d

0

1

)i+(1

)i+(1

=e

e

f

d

0

1


17/19

Covered interest arbitrage Suppose the interest rates are 4% in the U.S.

and 10% in Switzerland. The Swiss Franc spotrate is $0.8000 and 180-day forward rate is

$0.7800. Is covered arbitrage possible? Forward discount on SF

= (.78 -.80)/0.80 = -2.5% for 180 days

or -5% per year.Id = 4% while If+ discount = 10% - 5% = 5%

Therefore, arbitrage is possible.


18/19

Covered Arbitrage

1. Borrow $1,000,000 in US @ 4% per year or 2% for half year.Loan plus Interest to be paid in 180 days = $1,020,000

2. Convert $ to SF at the spot rate:$1,000,000/0.80 = SF 1,250,000

3. Invest SF 1,250,000 @ 10% for 180 days:Will receive SF 1,250,000 (1+10%/2) = SF 1,312,500 in 180 days

4. Sell SF 1,312,500 in forward market @180 forward rate $0.78/SF

Will receive 1,312,500 $0.78/SF = $1,023,750 in 180 days

5. After 180 days receive $1,023,750 from forward contract, and pay-offloanNet profit form arbitrage: $1,023,750 -1,020,000 = $3,750


19/19

Prices, Interest Rates and

Exchange Rates in EquilibriumForecast change inspot exchange rate

+ 4 %(yen strengthens)

Forecast difference

in rates of inflation

- 4 %(less in Japan)

Purchasing power

parity

( A )

Forward premium

on foreign currency

+ 4 %(yen strengthens)

Interest

rate parity

( D )

International

Fisher

Effect

( C )

Forward rate

as an unbiased

predictor

( E )

Difference in nominal

interest rates

- 4 %

(less in Japan)

Fisher effect

( B )

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