Post on 04-Apr-2018
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THEORIES OF
FOREIGN EXCHANGE
International Parity Conditions
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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
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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.
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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.
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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.
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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%
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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
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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
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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
*
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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
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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
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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
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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
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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.
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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
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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 )