CHAPTER 4 Parity Conditions (Textbook Chapter 4)

OUTLINE The Law of One Price Parity Conditions Purchasing Power Parity (PPP) Fisher Effect (FE) International Fisher Effect (IFE) Interest Rate Parity (IRP) Forward Rates as Unbiased predictor of future spot rates (UFR) 2

ARBITRAGE AND THE LAW OF ONE PRICE I.THE LAW OF ONE PRICE A.States that identical goods sell for the same price worldwide. 3

ARBITRAGE AND THE LAW OF ONE PRICE B. Theoretical basis: If the prices after exchange-rate adjustment were not equal, arbitrage for the goods worldwide ensures that eventually they will. 4

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) 5

ARBITRAGE AND THE LAW OF ONE PRICE D. Five Parity Conditions 6

ARBITRAGE AND THE LAW OF ONE PRICE E.THE LAW OF ONE PRICE - enforced by international arbitrage. 7

PURCHASING POWER PARITY (PPP) 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 II. ABSOLUTE PURCHASING POWER PARITY A. Price levels adjusted for exchange rates should be equal between countries B. One unit of currency has same purchasing power globally. 9

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 10

PURCHASING POWER PARITY 1.In mathematical terms: where e t = future spot rate e 0 = spot rate i h = home inflation i f = foreign inflation t= the time period 11

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

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. 13

PURCHASING POWER PARITY 14

PURCHASING POWER PARITY 4.PPP states: the currency with the higher inflation rate is expected to depreciate relative to the currency with the lower rate of inflation 15

PURCHASING POWER PARITY B.Real Exchange Rates: the quoted or nominal rate adjusted for a country’s inflation rate is 16

PURCHASING POWER PARITY C.Real exchange rates If exchange rates adjust to inflation differential, PPP states that real exchange rates stay the same. 17

Example: Real Exchange Rate Between 1982 and 2006, the ¥/$ exchange rate moved from ¥249.05/$ to ¥116.34/$. During this same 25-year period, the consumer price index (CPI) in Japan rose from to and the U.S. CPI rose from to a. If PPP had held over this period, what would the ¥/$ exchange rate have been in 1995? b. What happened to the real value of the yen in terms of U.S. dollars during this period? 18

THE FISHER EFFECT (FE) A. Definition: states that nominal interest rates (r) are a function of the real interest rate (a) and a premium (i) for inflation expectations. which is often approximated by 19

THE FISHER EFFECT B.Real Rates of Interest 1. Should tend toward equality everywhere through arbitrage. 2. With no government interferencenominal rates vary by inflation differential or r h - r f = i h - i f 20

THE FISHER EFFECT C.According to the Fisher Effect: countries with higher inflation rates have higher interest rates 21

THE INTERNATIONAL FISHER EFFECT (IFE) 22

Example: Forecast US$ and SFr Rates In July, the one-year interest rate is 2% on Swiss francs and 7% on U.S. dollars. a.If the current exchange rate is SFr 1 = $0.91, what is the expected future exchange rate in one year? b.If a change in expectations regarding future U.S. inflation causes the expected future spot rate to rise to $1.00, what should the U.S. interest rate be? 23

THE INTERNATIONAL FISHER EFFECT B.Simplified IFE equation: (if r f is relatively small) 24

THE INTERNATIONAL FISHER EFFECT 25

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 2. Financial market arbitrage: insures interest rate differential is an unbiased predictor of change in future spot rate. 26

INTEREST RATE PARITY (IRP) THEORY A. The Theory states: the forward rate (f 1 ) differs from the spot rate (S) at equilibrium by an amount equal to the interest differential (r h - r f ) between two countries where r h = the home rate r f = the foreign rate 27

INTEREST RATE PARITY THEORY 28

INTEREST RATE PARITY THEORY 29

INTEREST RATE PARITY THEORY B. In summary, IRP states 1.Higher interest rates on a currency are offset by forward discounts 2.Lower interest rates are offset by forward premiums 30

Example: Arbitrage Opportunity Suppose the annualized interest rate on 180-day U.S. dollar deposits is 6 7/16 – 5/16%, meaning that U.S. dollars can be borrowed at 6 7/16% (the ask or offered rate) and lent at 6 5/16% (the bid rate). At the same time, the annualized interest rate on 180-day Thai baht (B) deposits is 9 3/8 – 1/8%. Spot and 180-day forward quotes on Thai baht are B /$ and B /$, respectively. Is there an arbitrage opportunity? Compute the profit using B 10,000,

THE FORWARD AND THE FUTURE SPOT RATE 32

THE FORWARD AND THE FUTURE SPOT RATE 33

SUMMARY Law of one price In the absence of market imperfections, arbitrage ensures that exchange-adjusted prices of identical traded goods and financial assets are within transaction costs worldwide. 34

SUMMARY (Cont’d) Parity Conditions Purchasing Power Parity (PPP) Fisher Effect (FE) which is often approximated by 35

SUMMARY (Cont’d) 36

SUMMARY (Cont’d) 37