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Exchange Rates and Interest Rates
Interest Parity
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PPP and IP
Relationship between exchange rates andprices ------ Purchasing Power Parity
PPP is expected to hold when there is noarbitrage opportunity in goods markets.
Relationship between exchange rates andinterest rates ------ Interest Parity
IP is expected to hold when there is noarbitrage opportunity in financial markets.
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PPP and IP
Financial- asset prices adjust to newinformation more quicklythan goods
prices PPP does not hold in the shortrun
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Interest Parity
1/30/02 FT
US$ Libor (3 months): 1.870 = i$ Euro Libor (3 months): 3.351 = i Euro spot: 0.8617 = E$/ Euro 3 months forward: 0.8585 = F
$/
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Euro currency
Offshore Banking
Euro dollar, Euro yen
Euro banks
Libor = London Interbank Offer Rate
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Interest Parity
By investing $1,000 for 3 months, aninvestor in the US can earn 1,000 x (1+i$)
= 1,000 x [1+(0.018704)] = 1,004.67dollars at home.
Alternatively, she can invest in the EU by
converting dollars to euros and theninvesting the euros.
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Interest Parity
$1,000 equal to 1,000 E$/= 1,000 0.8617 = 1,160.50 euros, which is the
quantity of euros resulting from the 1,000dollars invested.
After three months, she will receive
1,160.50 x (1+i) = 1,160.50 x [1+(0.033514)] = 1,170.22 euros.
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Interest Parity
She will have to convert this investmentreturn to dollars at the exchange rate that
will prevail 3 months later, which isunknown today.
To avoid this uncertainty, she can cover
the investment in euro with a forwardcontract.
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Interest Parity
She sells1,170.22 to be received in 3months in the forward market today.
The covered returnis (1,000 E$/) x(1+i
) x F$/= 1,170.22 x F$/
= 1,170.22 x0.8585 = 1,004.64 dollars, which is pretty
close to $1,004.67.
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Interest Parity
Arbitrage makes the difference betweenthe returns on two investment
opportunities equal to zero. In other words,
1+i$= (1+i)(F$//E$/)
or
(1+i$)/ (1+i) = (F$//E$/)
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Interest Parity
Interest rate paritycondition is given by
(i$-i)/ (1+i) = (F$/-E$/) /E$/
which is approximated by
i$-i= (F$/-E$/) /E$/ (Covered InterestParity)
In other words, the interest differential betweenthe US and the EU is equal to the forwardpremium of the euro.
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Interest Parity
To check CIP:
(i$-i) = (1.8703.351)400 = -0.0037
(F$/-E$/) /E$/= (0.85850.8617)0.8617= -0.0037
CIP can be rewritten as
i$=i+ (forward premium)
where (forward premium) = (F$/-E$/) /E$/
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Uncovered Interest Parity
Suppose that a US investor is buying a UKbond without using the forward market.
The 6 months Libor is 4.17250 %, butthis is not the rate of return relevant for theUS investor.
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UIP
The effective rate is given by
i + (Ee$/-E$/) /E$/
= (UK interest rate) + (Expected rate of
depreciation)
where Ee$/
stands for the expectedexchange rate 3 month ahead.
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UIP
In other words, the expected return on apound investment is the UK interest rate
plus the expected rate of depreciation ofthe dollar against the pound.
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UIP: an example
Suppose an investor expects the dollar toappreciate by 1.15% over six months.
Then, the expected return on a UK bond is(4.172502)1.15 = 0.936 %.
This is almost same as the return on a US
bond: 1.8702 = 0.935 %.
In such a case, we say that UncoveredInterest Parityholds.
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Inflation and Interest Rates
Nominal interest rate = i : the observedrate
Real interest rate = r : the rate adjustedfor inflation
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Fisher Effect
Nobody lends someone money at 5%interest rate when the inflation rate is
expected to be 6% for the next year.(Why?)
The nominal interest rate incorporates
inflation expectations to provide lendersenough level of real return. Fisher Effect
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Fisher Equation
i = r + e
where e = expected rate of inflation
Higher the inflation expectations, higherwill be the nominal interest rates.
The interest rates were high in 1970s and
80s.
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Exchange rates, interest ratesand inflation
Fisher equations for two countries:
i$= r$+ USe
i= r+ Je
If the real rate is the same between twocountries, that is, r$= r, then
i$- i = USe- J
e= (F$/-E$/) /E$/
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CIP, PPP, and FE
Covered Interest Parity:
i$- i = (F$/-E$/) /E$/
Relative PPP:US
e- Je= %E$/= (F$/-E$/) /E$/
Fisher equations for two countries:
i$= r$+ USe
i= r+ Je
CIP + Relative PPP + FE implies r$ = r
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Implications
Suppose initially CIP holds:
i$- i = (F$/-E$/) /E$/ Suppose further that the Democrats take
over the senate and congress and startmassive spending.
Then,
US
e
. (Why?) This implies i$by Fisher equation
(Why?)
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Three possible cases
1. Possibly, Ee. Then F . (Why?)
2. More likely, Eedoes not change. Then E .(Why?)
3. Suppose that the US or Japan or bothintervene the FX markets, trying to keep theexchange rate constant. Then, there will be nochange in i
$- i
(Why?)
But i$(Why?)
So, i has to go up.
Then, J will also go up. (Why?)
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Expected exchange rate and theTerm Structure of Interest Rates
How different are the interest rates fordifferent maturities? Term Structure of
Interest Rates In bonds market, there are 3-month, 6-
month, 1-year, 3-year, 10-year, and 30-year bonds.
Short-term, medium-term, long-terminterest rates.
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Term Structure of Interest Rates
Expectations Hypothesis:
The expected return from the long-term bond
tends to be equal to the return generated fromholding the series of short-term bonds.
Liquidity Premium
Risk-averse investors more prefer lendingshort-term than long-term. (Why?)
Long-term bonds incorporate a risk-premium.
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