Foreign Exchange Markets

Foreign Exchange Markets Dr Bryan Mills Based on http://faculty.washington.edu/karpoff/FIN%20509/FIN509_session7.ppt

Outline of these slides • The foreign exchange (FX) market • Basic questions and definitions • Four theories • Purchasing Power Parity • Interest Rate Parity • Fisher condition for capital market equilibrium • Expectations theory of forward rates

1. The Foreign Exchange Market Sell buy Reuters 19/4/2010

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. 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?

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

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

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

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$

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

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): where P€ = i (wFR,i p€,i ) PUS = i (wUS,i pUS,i ) S€/$ = P€ / PUS

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 € / $1485.01 = 0.83215 €/$

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€/$

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€/$

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.

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

Deviations from PPP • 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 Simplistic model Imperfect Markets Statistical difficulties

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

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

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.

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

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$s€/$

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?

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

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

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 )

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$

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

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€/$) f€/$ = E(s€/$ ) s€/$s€/$

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 2:Contracted to • pay out € in six months • Wait six months and • convert $ to € • or • Buy € forward

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

Foreign Exchange Markets