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CHAPTER 4. PARITY CONDITIONS AND CURRENCY FORECASTING. 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. ARBITRAGE AND THE LAW OF ONE PRICE. B. Theoretical basis: If the price after exchange-rate

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chapter 4

CHAPTER 4

PARITY CONDITIONS AND CURRENCY FORECASTING

part i arbitrage and the law of one price
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.
arbitrage and the law of one price
ARBITRAGE AND THE LAW OF ONE PRICE
  • B. Theoretical basis:
  • If the price after exchange-rate
  • adjustment were not equal, arbitrage in the goods worldwide ensures eventually it will.
arbitrage and the law of one price4
ARBITRAGE AND THE LAW OF ONE PRICE
  • C. Five Parity Conditions Result From These 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)
arbitrage and the law of one price5
ARBITRAGE AND THE LAW OF ONE PRICE
  • D. Five Parity Conditions Linked by
  • The adjustment of various
  • rates and prices to inflation.
arbitrage and the law of one price6
ARBITRAGE AND THE LAW OF ONE PRICE
  • E. Inflation and home currency depreciation:
  • 1. jointly determined by the growth of domestic money supply;
  • 2. Relative to the growth of
  • domestic money demand.
arbitrage and the law of one price7
ARBITRAGE AND THE LAW OF ONE PRICE
  • F. THE LAW OF ONE PRICE
  • - enforced by international
  • arbitrage.
part ii purchasing power parity
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.
purchasing power parity
PURCHASING POWER PARITY
  • II. ABSOLUTE PURCHASING
  • POWER PARITY
  • A. Price levels adjusted for
  • exchange rates should be
  • equal between countries
purchasing power parity10
PURCHASING POWER PARITY
  • II. ABSOLUTE PURCHASING
  • POWER PARITY
  • B. One unit of currency has same purchasing power globally.
purchasing power parity11
PURCHASING POWER PARITY
  • III. 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.
purchasing power parity12
PURCHASING POWER PARITY
  • 1. In mathematical terms:
  • where et = future spot rate
  • e0 = spot rate
  • ih = home inflation
  • if = foreign inflation
  • t = the time period
purchasing power parity13
PURCHASING POWER PARITY
  • 2. If purchasing power parity is
  • expected to hold, then the best
  • prediction for the one-period
  • spot rate should be
purchasing power parity14
PURCHASING POWER PARITY
  • 3. A more simplified but less precise relationship is
  • that is, the percentage change should be approximately equal to the inflation rate differential.
purchasing power parity15
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.
purchasing power parity16
PURCHASING POWER PARITY
  • B. Real Exchange Rates:
  • the quoted or nominal rate adjusted for a country’s inflation rate is
purchasing power parity17
PURCHASING POWER PARITY
  • C. Real exchange rates
  • 1. If exchange rates adjust to inflation differential, PPP states that real exchange rates stay the same.
part iii the fisher effect fe
PART III.THE FISHER EFFECT (FE)
  • 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
the fisher effect
THE FISHER EFFECT
  • B. 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
part iv the international fisher effect ife
PART IV. THE INTERNATIONAL FISHER EFFECT (IFE)
  • I. IFE STATES:
  • A. the spot rate adjusts to the interest rate differential between two countries.
the international fisher effect22
THE INTERNATIONAL FISHER EFFECT
  • B. Fisher postulated
  • 1. The nominal interest rate differential should reflect the inflation rate differential.
the international fisher effect23
THE INTERNATIONAL FISHER EFFECT
  • B. Fisher also postulated that
  • 2. Expected rates of return are equal in the absence of government intervention.
the international fisher effect24
THE INTERNATIONAL FISHER EFFECT
  • C. Simplified IFE equation:
  • (if rf is relatively small)
the international fisher effect25
THE INTERNATIONAL FISHER EFFECT
  • D. Implications of IFE
  • 1. Currency with the lower interest rate is expected to appreciate relative to the one
  • with a higher rate.
the international fisher effect26
THE INTERNATIONAL FISHER EFFECT
  • D. Implications of IFE
  • 2. Financial market arbitrage:
  • insures interest rate differential is an unbiased predictor of change in future spot rate.
part vi interest rate parity theory
PART VI. 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.
interest rate parity theory
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
interest rate parity theory29
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
interest rate parity theory30
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.
interest rate parity theory31
INTEREST RATE PARITY THEORY
  • 3. Market pressures develop:
  • a. As one currency is more demanded spot and sold forward.
  • b. Inflow of fund depresses interest rates.
  • c. Parity eventually reached.
interest rate parity theory32
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.
part vi the relationship between the forward and the future spot rate
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