Parity Conditions in International Finance and Currency Forecasting

1
Parity Conditions in International Finance and
Currency Forecasting

• Chapter 4

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ARBITRAGE AND THE LAW OF ONE PRICE

• Five Parity Conditions Result From Arbitrage
  Activities
• 1. Purchasing Power Parity (PPP)
• 2. The Fisher Effect (FE)
• 3. The International Fisher Effect
• (IFE)
• 4. Interest Rate Parity (IRP)
• 5. Unbiased Forward Rate (UFR)

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PART I. ARBITRAGE AND THE LAW OF ONE PRICE

• I. THE LAW OF ONE PRICE
• A. Law states
• Identical goods sell for the same price
  worldwide.
• B. Theoretical basis
• If the price after exchange-rate
• adjustment were not equal, arbitrage in
  the goods worldwide ensures eventually it will.

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ARBITRAGE AND THE LAW OF ONE PRICE

• C. Five Parity Conditions Linked by
• The adjustment of rates and prices
• to inflation

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ARBITRAGE AND THE LAW OF ONE PRICE

• D. Inflation and home currency depreciation
  are
• 1. Jointly determined by the growth of
  domestic money supply (Ms) and
• 2. Relative to the growth of
• domestic money demand.

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PART II.PURCHASING POWER PARITY

• I. THE THEORY OF PURCHASING
• POWER PARITY
• states that spot exchange rates between
  currencies will change to the differential in
  inflation rates between
• countries.

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PURCHASING POWER PARITY

• II. RELATIVE PURCHASING POWER PARITY
• A. states that the exchange rate of one
  currency against another will adjust to
  reflect changes in the price levels of the two
  countries.

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PURCHASING POWER PARITY

• 1. In mathematical terms
• et (1 ih)t
• e0 (1 if)t
• where et future spot rate
• e0 spot rate
• ih home inflation
• if foreign inflation
• t time period

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PURCHASING POWER PARITY

• 2. If purchasing power parity is
• expected to hold, then the best
• prediction for the one-period
• spot rate should be
• et e0(1 ih)t
• (1 if)t

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PURCHASING POWER PARITY

• 3. A more simplified but less precise
• relationship is
• et - e0 ih - if
• e0
• that is, the percentage change should be
  approximately equal to
• the inflation rate differential.

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PURCHASING POWER PARITY

• 4. PPP says
• the currency with the higher inflation rate
  is expected to depreciate relative to the
  currency with the lower rate of inflation.

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Sample Problem

• Projected inflation rates for the U.S. and
  Germany for the next twelve months are 10 and
  4, respectively. If the current exchange rate
  is .50/dm, what should the future spot rate be
  at the end of next twelve months?

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PART III.THE FISHER EFFECT

• I. THE FISHER EFFECT
• states that nominal interest rates (r) are a
  function of the real interest rate (a) and a
  premium (i) for inflation expectations.
• R a i

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PART IV. THE INTERNATIONAL FISHER EFFECT

• A. Real Rates of Interest
• 1. Should tend toward equality
• everywhere through arbitrage.
• 2. With no government interference
• nominal rates vary by inflation
• differential or
• rh - rf ih - if

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THE INTERNATIONAL FISHER EFFECT

• B. According to the IFE,
• countries with higher inflation rates have
  higher interest rates.
• C. Due to capital market integration
  globally, interest rate differentials are
  eroding.

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THE INTERNATIONAL FISHER EFFECT

• I. IFE STATES
• A. the spot rate adjusts to the interest rate
  differential between two countries.
• B. IFE PPP FE
• et (1 rh)t
• e0 (1 rf)t

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THE INTERNATIONAL FISHER EFFECT

• B. Fisher postulated
• 1. The nominal interest rate differential
  should reflect the inflation rate
  differential.
• 2. Expected rates of return are equal in the
  absence of government intervention.

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THE INTERNATIONAL FISHER EFFECT

• C. Simplified IFE equation
• rh - rf et - e0
• e0

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THE INTERNATIONAL FISHER EFFECT

• D. Implications if IFE
• 1. Currency with the lower interest rate
  expected to appreciate relative to one
• with a higher rate.
• 2. Financial market arbitrage
• insures interest rate differential
• is an unbiased predictor of change in
  future spot rate.

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The International Fisher Effect
If the / spot rate is 108/ and the interest
rates in Tokyo and New York are 6 and 12,
respectively, what is the future spot rate two
years from now?
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PART V.INTEREST RATE PARITY THEORY

• I. INTRODUCTION
• A. The Theory states
• the forward rate (F) differs from the spot
  rate (S) at equilibrium by an amount equal to
  the interest differential (rh - rf) between two
  countries.

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INTEREST RATE PARITY THEORY

• 2. The forward premium or
• discount equals the interest
• rate differential.
• F - S/S (rh - rf)
• where rh the home rate
• rf the foreign rate

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INTEREST RATE PARITY THEORY

• 3. In equilibrium, returns on
• currencies will be the same
• i. e. No profit will be realized
• and interest parity exists
• which can be written
• (1 rh) F
• (1 rf) S

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INTEREST RATE PARITY THEORY

• B. Covered Interest Arbitrage
• 1. Conditions required
• interest rate differential does not equal
  the forward premium or discount.
• 2. Funds will move to a country
• with a more attractive rate.

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INTEREST RATE PARITY THEORY

• 3. Market pressures develop
• a. As one currency is more
• demanded spot and sold
• forward.
• b. Inflow of funds depresses
• interest rates.
• c. Parity is eventually reached.

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INTEREST RATE PARITY
If the Swiss franc is .68/SF on the spot market
and the annualized interest rates in the U.S.
and Switzerland, respectively, are 7.94 and 2,
what is the 180 day forward rate under parity
conditions?
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INTEREST RATE PARITY THEORY

• C. Summary
• Interest Rate Parity states
• 1. Higher interest rates on a
• currency offset by forward
• discounts.
• 2. Lower interest rates are offset
• by forward premiums.

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PART VI.THE RELATIONSHIP BETWEEN THE FORWARD AND
THE FUTURE SPOT RATE

• I. THE UNBIASED FORWARD RATE
• A. States that if the forward rate is
• unbiased, then it should reflect the
• expected future spot rate.
• B. Stated as
• ft et