Foreign Exchange Markets

1. Foreign Exchange Markets

2. Foreign Exchange • Market Participants • Market Instruments • Spot • Forward & Futures • Options • Futures Options • Market Organization

3. Foreign Exchange • View foreign currency as a commodity • Price is $ per unit of foreign currency • This is the “exchange rate” • Often counterintuitive • Japanese Yen are quoted as 122 ¥/$ • Increase is called “appreciation” or “revaluation” • Decrease is called “depreciation” or “devaluation”

4. Market Participants • Importers (demand foreign currency) • Exporters (supply foreign currency) • Speculators • Commercial Banks • Central Banks

5. Households & Firms • May be importers, exporters & speculators • Large corporations often have in-house traders who buy and sell for a variety of reasons, including hedging risk and speculation

6. Market Instruments • Spot rate • Exchange currencies now • Forward or Futures rate • Agree to exchange currencies at a future date using a rate chosen now • Option • Option to sell “put” or buy “call” a specified amount of a currency at a future date at a specified rate “strike price”

9. Market Organization • Over-the-Counter (OTC) market • No central face-to-face clearing house • Traders are linked via a high speed data network • Run by same data provider as Reuters news service • Traders also communicate via telephone

10. Market Organization • Major international trading locations: • London • New York • Tokyo • Singapore

11. Market Organization • Major regional locations: • Sydney (opens first) • Hong Kong • Frankfurt • Zurich • Paris • San Francisco (closes last)

12. Market Organization • Major “vehicle” currencies • US dollar ($ - USD) • Euro (€ - EUR) • Japanese Yen (¥ - JPY) • British Pound (₤ - GBP) • Swiss Franc (Fr - CHF)

15. Arbitrage • Spatial Arbitrage • Triangular

16. Spatial Arbitrage Reflected by bid/ask spreads • Bid – price the bank will pay when it buys a unit of foreign currency • Ask – price the bank accepts when it sells a unit of foreign currency • Ask > Bid or the bank makes no money • Competition drives this spread to the cost of providing foreign exchange <.1% http://www.ozforex.com.au/cgi-bin/spotrates.asp

17. Bid-Ask Spreads 3/15/06

18. Triangular Arbitrage Series of 3 trades yields a profit no-arbitrage condition is: or equivalently $/£: 1.6793 - 801 ¥/$ 140.55 - 62 ¥/£ 236.02 - 26 implies £/¥ .0042326 - 69 check condition 1.6801 x .0042326 x 140.55 = .99901 < 1 check it the other way 1.6793 x .0042369 x 140.62 = .1.0010 > 1

19. Interest Rate Parity Conditions • Covered Interest Rate Parity • (CIRP) • Uncovered Interest Rate Parity • (UIRP)

20. Covered Interest Rate Parity • $1,000,000 to invest today for one year • Domestic strategy • Invest in domestic financial asset and earn rate of return i • rD = 1+i

21. Covered Interest Rate Parity • $1,000,000 to invest today for one year • Foreign strategy • Buy foreign currency on the spot market at price, 1/s • Invest in foreign financial asset and earn rate, i* • Convert back to $ next year using a forward contract at price f • rF = (1+i*)(f/s)

22. Covered Interest Rate Parity • Since both strategies involve the same risk (perhaps zero), investors should be indifferent only if they give the same return • rD = rF • 1+i=(1+i*)(f/s) • Taking natural logs of both sides • i=i*+f • f=ln(f)-ln(s) is the “forward premium”

23. Forward Premium • % by which today’s forward rate exceeds today’s spot rate • Forward rates have different horizons, and therefore so do forward premia • Usually these premia are quoted in annualized rates

24. Forward Premium • Denote the horizon for the forward rate as 1/N, that is one-Nth of a year. • The formula for the annualized forward premium is: • Or is approximated by:

25. Covered Interest Rate Parity • Hence a CIRP condition is:

26. Uncovered Interest Rate Parity • $1,000,000 to invest today for one year • Domestic strategy • Invest in domestic financial asset and earn rate of return i • rD = 1+i

27. Uncovered Interest Rate Parity • $1,000,000 to invest today for one year • Foreign strategy • Buy foreign currency on the spot market at price, 1/s • Invest in foreign financial asset and earn rate, i* • Convert back to $ next year using a next year’s spot price, s’ • rF = (1+i*)(s’/s)

28. Uncovered Interest Rate Parity • E{rD} = E{rF} • 1+i=(1+i*)(E{s’}/s) • Taking natural logs of both sides • i=i*+E{ε’} • ε’=ln(s’)-ln(s) is the appreciation in the price of foreign currency • ε will also need to be annualized

29. Uncovered Interest Rate Parity • Hence a UIRP condition is:

30. Testing interest rate parity • CIRP • i-i*=φ • Holds as an arbitrage condition • UIRP • i-i*=E{ε’} • Need data on expectations • Usually does not hold, why?

31. Risk Premia • Investor has three options • Home investment • (1+i) with no risk • Covered foreign • (1+i*)(f/s) with no risk • Uncovered foreign • (1+i*)(E{s’}/s) risky

32. Risk Premia • Investor is indifferent between home and covered foreign if CIRP holds. • Investor is NOT indifferent between these two and uncovered, even if UIRP holds if the investor is “risk averse”

33. Risk Premia • A risk premium is the extra return needed to make the investor indifferent between the riskless and risky investments • (1+i)(1+ρ) = (1+i*)(E{s’}/s) • In this case ρ>1

34. Testing interest rate parity • Jointly test the following: • CIRP • i-i*=φ • UIRP • i-i*=E{ε’}+ρ • Rational Expectations • E{ε’}= ε’+u • u is mean zero random error • (1+ρ)

35. Testing interest rate parity • Using CIRP & UIRP • φ=E{ε’}+ρ • Using Rational Expectations • φ= ρ+ ε’+u • Test using linear regression • φ= c+b ε’+u • Ho: b=1 • Rejected soundly

36. Explaining the forward bias • Why do we reject? • CIRP does not hold This has been independently tested • RE does not hold Possible, but unlikely • UIRP does not hold This is a possible explanation if the risk premium is not constant over time

37. Explaining the forward bias • Economic theory gives the following: • ρ=γCov(s,RP) • γ is a measure of risk aversion • RP is the average return on all assets in the economy