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1. The Foreign Exchange Market Some currency rates as of May 21, 2004: Per U.S. dollar: Brazil (Real) Mexico (Peso) Japan (Yen) 3.1939 11.5754 112.2839 Indonesia (Rupiah) 89066 South Africa (Rand) 6.7295 United Kingdom (Pound) 0.5593 1 The Foreign Exchange Market... Some forward currency rates as of May 24, 2004: U.S. dollars per Euro (bid prices): Spot rate 1.2017 One-month forward 1.20062 3 months forward 1.19898 6 months forward 1.19789 12 months forward 1.19854 24 months forward 1.19804 2 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? 3 Definitions r$ : dollar rate of interest (r¥, rHK$,…) i$ : 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 $1.2017 4 3. Four theories . Difference in interest rates 1 + r€ 1 + r$ Fisher Theory Interest Rate parity Exp. difference in inflation rates 1 + iSFr 1 + i$ Relative PPP Difference between forward & spot rates F€/$ Exp. Theory s€/$ of forward rates Expected change in spot rate E(s€/$) S€/$ 5 Theory #1: Purchasing power parity Law of One Price Versions of PURCHASING POWER PARITY Absolute PPP Relative PPP 6 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$ 7 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 € = $4.15 When law of one price does not hold, supply and demand forces help restore the equality 8 Absolute PPP Extension of law of one price to a basket of goods Absolute PPP examines price levels Apply the law of one price to a basket of goods with price P€ and PUS (use upper-case P for the price of the basket): S€/$ = P€ / PUS where P€ = i (wFR,i p€,i ) PUS = i (wUS,i pUS,i ) 9 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€ / PUS = 1235.75 € / $1482.07 = 0.8338 €/$ May 24: s€/$ = 1235.75 € / $1485.01 = 0.83215 €/$ 10 Relative PPP Absolute PPP: P€ = s€/$ P$ 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$) Using absolute PPP to cancel terms and rearranging: Relative PPP: 1 + i€ = E(s€/$) 1 + i$ s€/$ 11 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€/$ 12 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. 13 Deviations from PPP Simplistic model Why does PPP not hold? Imperfect Markets Statistical difficulties 14 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 15 Summary of theory #1: . Exp. difference in inflation rates 1 + i€ 1 + i$ Relative PPP Expected change in spot rate E(s€/$) S€/$ 16 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 17 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. 18 Interest Rate Parity START (today) $117,228 r$=2.24% END (in one year) $117,228 1.0224 = $119,854 (Invest in $) s€/$=0.83215 $117,228 0.83215 = 97,551€ One year (Invest in €) f€/$=0.83435 97,551€ 1.0251 = 100,000€ r€=2.51% 19 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€/$ 20 Interest rate parity example Suppose the following were true: 12 month interest rate U.S Dollar Euro 2.24% 2.70% Spot rate 1.2017 € / $ Forward rate 1.19854 € / $ Does interest rate parity hold? Which way will funds flow? How will this affect exchange rates? 21 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 22 Summary of theories #1 and #2: . Difference in interest rates 1 + r€ 1 + r$ Interest Rate parity Difference between forward & spot rates f€r/$ s€/$ Exp. difference in inflation rates 1 + i€ 1 + i$ Relative PPP Expected change in spot rate E(s€/$) s€/$ 23 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 + rNominal) = (1 + rReal)(1 + i ) (1 + rReal) = (1 + rNominal) / (1 + i ) 24 Example of capital market equilibrium Fisher condition in U.S. and France: (1 + r$(Real)) = (1 + r$) / (1 + i$) (1 + r€(Real)) = (1 + r€) / (1 + i€) If real rates are equal, then the Fisher condition implies: 1 + r€ = 1 + i€ 1 + r$ 1 + i$ The difference in interest rates is equal to the expected difference in inflation rates 25 Summary of theories 1-3: . Difference in interest rates 1 + r€ 1 + r$ Interest Rate parity Difference between forward & spot rates f€/$ s€/$ Fisher Theory Exp. difference in inflation rates 1 + i€ 1 + i$ Relative PPP Expected change in spot rate E(s€/$) s€/$ 26 Theory #4: Expectations theory of forward rates Main idea: The forward rate equals expected spot exchange rate f€/$ = E(s€/$) Expectations theory of forward rates: f€/$ = E(s€/$ ) s€/$ s€/$ 27 Expectations theory of forward rates With risk, the forward rate may not equal the spot rate Group 1: Receive € in six months, want $ Group 2: Contracted to pay out € in six months • Wait six months and convert € to $ • Wait six months and convert $ to € • Sell € forward • Buy € forward or or If Group 1 predominates, then E(s€/$) < f€/$ If Group 2 predominates, then E(s€/$) > f€/$ 28 Takeaway: Summary of all four theories . Difference in interest rates 1 + r€ 1 + r$ Fisher Theory Interest Rate parity Exp. difference in inflation rates 1 + i€ 1 + i$ Relative PPP Difference between forward & spot rates f€/$ Exp. Theory s€/$ of forward rates Expected change in spot rate E(s€/$) s€/$ 29