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1. The theory of INTEREST RATE POWER PARITY ( IRP) 1 TOPIC 5

2. MAIN CONTENT The converted interest rate and the choice of currency in investment The theory of the Interest Rate Parity ( IRP) The International Fisher Effect (International Fisher Effect - IFE) Factors make CIP does not hold 2

3. 1 3 The converted interest rate and the choice of currency in investment

4. 1.1. The converted interest rate Example: Choosing a currency to invest when an investor has P = 200.000 VND . VND (T ): annual interest rate r T = 10 %/year USD (C ): annual interest rate r C = 4 %/year Duration of 6 months ( 0.5 year) ( n = 1/t = 2 the times of turnover in a year) The spot rate: S(USD/VND ) = 20.000 The forward rate for 0.5 year: F 1/2 (USD/VND ) = 21.000 4

5. 1.1. The converted interest rate Scenario 1: Investing in VND The rate of return = the annual rate r T = 10%/year Scenario 2: Investing in USD Step 1: Converting VND to USD 200,000(VND)  Formula: P (VND)  5

6. 1.1. The converted interest rate Step 2: Investing in USD After 06 months: Formula: Step 3: Concerting USD back to VND 10.2 (USD)  10.2 x 21,000 = 214,200 (VND) Formula: 6

7. 1.1. The converted interest rate The rate of return: /6 months  The annual rate of return: 7.1% x 2 = 14.2%/year 7 Investing in VND: 10%/year Investing in USD: 14.2%/year <

8. 1.1. The converted interest rate Formula to convert the interest rate of C to T : The decision of the currency to invest/borrow: Comparing r T and r C T - Scenario 1: r T (VND) < r C T (USD)  ? Scenario 2: r T (VND) > r C T (USD)  ? Scenario 3: r T (VND) = r C T (USD)  ? 8

9. 1.1. The converted interest rate Example: Choosing a currency to invest when an investor has P = 200.000 VND . VND (T ): annual interest rate r T = 10 %/year USD (C ): annual interest rate r C = 4 %/year Duration of 6 months ( 0.5 year) ( n = 1/t = 2 is the times of turnover in a year) The spot rate: S(USD/VND ) = 20.000 The forward rate for 0.5 year: F 1/2 (USD/VND ) = 21.000 9

10. 1.1. The converted interest rate Example: Choosing a currency to invest when an investor has P = 10 USD . VND (T), annual interest rate r T = 10 %/year USD (C), annual interest rate r C = 4 %/year Duration of 1 year ( n = 1/t = 1 is the times of turnover in a year) The spot rate: S(USD/VND ) = 20.000 The forward rate for 1 year: F 1 (USD/VND ) = 21.000 10

11. 1.1. The converted interest rate Formula to convert the interest rate of C to T Formula to convert the interest rate of T to C 11

12. 1.1. The converted interest rate ATTENTION !!! The currency C has 2 types of interest rates: r C is the normal listed interest rate r C T is the converted-to-T interest rate The currency T has 2 types of interest rates : r T is the normal listed interest rate r T C is the converted-to-C interest rate 12

13. The annual interest rates of USD and EUR are 2.3% and 4.6% respectively; the spot rate is 1.2540; the 4-month forward rate is 1.2605 . A. which currency will you choose to invest? B. If you take a loan, which currency will you choose to borrow? 13

14. S (USD/JPY) = 139,34 S (EUR/ USD) = 1,3105 rJPY = 3,5%/ năm rUSD = 0,5 %/năm rEUR = 1,5%/năm Forward rate in 20days : F(JPY) = 140, 25 F(EUR) = 1,3249. If you take a loan, which currency will you choose to borrow? 14

15. 2 15 The theory of Interest rate Parity (IRP)

16. 2. The Interest Rate Parity – IRP Content: The lending/borrowing activities in the money market will have the same interest rate when being converted into one currency, regardless what currency it is. 16

17. 2. The Interest Rate Parity – IRP Formula to convert the interest rate of C to T Formula to convert the interest rate of T to C 17

18. 18 2. The Interest Rate Parity – IRP SIMILAR TO LOOP?!? THE LAW OF ONE PRICE

19. 2. The Interest Rate Parity – IRP Assumptions in the theory of IRP: No transaction costs No capital barriers No risk in the international trade All securities have the same quality (perfectly substitution) A perfectly competitive market 19

20. 2. The Interest Rate Parity – IRP The IRP has 2 mechanisms: 2.1. The Covered Interest Rate Parity (CIP): in the process of lending/borrowing, an investor uses the forward rate to convert the principle and interest from one currency to another, therefore the foreign exchange risk is eliminated (covered). 2.2. The Uncovered Interest Rate Parity ( UIP): in the process of lending/borrowing, an investor uses the expected spot rate to convert the principle and interest from one currency to another, therefore the foreign exchange risk is not eliminated (uncovered ). 20

21. 2.1 21 The covered interest rate parity (CIP) 2.1.1. The content of the CIP 2.1.2. Different forms of the CIP

22. 2.1.1. The content of the CIP Content: In the hedged lending/borrowing activities (from exchange rate risk), market forces always tend to push different interest rates of different markets to one level when being converted into one common currency. Forming mechanism: The CIP is formed based on the arbitrage trading activities in the money market. 22

23. 2.1.1. The content of the CIP Formula to convert the interest rate of C to T Formula to convert the interest rate of T to C 23

24. 2.1.1. The content of the CIP Forming mechanism (arbitrage trading activities): Assuming of a difference:  Step 1: LHS increases  Step 2: RHS decreases  Step 3: RHS decreases  Step 4: RHS decreases 24 (Similarly, )

25. 2.1.2. Different forms of the CIP 3 different forms of the CIP: For the period of 1 year For the period of <1 year For the period of >1 year with: r T = r is the annual interest rate of the term currency r C = r * is the annual interest rate of the commodity currency 25

26. 2.1.2.1. The CIP for the period of 1 year The absolute form: Explaination : với n = 1 The relative form: ( Approximate:p = r–r*) 26

27. 2.1.2.1. The CIP for the period of 1 year Meaning: The interest rates of 2 currencies help to determine the forward rate The difference between 2 interest rates is the basis to determine the forward point (forward premium versus forward discount) 27 The absolute form : The relative form: ( Approximate:p = r–r*)

28. 2.1.2.2. The CIP for the period of <1 y ear The absolute form: The relative form: (Approximate:(r – r*)/n) (With t is the length of the contract, n = 1/t is the number of turnover of the contract in a year) Explaination : 28

29. 2.1.2.3. The CIP for the period of >1 year The absolute form: The relative form: (With t is the length of the contract) Explaination : 29

30. 30

31. 2.2 31 The uncovered interest rate parity (UIP) 2.2.1. The content of the UIP 2.2.2. Different forms of the UIP

32. Content: The forward rate reflects the expected spot rate at the maturity date of the forward contract. Formation Mechanism: The UIP is formed under the force of the exchange rate speculation. 0 t S S t F t is signed F t is excuted 2.2.1. The content of the UIP 32

33. 2.2.2. Different forms of the UIP Length of the period The absolute form The relative form 1 year < 1 year > 1 year 33

34. 2.2.2. Different forms of the UIP Meaning: The difference between the 2 interest rates reflects the expected change of the spot exchange rate. The forecast of the expected spot rate is a market force that affects the current spot rate. 34

35. Some empirical studies and conclusions Some empirical studies show that generally the CIP may hold, however , the accuracy of the theory depends on costs, different types of risk, tax ... 35

36. 3 36 The International Fisher Effect ( IFE)

37. IFE - UIP The difference between the 2 levels of interest rate in 2 countries reflect the expected change of the exchange rate: r: the annual interest rate of the term currency r*: the annual interest rate of the commodity currency Δe e t : the estimated change in the exchange rate after a time t 37

38. IFE - PPP The difference between the 2 levels of inflation rate in 2 countries reflect the expected change of the exchange rate: hoặc π e t : the estimated domestic inflation rate after a time t π e* t : the estimated foreign inflation rate after a time t Δe e t : the estimated change in the exchange rate after a time t 38

39. 3. The international Fisher effect UIP (expected form of IRP): PPP (expected form): The international Fisher effect: Content: The international Fisher effect in the open economy tells that all the real interest rate levels must be equal to each other. 39

40. 3. The international Fisher effect 40

41. 3. The international Fisher effect 41

42. 3. The international Fisher effect 42 The IFE’s implications: - Investors, who are trying to invest in a country with high interest rates, may be adversely affected by the impact of high inflation in that country. - The currencies with higher expected interest rates will also have higher expected inflations, therefore they are expected to depreciate. Investors do not necessarily invest in profitable securities in countries with higher interest rates because the impact of the exchange rate can offset the interest rate advantage in every phase.

43. 43

44. 4 44 Factors make the CIP does not hold

45. 4 . Factors make the CIP does not hold 1. The transaction costs 2. The costs of collecting and process data 3. The government’s intervention 4. The financial obstacles and market imperfections 5. The heterogeneity of assets 45

46. Ex about convert interest rate Ex1: Suppose that VCB need a loan of 100 million VND in 3 months r VND = r T = 9 % per year r USD = r C = 2 % per year S (USD/VND) = 23,235 F(USD/VND) = 23,470 Choosing currency to borrowing 46

47. Year Inflation rate of GBP Inflation rate of USD Year Inflation rate of GBP Inflation rate of USD 2016 6 4.55 2018 5 3.25 2017 7 3.75 2019 5 2.5 47 Providing annual inflation rate s of GBP , USD : Question: 1. Calculate the percentage of change of GBP / USD exchange rate when comparing the end of 2019 with the end of 2017 using PPP. 2. Calculate the exchange rate at the end of 2019 know ing that the exchange rate at the end of 2016: 1 GBP = 1.1727 USD

48. Interest rates for 2012 of GBP and USD are 0.5 % and 2% respectively. S = 1.5656 . Using PPP and IRP to compute: a. Using Fisher to calculate GBP inflation knowing that annual USD inflation is 1.85%. b. Calculate forward premium or discount using CIP? c. Assuming that 1-year forward rate of Bank X is 1.5800: If you are an interest rate arbitrageur, what would you do? If you are a speculator, what would you do to earn profit? 48

49. Practice Suppose that the one-year interest rates of USD and NZD are 5% and 3% respectively. The NZD/USD spot exchange rate is currently 0.6146 and the 6-month forward exchange rate is 0.6209. a. Show how you can make a covered interest arbitrage. b. Determine profit/loss B1. if a trader sells a 6-month forward contract worth 2 million NZD against USD at the forward rate above if the spot exchange rate is 0.6218 after one year. B2. if a trader buys a 6-month forward contract worth 2 million NZD against USD at the forward rate above if the spot exchange rate is 0.6218 after one year. 49

50. B3. if a trader sells a 6-month forward contract worth 2 million USD against NZD at the forward rate above if the spot exchange rate is 0.6218 after one year. B4. if a trader buys a 6-month forward contract worth 2 million USD against NZD at the forward rate above if the spot exchange rate is 0.6218 after one year. 50