Exchange Rates and Interest Rates
Interest Parity
PPP and IP
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Relationship between exchange rates and
prices ------ Purchasing Power Parity
PPP is expected to hold when there is no
arbitrage opportunity in goods markets.
Relationship between exchange rates and
interest rates ------ Interest Parity
IP is expected to hold when there is no
arbitrage opportunity in financial markets.
PPP and IP
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Financial- asset prices adjust to new
information more quickly than goods
prices  PPP does not hold in the short
run
Interest Parity
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1/30/02 FT
US$ Libor (3 months): 1.870 = i$
Euro Libor (3 months): 3.351 = i€
Euro spot: 0.8617 = E$/€
Euro 3 months forward: 0.8585 = F$/€
Euro currency
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Offshore Banking
Euro dollar, Euro yen
Euro banks
Libor = London Interbank Offer Rate
Interest Parity
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By investing $1,000 for 3 months, an
investor in the US can earn 1,000 x (1+i$)
= 1,000 x [1+(0.018704)] = 1,004.67
dollars at home.
Alternatively, she can invest in the EU by
converting dollars to euros and then
investing the euros.
Interest Parity
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$1,000 equal to 1,000 E$/€ = 1,000 
0.8617 = 1,160.50 euros, which is the
quantity of euros resulting from the 1,000
dollars invested.
After three months, she will receive
1,160.50 x (1+i€) = 1,160.50 x [1+(0.03351
4)] = 1,170.22 euros.
Interest Parity
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She will have to convert this investment
return to dollars at the exchange rate that
will prevail 3 months later, which is
unknown today.
To avoid this uncertainty, she can cover
the investment in euro with a forward
contract.
Interest Parity
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She sells €1,170.22 to be received in 3
months in the forward market today.
The covered return is (1,000  E$/€) x
(1+i€) x F$/€ = 1,170.22 x F$/€ = 1,170.22 x
0.8585 = 1,004.64 dollars, which is pretty
close to $1,004.67.
Interest Parity
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Arbitrage makes the difference between
the returns on two investment
opportunities equal to zero.
In other words,
1+i$ = (1+i€)(F$/€ /E$/€)
or
(1+i$)/ (1+i€) = (F$/€ /E$/€)
Interest Parity
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Interest rate parity condition is given by
(i$-i€)/ (1+i€) = (F$/€-E$/€) /E$/€
which is approximated by
i$-i€ = (F$/€-E$/€) /E$/€ (Covered Interest
Parity)
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In other words, the interest differential between
the US and the EU is equal to the forward
premium of the euro.
Interest Parity
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To check CIP:
(i$-i€) = (1.870 – 3.351)400 = -0.0037
(F$/€-E$/€) /E$/€ = (0.8585 – 0.8617)0.8617
= -0.0037
CIP can be rewritten as
i$ =i€ + (forward premium)
where (forward premium) = (F$/€-E$/€) /E$/€
Uncovered Interest Parity
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Suppose that a US investor is buying a UK
bond without using the forward market.
The 6 months £ Libor is 4.17250 %, but
this is not the rate of return relevant for the
US investor.
UIP
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The effective rate is given by
i£ + (Ee$/€-E$/€) /E$/€
= (UK interest rate) + (Expected rate of
depreciation)
where Ee$/€ stands for the expected
exchange rate 3 month ahead.
UIP
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In other words, the expected return on a
pound investment is the UK interest rate
plus the expected rate of depreciation of
the dollar against the pound.
UIP: an example
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Suppose an investor expects the dollar to
appreciate by 1.15% over six months.
Then, the expected return on a UK bond is
(4.172502) – 1.15 = 0.936 %.
This is almost same as the return on a US
bond: 1.8702 = 0.935 %.
In such a case, we say that Uncovered
Interest Parity holds.
Inflation and Interest Rates
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Nominal interest rate = i : the observed
rate
Real interest rate = r : the rate adjusted
for inflation
Fisher Effect
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Nobody lends someone money at 5%
interest rate when the inflation rate is
expected to be 6% for the next year.
(Why?)
The nominal interest rate incorporates
inflation expectations to provide lenders
enough level of real return. Fisher Effect
Fisher Equation
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i = r + e
where e = expected rate of inflation
Higher the inflation expectations, higher
will be the nominal interest rates.
The interest rates were high in 1970s and
80s.
Exchange rates, interest rates
and inflation
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Fisher equations for two countries:
i$ = r$ + USe
i¥ = r¥ + Je
If the real rate is the same between two
countries, that is, r$ = r¥ , then
i$ - i¥ = USe - Je = (F$/¥-E$/¥) /E$/¥
CIP, PPP, and FE
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Covered Interest Parity:
i$ - i¥ = (F$/¥-E$/¥) /E$/¥
Relative PPP:
USe - Je = % E$/¥ = (F$/¥-E$/¥) /E$/¥
Fisher equations for two countries:
i$ = r$ + USe
i¥ = r¥ + Je
“CIP + Relative PPP + FE” implies r$ = r¥
Implications
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Suppose initially CIP holds:
i$ - i¥ = (F$/¥-E$/¥) /E$/¥
Suppose further that the Democrats take
over the senate and congress and start
massive spending.
Then, USe . (Why?)
This implies i$  by Fisher equation
(Why?)
Three possible cases
1.
2.
3.
Possibly, Ee . Then F . (Why?)
More likely, Ee does not change. Then E .
(Why?)
Suppose that the US or Japan or both
intervene the FX markets, trying to keep the
exchange rate constant. Then, there will be no
change in i$ - i¥ (Why?)
But i$  (Why?)
So, i¥ has to go up.
Then, J will also go up. (Why?)
Expected exchange rate and the
Term Structure of Interest Rates
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How different are the interest rates for
different maturities? Term Structure of
Interest Rates
In bonds market, there are 3-month, 6month, 1-year, 3-year, 10-year, and 30year bonds.
Short-term, medium-term, long-term
interest rates.
Term Structure of Interest Rates
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Expectations Hypothesis:
The expected return from the long-term bond
tends to be equal to the return generated from
holding the series of short-term bonds.
Liquidity Premium
Risk-averse investors more prefer lending
short-term than long-term. (Why?)
Long-term bonds incorporate a risk-premium.