Interest Parity

8/10/2019 Interest Parity

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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.

Interest Parity

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