1. 1 1. The Foreign Exchange Market Some currency rates as of May 21, 2004: Per U.S. dollar: Brazil (Real)3.1939 Mexico (Peso)11.5754 Japan (Yen)112.2839 Indonesia (Rupiah)89066 South Africa (Rand)6.7295 United Kingdom (Pound)0.5593

2. 2 The Foreign Exchange Market... Some forward currency rates as of May 24, 2004: U.S. dollars per Euro (bid prices): Spot rate1.2017 One-month forward1.20062 3 months forward1.19898 6 months forward1.19789 12 months forward1.19854 24 months forward1.19804

3. 3 2. Some basic questions Why aren’t FX rates all equal to one? Why do FX rates change over time? Why don’t all FX rates change in the same direction? What drives forward rates – the rates at which you can trade currencies at some future date?

4. 4 Definitions r $ : dollar rate of interest (r ¥, r HK$,…) i $ : expected dollar inflation rate f €/$ : forward rate of exchange s €/$ : spot rate of exchange “Indirect quote”: s €/$ = 0.83215  1 $ buys 0.83215 € “Direct quote”: s $/€ = 1.2017  1 € buys $1.2017

5. 5 3. Four theories. Difference in interest rates 1 + r € 1 + r $ Exp. difference in inflation rates 1 + i SFr 1 + i $ Difference between forward & spot rates F €/$ s €/$ Expected change in spot rate E(s €/$ ) S €/$ Fisher Theory Relative PPP Interest Rate parity Exp. Theory of forward rates

6. 6 Theory #1: Purchasing power parity Versions of PURCHASING POWER PARITY Versions of PURCHASING POWER PARITY Law of One Price Absolute PPP Relative PPP

7. 7 The Law of One Price A commodity will have the same price in terms of common currency in every country In the absence of frictions (e.g. shipping costs, tariffs,..) Example Price of wheat in France (per bushel): P € Price of wheat in U.S. (per bushel): P $ S €/$ = spot exchange rate P € = s €/$  P $

8. 8 The Law of One Price, continued Example: Price of wheat in France per bushel (p € ) = 3.45 € Price of wheat in U.S. per bushel (p $ ) = $4.15 S €/$ = 0.83215 (s $/€ = 1.2017) Dollar equivalent price of wheat in France= s $/€ x p € = 1.2017 $/€ x 3.45 € = $4.15  When law of one price does not hold, supply and demand forces help restore the equality

9. 9 Absolute PPP Extension of law of one price to a basket of goods Absolute PPP examines price levels Apply the law of one price to a basket of goods with price P € and P US (use upper-case P for the price of the basket): where P € =  i (w FR,i  p €,i ) P US =  i (w US,i  p US,i ) S €/$ = P € / P US

10. 10 Absolute PPP If the price of the basket in the U.S. rises relative to the price in Euros, the U.S. dollar depreciates: May 21 :s €/$ = P € / P US = 1235.75 € / $1482.07 = 0.8338 €/$ May 24:s €/$ = 1235.75 € / $1485.01 = 0.83215 €/$

11. 11 Relative PPP Absolute PPP: For PPP to hold in one year: P € (1 + i € ) = E(s €/$ )  P $ (1 + i $ ), or:P € (1 + i € ) = s €/$ [E(s €/$ )/s €/$ )]  P $ (1 + i $ ) Using absolute PPP to cancel terms and rearranging: Relative PPP: P € = s €/$  P $ 1 + i € = E(s €/$ ) 1 + i $ s €/$

12. 12 Relative PPP Main idea – The difference between (expected) inflation rates equals the (expected) rate of change in exchange rates: 1 + i € = E(s €/$ ) 1 + i $ s €/$

13. 13 What is the evidence? The Law of One Price frequently does not hold. Absolute PPP does not hold, at least in the short run. See The Economist’s Big McCurrencies The data largely are consistent with Relative PPP, at least over longer periods.

14. 14 Deviations from PPP Why does PPP not hold? Why does PPP not hold? Simplistic model Imperfect Markets Statistical difficulties

15. 15 Deviations from PPP Simplistic model Imperfect Markets Statistical difficulties  Transportation costs  Tariffs and taxes  Consumption patterns differ  Non-traded goods & services  Sticky prices  Markets don’t work well  Construction of price indexes - Different goods - Goods of different qualities

16. 16 Summary of theory #1:. Exp. difference in inflation rates 1 + i € 1 + i $ Expected change in spot rate E(s €/$ ) S €/$ Relative PPP

17. 17 Theory #2: Interest rate parity Main idea: There is no fundamental advantage to borrowing or lending in one currency over another This establishes a relation between interest rates, spot exchange rates, and forward exchange rates Forward market: Transaction occurs at some point in future BUY: Agree to purchase the underlying currency at a predetermined exchange rate at a specific time in the future SELL: Agree to deliver the underlying currency at a predetermined exchange rate at a specific time in the future

18. 18 Example of a forward market transaction Suppose you will need 100,000 € in one year Through a forward contract, you can commit to lock in the exchange rate f $/€ : forward rate of exchange Currently, f $/€ = 1.19854  1 € buys $1.19854  1 $ buys 0.83435 € At this forward rate, you need to provide $119,854 in 12 months.

19. 19 Interest Rate Parity START (today) END (in one year) $117,228 $117,228  1.0224 = $119,854 r $ =2.24% $117,228  0.83215 = 97,551€ s €/$ =0.83215 r € =2.51% 97,551€  1.0251 = 100,000€ f €/$ =0.83435 One year (Invest in $) (Invest in €)

20. 20 Interest rate parity Main idea: Either strategy gets you the 100,000€ when you need it. This implies that the difference in interest rates must reflect the difference between forward and spot exchange rates Interest Rate Parity: 1 + r € = f €/$ 1 + r $ s €/$

21. 21 Interest rate parity example Suppose the following were true: Does interest rate parity hold? Which way will funds flow? How will this affect exchange rates? U.S DollarEuro 12 month interest rate 2.24%2.70% Spot rate1.2017 € / $ Forward rate1.19854 € / $

22. 22 Evidence on interest rate parity Generally, it holds Why would interest rate parity hold better than PPP? Lower transactions costs in moving currencies than real goods Financial markets are more efficient that real goods markets

23. 23 Summary of theories #1 and #2:. Difference in interest rates 1 + r € 1 + r $ Exp. difference in inflation rates 1 + i € 1 + i $ Difference between forward & spot rates f €r/$ s €/$ Expected change in spot rate E(s €/$ ) s €/$ Relative PPP Interest Rate parity

24. 24 Theory #3: The Fisher condition Main idea: Market forces tend to allocate resources to their most productive uses So all countries should have equal real rates of interest Relation between real and nominal interest rates: (1 + r Nominal ) = (1 + r Real )(1 + i ) (1 + r Real ) = (1 + r Nominal ) / (1 + i )

25. 25 Example of capital market equilibrium Fisher condition in U.S. and France: (1 + r $(Real) ) = (1 + r $ ) / (1 + i $ ) (1 + r €(Real) ) = (1 + r € ) / (1 + i € ) If real rates are equal, then the Fisher condition implies: The difference in interest rates is equal to the expected difference in inflation rates 1 + r € = 1 + i € 1 + r $ 1 + i $

26. 26 Summary of theories 1-3:. Difference in interest rates 1 + r € 1 + r $ Exp. difference in inflation rates 1 + i € 1 + i $ Difference between forward & spot rates f €/$ s €/$ Expected change in spot rate E(s €/$ ) s €/$ Fisher Theory Relative PPP Interest Rate parity

27. 27 Theory #4: Expectations theory of forward rates Main idea: The forward rate equals expected spot exchange rate Expectations theory of forward rates: f €/$ = E(s €/$ ) s €/$ s €/$

28. 28 Expectations theory of forward rates With risk, the forward rate may not equal the spot rate If Group 1 predominates, then E(s €/$ ) < f €/$ If Group 2 predominates, then E(s €/$ ) > f €/$ Group 1: Receive € in six months, want $ Wait six months and convert € to $ or Sell € forward Group 1: Receive € in six months, want $ Wait six months and convert € to $ or Sell € forward Group 2: Contracted to pay out € in six months Wait six months and convert $ to € or Buy € forward Group 2: Contracted to pay out € in six months Wait six months and convert $ to € or Buy € forward

29. 29 Takeaway: Summary of all four theories. Difference in interest rates 1 + r € 1 + r $ Exp. difference in inflation rates 1 + i € 1 + i $ Difference between forward & spot rates f €/$ s €/$ Expected change in spot rate E(s €/$ ) s €/$ Fisher Theory Relative PPP Interest Rate parity Exp. Theory of forward rates