1. 1 Chapter 6: Interest Rate Parity 熊家财 江西财经大学会计学院 xiongjc-p@163.com

2. 2 Chapter 6: Interest Rate Parity 6.1The Theory of Covered Interest Rate Parity 6.2Covered Interest Rate Parity in Practice 6.3Problems Related to Testing Interest Rate Parity 6.4Hedging Transaction Risk in the Money Market 6.5The Term Structure of Forward Premiums and Discounts

3. 3 Ex 6.1 Kim ’ s choice Kim Deal, a portfolio manager for UBS, a Euro bank, is considering two alternative investment of €10 million - invest in euro deposits for 1 year - invest in yen deposits for 1 year Suppose Kim has the following data: EUR interest rate 3.5200% per annum(p.a) JPY interest rate 0.5938% p.a Spot exchange rate ¥146.0300/ € 1-year forward exchange rate ¥141.9021/ €

4. 4 Choice 1: Invest in euro deposit for 1 year, after 1 year she will have € 10 000 000 × （ 1+3.5200% ） = € 10 352 000 Ex 6.1 Kim ’ s choice Choice 2: Invest in yen deposit for 1 year: - convert euro €10 million to JPY: € 10 000 000 × ( ¥146.0300/ € )= ¥1 460 300 000 - invest her yen at 0.5938% for 1 year: ¥1 460 300 000 × (1+ 0.5938% )= ¥1 468 971 261 - convert yen to euro at ¥146.0300/ € ¥1 468 971 261 / (¥146.0300/ €)= €10 325 005

5. 5 Ex 6.2 Kevin ’ s choice Suppose Kevin has $10 million to invest, and he has the following data: USD interest rate 8.0% per annum(p.a) GBP interest rate 12.0 % p.a Spot exchange rate $ 1.6/ £ 1-year forward exchange rate $ 1.53/ £

6. 6 Choice 1: Invest in dollar deposit for 1 year, after 1 year she will have $ 10 000 000 × （ 1+8.0% ） = € 10 800 000 Ex 6.2 Kevin ’ s choice Choice 2: Invest in GBP deposit for 1 year: - convert $10 million to GBP: € 10 000 000 ÷ ( $ 1.6/ £ )= £ 6 250 000 - invest her GBP at 0.5938% for 1 year: £ 6 250 000 × (1+12 % )= £ 7 000 000 - convert GBP to dollar at $ 1.53/ £ £ 7 000 000 × $ 1.53/ £=$ 10 710 000

7. 7 Ex 6.2 Kevin ’ s choice – Arbitrage borrow pound and invest in dollar Kevin borrow £1 000 000 at 12%, in 1 year he will owe £1 000 000 * 1.12= £1 120 000 Invest in dollar - convert pound in to dollar: £1 000 000 × $ 1.6/ £ = $ 1 600 000 - invest dollar at 8% for 1 year: $ 1 600 000 × 1.08 = $ 1 728 000 - sell the dollar by engaging in a forward contract $ 1 728 000 ÷ ($ 1.53/ £)= £ 1 129 411.76

8. 8 Ex 6.2 Kevin ’ s choice – Arbitrage borrow pound and invest in dollar Borrow pound – raise the pound interest rate 12% ↑ Convert pound into dollar--- depreciate dollar-pound exchange rate $ 1.6/ £ ↓ invest in dollar -- lower the dollar interest 8% ↓ forward purchase of pounds would raise the dollar – pound forward exchange rate $ 1.53/ £ ↑ £1 000 000 * (1+12%) < £1 000 000 × $ 1.6/ £ × (1+8%) ÷ ($1.53/ £)

9. 9 6.1The Theory of Covered Interest Rate Parity The Theory of Covered Interest Rate Parity: Overview The Intuition Behind Interest Rate Parity Two Ways to Buy a Currency Forward Why There Must Be Interest Rate Parity Deriving Interest Rate Parity

10. 10 6.1The Theory of Covered Interest Rate Parity The Intuition Behind Interest Rate Parity Two Ways to Buy a Currency Forward Why There Must Be Interest Rate Parity Deriving Interest Rate Parity

11. 11 6.1The Theory of Covered Interest Rate Parity Two Ways to Buy a Currency Forward Buy a forward contract

12. 12 6.1The Theory of Covered Interest Rate Parity Why There Must Be Interest Rate Parity Covered interest rate arbitrage

13. 13 6.1The Theory of Covered Interest Rate Parity Deriving Interest Rate Parity A general expression for interest rate parity Interest rate parity and forward premiums and discounts

14. 14 A general expression for interest rate parity Notation: i= domestic currency interest rate for 1 period i* = foreign currency interest rate for 1 period S= the spot exchange rate (Domestic currency/ foreign currency) F= the one-period forward exchange rate (Domestic currency/ foreign currency)

15. 15 A general expression for interest rate parity Consider an investor who has one unit of domestic currency and is considering two alternative investment - invest in domestic currency - invest in foreign currency

16. 16 A general expression for interest rate parity Alternative 1: invest 1 unit in domestic currency, get [1+i] Alternative 2: invest 1 unit in foreign currency - convert one unit domestic into foreign currency: 1/S - invest in foreign currency: get [1/S] * [1+i*] - convert foreign into domestic: get [1/S] * [1+i*] * [F] No arbitrage: [1+i] = [1/S] * [1+i*] * [F]

17. 17 Interest rate parity and forward premiums and discounts (1) [1+i] = [1/S] * [1+i*] * [F]

18. 18 Exhibit 6.1 Diagram of Covered Interest Arbitrage

19. 19 Exhibit 6.2 Kevin Anthony ’ s Arbitrage

20. 20 6.2Covered Interest Rate Parity in Practice The External Currency Market Transaction costs in the external currency market How the external currency market affects other capital markets London interbank offer rate (LIBOR)

21. 21 Exhibit 6.3 Interest Rates in the External Currency Market

22. 22 6.2Covered Interest Rate Parity in Practice Covered Interest Arbitrage with Transaction Costs  An empirical test

23. 23 Exhibit 6.4 Covered Interest Rate Parity with Bid-Ask Rates

24. 24 Exhibit 6.5 – Panel A $/ £ Covered Interest Arbitrage into £

25. 25 Exhibit 6.5 – Panel B $/ £ Covered Interest Arbitrage into £

26. 26 6.3Problems Related to Testing Interest Rate Parity Default Risks Exchange Controls Political Risk The Thrilla in Manila

27. 27 Exhibit 6.6 External and Internal FRF Interest Rates and Difference

28. 28 6.4Hedging Transaction Risk in the Money Market Hedging Transaction Risk - Money Market: Overview Introduction Hedging a Foreign Currency Liability Hedging a Foreign Currency Receivable

29. 29 6.4Hedging Transaction Risk in the Money Market Introduction Synthetic forward Money market hedge

30. 30 6.4Hedging Transaction Risk in the Money Market Hedging a Foreign Currency Liability EX 6.3 Zachy has just contract to import Wine from France. You has to pay € 4 million in 90 days. You have the following data: spot exchange rate $ 1.10/ € 90-days forward exchange rate $ 1.08/ € 90-days dollar interest rate: 6.00% p.a. 90-days euro interest rate 13.519% p.a

31. 31 Hedging a Foreign Currency Liability Eliminate the risk by buying euro forward. -- The dollar paid in 90 days is equal to: € 4 000 000 * $ 1.08/ € = $ 4 320 000 -- the present value of these dollar: $ 4 320 000 ÷[1+ 6%*(1/4)]= $ 4 256 157.64

32. 32 Hedging a Foreign Currency Liability hedge the risk in the money market Acquire € 4 million euro asset in 90 days -- The PV of € 4 million at 13.519% p.a is € 4 000 000 ÷ [1+13.519%*(1/4)] =€ 3 869 229.71 -- the dollar cost : € 3 869 229.71 * $ 1.10/ € = $ 4 256 152.68

33. 33 6.4Hedging Transaction Risk in the Money Market Hedging a Foreign Currency Receivable Ex 6.4 Sland have agreed to ship sweater to Japan, and will receive ¥500 000 000 in 30 days. You have the following data: spot exchange rate ¥ 179.5 / £ 30-days forward exchange rate ¥ 180 / £ 30-days pound interest rate: 2.70% p.a. 30-days yen interest rate 6.01% p.a

34. 34 Hedging a Foreign Currency Receivable Eliminate the risk by selling yen forward. -- The pound receive in 30 days is equal to: ¥500 000 000 / (¥ 180 / £ )= £ 2 777 778 hedge the risk in the money market Acquire ¥ 50 million yen liability in 30 days -- The PV of ¥ 50 million yen at 6.05% p.a is ¥ 50 000 000 million ÷ [1+6.05%*(1/4)] = ¥ 497 508 313 -- sell yen for pound : ¥ 497 508 313 ÷ (¥ 179.5 / £)= ¥ 179.5 / £

35. 35 Hedging a Foreign Currency Liability hedge the risk in the money market Acquire ¥ 50 million yen liability in 30 days -- The PV of ¥ 50 million yen at 6.05% p.a is ¥ 50 000 000 million ÷ [1+6.05%*(1/4)] = ¥ 497 508 313 -- sell yen for pound : ¥ 497 508 313 ÷ (¥ 179.5 / £)=£ 2 771 634 -- invest pound at 2.70% £ 2 771 634 *[1+2.7%*(30/365)]= £ 2777 785

36. 36 6.5 The Term Structure of Forward Premiums and Discounts The Term Structure of Interest Rates  Spot Interest Rates  A Review of Bond Pricing  Yields to Maturity  Deriving Long-Term Spot Interest Rates

37. 37 6.5 The Term Structure of Forward Premiums and Discounts Long-Term Forward Rates and Premiums

38. Problem 1. Assume that you are an importer of grain into Japan from the United States. You have agreed to make a payment in dollars, and you are scheduled to pay $377,287 in 90 days after you receive your grain. You face the following exchange rates and interest rates: Spot exchange rate: ¥ 106.35/$ 90-day forward exchange rate: ¥106.02/$ 90-day dollar interest rate:3.25% p.a. 90-day yen interest rate: 1.9375% p.a. a.Describe the nature and extent of your transaction foreign exchange risk. b.Explain two ways to hedge the risk. c.Which of the alternatives in part b is superior?

39. A. Any weakening of the yen versus the dollar will increase the yen cost of your grain. The possible loss is unbounded. B. Choice1:buying dollars forward at ¥106.02/$ Choice 2: determine the present value of the dollars that you owe and buy that amount of dollars today in the spot market.

40. C : The cost of two choices: (1) buying dollars forward at ¥106.02/$ $377,287 × ¥106.02/$ = ¥39,999,967.74 in 90 days. (2) The present value of $377,287 at 3.25% $377,287 / [1+(3.25/100) (90/360) ] = $374,246.25 Purchasing this amount of dollars in the spot market costs ¥106.35/$ × $374,246.25 = ¥39,801,088.69 the future value of this Yen is ¥39,801,088.69 * [1+ (1.9375/100) (90/360) ]= ¥39,993,875.2 1

41. Problem 2. Assume that you are an exporter of grain from Japan to the United States. You are scheduled to receive $377,287 in 90 days after you exporter your grain. You face the following exchange rates and interest rates: Spot exchange rate: ¥ 106.35/$ 90-day forward exchange rate: ¥106.02/$ 90-day dollar interest rate:3.25% p.a. 90-day yen interest rate: 1.9375% p.a. a. Explain two ways to hedge the risk. b. Which of the alternatives in part b is superior?

42. Choice 1: selling dollars forward at ¥106.02/$ $377,287 × ¥106.02/$ = ¥39,999,967.74 in 90 days. Choice 2: a. determine the present value of the dollars that you receive and sell that amount of dollars today in the spot market. b. The present value of $377,287 at 3.25% $377,287 / [1+(3.25/100) (90/360) ] =$374,246.25 c. sell dollar it for Yen in the spot market ¥ 106.35/$ $374,246.25 × ¥ 106.35/$ = ¥39,801,088.69 d. invest yen at 1.9375%, the future value of yen is ¥39,801,088.69 * [1+ (1.9375/100) (90/360) ]= ¥39,993,875.2 1