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Parity Conditions in International Finance and Currency Forecasting

Parity Conditions in International Finance and Currency Forecasting. Chapter 4. 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)

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Parity Conditions in International Finance and Currency Forecasting

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  1. Parity Conditions in International Finance and Currency Forecasting Chapter 4

  2. 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)

  3. Inflation FE PPP IFE Changes in Exchange rates Changes in Interest rates Changes in Forward Rates UFR IRP

  4. ARBITRAGE AND THE LAW OF ONE PRICE • A. Five Parity Conditions Linked by • the adjustment of • rates and prices • to inflation

  5. INFLATION • (ΔMs) > (Δ MD)

  6. ARBITRAGE AND THE LAW OF ONE PRICE • B. 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 (MD).

  7. 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.

  8. Purchasing Power Parity:Conditions • In order to exist PPP we assume: • 1. All goods and services are tradable • 2. Transportation and other Trading costs are zero • 3. Consumers in all countries consume the same proportions of goods and services • 4. The LAW OF ONE PRICE prevails

  9. PART I.ARBITRAGE AND THE LAW OF ONE PRICE • II. 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 was not equal, arbitrage worldwide ensures that eventually it will. • C. Absolute Purchasing Power Parity

  10. 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.

  11. PURCHASING POWER PARITY • 1. In mathematical terms: • where et = future spot rate • e0 = spot rate • ih = home inflation expected • if = foreign inflation exp • t = time period

  12. PURCHASING POWER PARITY • 2. If purchasing power parity is • expected to hold, then the best • prediction for the one-period • spot rate should be

  13. PURCHASING POWER PARITY • 3. A more simplified but less precise • relationship is • that is, the percentage change in rates should be approximately equal to the inflation rate differential.

  14. 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.

  15. 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?

  16. 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

  17. 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

  18. THE INTERNATIONAL FISHER EFFECT • B. According to the IFE, • countries with higher expected inflation rates have higher interest rates.

  19. THE INTERNATIONAL FISHER EFFECT • II. IFE STATES: • A. the spot rate adjusts to the interest rate differential between two countries. • B. IFE = PPP + FE

  20. THE INTERNATIONAL FISHER EFFECT • C. Fisher postulated • 1. The nominal interest rate differential should reflect the inflation rate differential.

  21. THE INTERNATIONAL FISHER EFFECT • D. Simplified IFE equation:

  22. THE INTERNATIONAL FISHER EFFECT • E. Implications if IFE is at work: • 1. Currency with the lower interest rate expected to appreciate relative to one • with a higher rate.

  23. 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?

  24. 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.

  25. INTEREST RATE PARITY THEORY • B. The forward premium or discount equals the interest rate differential. • (F – S)/S = (rh - rf) • where rh = the home rate • rf = the foreign rate • F = the forward rate • S = the spot rate

  26. INTEREST RATE PARITY THEORY • C. In equilibrium, returns on currencies will be the same • i. e. No profit will be realized and interest rate parity exists which can be written

  27. INTEREST RATE PARITY THEORY • D. 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.

  28. 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 eventually reached.

  29. 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?

  30. INTEREST RATE PARITY THEORY • E. 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.

  31. 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

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