Parity Conditions in International Finance

1

• Parity Conditions in International Finance
• (Fisher Effect, International Fisher Effect,
• and Interest Rate Parity)
• (Shapiro Chapter 4)

2
The Fisher Effects

• An increase (decrease) in the expected rate of
  inflation will cause a proportionate increase
  (decrease) in the interest rate in the country.
• 1 r (1 ? ) E(1 I)
• 1Nominal interest rate (1 Real interest
  rate) x
• (1
  Expected Inflation rate)
• Fisher effect (approximate version)
• Nominal interest rate Real interest rate
  Expected inflation
• If the real interest rate between countries is
  the same then expected inflation differences
  between countries depend only on the nominal
  interest rate differences

3
Combining this with relative PPP

• ? S (/) (I - I) / (1I)
• Or ? S (/) I I
• E.g. Real interest rates are 3 in the US and
  Japan whereas the nominal interest rate is 10 in
  Japan compared to 6 in the US.
• This would imply that inflation in Japan is
  expected to be 7 versus 3 in the US
• Hence ? S(/) (I - I) 3 - 7 -4
• i.e. The yen is expected to depreciate by 4

4

• If the Fisher effect holds in the U.S.
• 1 r (1 ? ) E(1 I)
• and the Fisher effect holds in Japan,
• 1 r (1 ? ) E(1 I)
• and if the real rates are the same in each
  country
• ? ?
• then we get the
• Fisher Effect
• (Note or r r I I )

5
Example

• Assume IDM 4, I 6, and r 8.5
• What is rDM?
• Assuming similar real rates of return,
• 1.085/(1 rDM) 1.06/1.04
• Þ rDM 0.0645 6.45
• or
• 0.085 - rDM 0.06 -0.04
• Þ rDM 0.065 6.5
• the GER interest rate is lower because the German
  inflation
• rate is expected to be lower

6
International Fisher Effect

• Example In July, the one-year interest rate is
  4 on Swiss francs and 13 on U.S. dollars.
• a. If the current exchange rate is SFr 10.63,
  what is the expected future exchange rate in one
  year?
• Ans 0.6845/SFr
• b. If a change in expectations regarding future
  U.S. inflation causes the expected future spot
  rate to rise to 0.70, what should happen to the
  U.S. interest rate?
• Ans r15.56

7
Evidence on the International Fisher effect

• Short term evidence suggests that exchange rates
  are more volatile than interest rates
• Long term data is more consistent with IFE
• Currencies with high interest rates tend to
  depreciate and vice versa consistent with the IFE

8
Interest Rate Parity

• Spot and forward rates are linked via interest
  rates
• Interest rate parity condition ensures
  equilibrium between the spot and forward market
  rates
• If IRP did not hold, then it would be possible
  for an astute trader to make unlimited amounts of
  money exploiting the arbitrage opportunity.

9
Interest Rate Parity Defined

• Depending upon how you quote the exchange rate (
  per or per ) we have
• IRP is sometimes approximated as
• r - r F/ S /
• S /

or
10
IRP and Covered Interest Arbitrage

• If IRP failed to hold, an arbitrage would exist.
  Its easiest to see this in the form of an
  example.
• Consider the following set of foreign and
  domestic interest rates and spot and forward
  exchange rates.

11
IRP and Covered Interest Arbitrage

• A trader with 1,000 to invest could invest in
  the U.S., in one year his investment will be
  worth 1,071 1,000?(1 r) 1,000?(1.071)
• Alternatively, this trader could exchange 1,000
  for 800 at the prevailing spot rate, (note that
  800 1,0001.25/) invest 800 at r
  11.56 for one year to achieve 892.48. Translate
  892.48 back into dollars at F360(/) 1.20/,
  the 892.48 will be exactly 1,071.

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Interest Rate Parity
1,000
1,071

• Trade 1,000 for 800

1,071

• One year later, trade 892.48 for at F360(/)
  1.20/

• Invest 800 at 11.56 r

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Interest Rate Parity Exchange Rate
Determination

• According to IRP only one 360-day forward rate,
• F360(/), can exist. It must be the case that
• F360(/) 1.20/
• Why?
• If F360(/) ? 1.20/, an astute trader could
  make money with one of the following strategies

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Arbitrage Strategy I

• If F360(/) gt 1.20/
• i. Borrow 1,000 at t 0 at r 7.1.
• ii. Exchange 1,000 for 800 at the prevailing
  spot rate, (note that 800 1,0001.25/)
  invest 800 at 11.56 (r) for one year to
  achieve 892.48
• iii. Translate 892.48 back into dollars, if
• F360(/) gt 1.20/ , 892.48 will be more than
  enough to repay your dollar obligation of 1,071.

15
Arbitrage Strategy II

• If F360(/) lt 1.20/
• i. Borrow 800 at t 0 at r 11.56 .
• ii. Exchange 800 for 1,000 at the prevailing
  spot rate, invest 1,000 at 7.1 for one year to
  achieve 1,071.
• iii. Translate 1,071 back into pounds, if
• F360(/) lt 1.20/ , 1,071 will be more than
  enough to repay your obligation of 892.48.

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Observations

• IRP provides a linkage between interest rates
  differential and forward premium
• Interest rates are more stable the XRs. Thus, in
  IRP the F and S change to accommodate the demand
  and supply for currencies
• If F360(/) gt S (1 r)/ (1 r) borrow in
  and lend in
• If F360(/) lt S (1 r)/ (1 r) lend in and
  borrow in
• If (1 r) gt (F/ S )(1 r) lend in and
  borrow in
• If (1 r) lt (F/ S )(1 r) borrow in and
  lend in

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Example

• 3 month forward exchange rate 1.598 /
• Current spot rate 1.60/
• Annual interest rate in the US 8
• Annual interest rate in Germany 5
• To determine if IRP holds
• Is 1r gtlt F( /) / S( /) x (1r) The
  forward rate is a 3 month rate so we need to
  convert to a 3 month interest rate
• 3 month Euro interest rate 5/4 1.25
• 3 month US interest rate 8/4 2
• LHS 1.0125
• RHS 0.99875 x 1.02 1.0187 and hence LHS ltRHS

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Strategy for arbitrage

• Hence you should borrow in Euro and invest in
  dollars and at the same time buy Euro forward
• 1. Borrow Euro 1,600,000
• 2. Convert to 1,600,000 / 1.60 1,000,000
• 3. Invest in the US at 2 for 3 months
• 4. Buy Euro 1,620,000 forward (1,600,000 x
  1.0125)

Note Forward Contract The purchase or sale of a
specific asset or commodity at a current price
but with delivery and settlement at a future date
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Arbitrage profits

• At the end of 3 months
• Receive 1,000,000 x 1.02 1,020,000
• Buy Euro 1,620,000 at the forward price
• I.e. pay 1,620,000 / 1.598 1,013,767.20
• Hence the difference of 1,020,000 -
  1,013,767.20 6,232 represents arbitrage
  profits

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Problem

• Assume that the one year interest rate in
  Switzerland is 11 while that in the US is 10.
  The spot rate of the Swiss franc is 0.50 and the
  forward rate is 0.54. Is covered interest
  arbitrage feasible for investors?

21
Uncovered -IRP
Covered IRP arbitrage condition
Un-Covered IRP
22
IRP and Hedging Currency Risk

• You are a U.S. importer of British woolens and
  have just ordered next years inventory. Payment
  of 100M is due in one year.

IRP implies that there are two ways that you fix
the cash outflow to a certain U.S. dollar
amount a) Put yourself in a position that
delivers 100M in one yeara long forward
contract on the pound. You will pay
(100M)(1.2/) 120M b) Form a forward market
hedge as shown below.
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IRP and a Forward Market Hedge
To form a forward market hedge Borrow 112.05
million in the U.S. (in one year you will owe
120 million). Translate 112.05 million into
pounds at the spot rate S(/) 1.25/ to
receive 89.64 million. Invest 89.64 million in
the UK at r 11.56 for one year. In one year
your investment will have grown to 100
millionexactly enough to pay your supplier.
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Forward Market Hedge
Where do the numbers come from? We owe our
supplier 100 million in one yearso we know that
we need to have an investment with a future value
of 100 million. Since r 11.56 we need to
invest 89.64 million at the start of the year.
How many dollars will it take to acquire 89.64
million at the start of the year if S(/)
1.25/?
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Reasons for Deviations from IRP

• Transactions Costs
• The interest rate available to an arbitrageur for
  borrowing, rb, may exceed the rate he can lend
  at, rl.
• There may be bid-ask spreads to overcome,
• Fb/Sa lt F/S
• Ex If (1 r) lt (F/ S )(1 r) exists, the
  arbitrage strategy involves lending in and
  borrowing in .
• With transaction costs, it is possible that
• (Fb/Sa)(1 r l) ? (1 r b) ? 0
• Capital Controls
• Governments sometimes restrict import and export
  of money through taxes or outright bans.

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Empirical evidence on IRP

• Early studies - Officer and Willett (1970),
  Frenkel and Levich (1975) - find evidence of
  deviations from IRP attributable to transactions
  costs
• Long term IRP
• Hilley (1981) - substantial deviations from IRP
  using long forward contracts
• Other studies by Popper (1993) found smaller and
  by Fletcher and Taylor (1994) found larger
  deviations at the longer horizons