TTh 3:15-4:30 Gates B01. Handout #7 International Parity Conditions Interest Rate Parity and the Fisher Parities

Transcription

1 TTh 3:15-4:30 Gates B01 Handout #7 International Parity Conditions Interest Rate Parity and the Fisher Parities Yee-Tien Ted Fu Course web page:

2 Additional Reading Assignments for this Week Scan Read Levich Chap 5 Pages International Parity Conditions Luenberger Chap Pages Solnik Eun Chap 2 Pages Foreign Exchange Parity Relations Chap 9 Pages Wooldridge Chap 7 Pages Multiple Regression Analysis with Qualitative Information: Binary (or Dummy) Variables 5-2

3 Major Central Banks Overview Central Bank Bank of Canada Bank of England World Interest Rates Table Next Meeting Jul Jul Last Change Apr Apr Current Interest Rate 3% 5% Bank of Japan Jul Feb % European Central Bank Aug Jul % Federal Reserve Aug Apr % Swiss National Bank Sep Sep % The Reserve Bank of Australia Aug Mar % 5-3

4 5-4

5

6 Exchange Rates Table 5-6

7 5-7

8 July nomist.com/ma rkets/bigmac/ 5-8

9 June 24, nomist.com/ma rkets/bigmac/ 5-9

10 Feb 04, nomist.com/ma rkets/bigmac/ 5-10

11 International Parity Relations Linear Approximation where Spot Rate S are in indirect quote (FC/DC or FC/$) Purchasing Power Parity (relative version) PPP FRU Forward Rate Unbiased Property FIE IRP Uncovered Interest Parity or Fisher International Effect Interest Rate Parity Solnik

12 It takes three to five years to see a significant (+)(-)valuation to be cut in half. Source: Page 129 of Levich 2E 5-12

13 Foreign Exchange Markets International Parity Conditions Interest Rate Parity and the Fisher Parities MS&E 247S International Investments Yee-Tien (Ted) Fu

14 Long-Run versus Short-Run The long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us when the storm is long past, the ocean will be flat. - John Maynard Keynes 5-14

15 Building Blocks of The Parity Framework Key Interest Exchange Rates Linkages Purchasing Power Parity + Uncovered Interest Parity (Fisher International Effect) Four Definitions: S, F, r, I Forward Rate Unbiased Property + Interest Rate Parity Four Derived Key Terms: r F -r D, I F -I D, f, s The Parity Framework 5-15

16 Four Definitions The spot exchange rate, S. The rate of exchange of two currencies tells us the amount of foreign currency that one unit of domestic currency can buy. Spot means that we refer to the exchange rate for immediate delivery. The forward exchange rate, F. The rate of exchange of two currencies set on one date for delivery at a future specified date, the forward rate is quoted today for a delivery taking place at a future date. The interest rate, r. The rate of interest for a given time period is a function of the length of the time period and the denomination of the currency. Interest rates are usually quoted in the market place as an annualized rate. The inflation rate, I. This is equal to the rate of consumer price increase over the period specified. The inflation differential is equal to the difference of inflation rates between two countries. 5-16

17 Four Derived Key Terms The interest rate differential, r F -r D. The interest rate differential is equal to the difference in interest rates between two countries. The inflation differential, I F -I D. The inflation differential is equal to the difference of inflation rates between two countries. The forward discount or premium, f. This is often calculated as an annualized percentage deviation from the spot rate: annualized forward premium = forward rate - spot rate spot rate 12 no. months forward 100 % (discount) The exchange rate movement, s. This is equal to the spot exchange rate movement over the period specified. f = (F-S 0 )/S 0 and s = (S 1 -S 0 )/S

18 Spot rate: S 0 current time = S Forward rate: F 0,1 = F contract signing time, time to maturity F 0,2 F 1,2 F 0,1 F 1,1 S 0 S 1 S 2 S 3 t = n Forward exchange rate premium f = (F-S 0 )/S 0 Exchange rate movement over the period specified s = (S 1 -S 0 )/S

19 You operate a sesame oil plant, buying sesame seeds and produce sesame oil out of it. You have an MBA degree and you learned in your finance course that you should obtain price forecast from commodity futures market. You just found on the futures market that the futures price of sesame seeds and sesame oil are about the same next year. How should you modify your production plan for the next year? Should you contract out / swap your next year s capacity to another oil plant? Should you mothball your business for one year? Should you upgrade to other value-adding and profitable operations? What other key information (e.g., futures price for ten years into the future) may also help you make a prudent and informed decision? 5-19

20 Key Interest Rate-Exchange Rate Linkages: The Parity Framework Please note that parity conditions are long-term equilibrium conditions. It might not happen in the near future (e.g., in three months) but it more likely to happen in the long-run (e.g., in six years). Parity conditions are useful when parity holds Parity conditions are useful when parity does not hold 5-20

21 Four International Parity Conditions Purchasing Power Parity linking spot exchange rates and inflation Absolute PPP: The price of a market basket of U.S. goods equals the price of a market basket of foreign goods when multiplied by the exchange rate. Relative PPP: The percentage change in the exchange rate equals the percentage change in U.S. goods prices less the percentage change in foreign goods prices. Uncovered Interest Parity linking interest rates and inflation Fisher Effect: For a single economy, the nominal interest rate equals the real interest rate plus the expected rate of inflation. International Fisher Effect: For two economies, the U.S. interest rate minus the foreign interest rate equals the expected difference of inflation rates between two countries. 5-21

22 Four International Parity Conditions Interest Rate Parity linking forward exchange rates and expected spot exchange rate The forward exchange rate premium equals (approximately) the U.S. interest rate minus the foreign interest rate. Forward Rate Unbiased Property linking forward exchange rates and expected spot exchange rates Foreign Exchange Expectations: Today s forward premium (for delivery in n days) equals the expected percentage change in the spot rate (over the next n days). 5-22

23 International Parity Relations Linear Approximation where Spot Rate S are in indirect quote (FC/DC or FC/$) Purchasing Power Parity (relative version) PPP FRU Forward Rate Unbiased Property FIE IRP Uncovered Interest Parity or Fisher International Effect Interest Rate Parity Solnik

24 Parity Conditions We will now look at the parity conditions that link the spot and forward exchange markets with the international money and bond markets. We first develop the parity conditions in a theoretical setting, starting with the perfect capital market (PCM) assumptions. Then we analyze the impact of relaxing the PCM assumptions (e.g., no taxes, complete certainty). 5-24

25 Parity Conditions We will begin with interest rate parity. The interest rate parity condition offers us an easy opportunity to relax the PCM assumptions and show the effect of introducing taxes into our financial calculations. Secondly, we present the Fisher parities, named after Irving Fisher who derived these relationships in the late 19th century. Thirdly, we introduce the forward rate unbiased condition as the final parity relationship. 5-25

26 The Usefulness of the Parity Conditions While PPP involves arbitrage in goods, the other three parity conditions involve arbitrage opportunities in financial markets where transaction costs are usually lower. However, financial markets are often subjected to controls or restrictions and taxes that limit the ability of market participants to complete an arbitrage transaction. 5-26

27 The Usefulness of the Parity Conditions When controls or taxes that are present create a deviation from a parity condition, the magnitude of the deviation reveals how profitable it will be for an agent to overcome that control or tax. 5-27

28 The Usefulness of the Parity Conditions As with PPP, financial market transactions often involve risk. Some of the risks, such as price risk, credit risk, country risk, etc., may apply to the parity financial conditions if the agent is unable to hedge them. [credit risk: the risk that a borrower will be unable to make timely payment of interest or principal] If a parity condition is violated because of uncertainty, agents must compare their risk aversion to that in the market. Agents who are less (more) risk averse than the overall market will find that the violation of parity presents a profit (hedging) opportunity. 5-28

29 Old Data, Old Data, Old Data In which country would you invest in the short-term and in the long-term? Interest rates One year Inflation rates,% Belgian franc 6 11 / / Deutschmark 5 5 / / Sterling 7 5 / / Swiss franc / US dollar 6 11 / / Italian lira 11 3 / / Japanese yen 2 1 / Rx 5-29

30 Major Central Banks Overview Central Bank Bank of Canada Bank of England World Interest Rates Table Next Meeting Jul Jul Last Change Apr Apr Current Interest Rate 3% 5% Bank of Japan Jul Feb % European Central Bank Aug Jul % Federal Reserve Aug Apr % Swiss National Bank Sep Sep % The Reserve Bank of Australia Aug Mar %

31 5-31

32

33 Exchange Rates Table 5-33

34 July

35 Rx If an investor can receive a higher interest rate by lending money in a foreign currency than by lending money in the domestic currency, it makes sense for the investor to lend in the foreign currency. This is done by exchanging the domestic currency for foreign currency, lending the foreign currency, and then converting the money plus interest back into the domestic currency at the maturity of the loan. However, as the exchange rate may vary over the tenor of the loan, the investor is exposed to the risk that the foreign currency may depreciate against the domestic currency by more than the difference between the two interest rates. In this case, the investor will make a loss by lending in foreign currency. 5-35

36 Korean Won: Depreciation versus Interest Rate Differential (in % per year) Solnik

37 From 1991 to 1996, the won had a much higher interest rate than the dollar (an annual differential around 10%), but the exchange rate with the dollar remained stable. In 1997, the Asian crisis hit many currencies in the region and the won was devalued by some 50%. Averaging over the period, we find that the interest rate differential roughly matches the currency depreciation. So any investor applying the strategy to invest in this high-interest-rate currency would have made a profit for several years and lost all of it in Solnik

38 Interest Rate Parity Interest Rate Parity: The Relationship between Interest Rates, Spot Rates, and Forward Rates The forward exchange rate premium equals (approximately) the U.S. interest rate minus the foreign interest rate. ( F S ) S = i $ i Driven by arbitrage between the spot and forward exchange rates, and money market interest rates. 5-38

39 Interest Rate Parity The Relationship among Interest Rates, Spot Rates, and Forward Rates IRP draws on the principle that, in equilibrium, two investments that are exposed to the same risks must have the same return. IRP is maintained by arbitrage. 5-39

40 Interest Rate Parity in a Perfect Capital Market Suppose an investor invests $1 in a US$ security with interest rate i $ for one period. At the end of one period, wealth = $1 x (1 + i $ ). Alternative: Convert the $1 into (1/St) at the current spot rate St ($/ ), and then invest it in a security with i. At the same time, cover exposure to by selling the entire proceeds at the current one-period forward rate, F t, 1. ending = $1 x 1.0 wealth x (1 + i ) x F t, 1 St 5-40

41 Interest Rate Parity in a Perfect Capital Market Equating the two: $1 x 1.0 x (1 + i ) x F t, 1 = $1 x (1 + i $ ) St Rearranging terms: F t, 1 St = 1 + i $ 1 + i Subtracting 1 from each side: F t, 1 - St St = i $ - i 1 + i (5.1) 5-41

42 Subject: The Intuition of Covered and Uncovered Interest Parity (1) In equation 5.1 on covered interest parity, if sterling interest rates are low, how can we get US$ based investors to hold sterling assets? The answer is that we offer them a more favorable forward rate (higher F in terms of $/GBP) to offset the low GBP interest rate. So the market is working by pricing F to offset a known low GBP interest rate. F t,1 S t S t = i $ 1 + i i (5.1) Tips -- Intuition Check from Professor Levich 5-42

43 Interest Rate Parity US Capital Gains Tax τ k < US Income Tax τ y Suppose an investor invests $1 in a US$ security with interest rate i $ for one period. At the end of one period, wealth = $1+ (1-τ y )i $ since the interest income will be taxed τ y %. Alternative: Convert the $1 into (1/St) at the current spot rate St ($/ ), and then invest it in a security with i. At the same time, cover exposure to by selling the entire proceeds at the current one-period forward rate, F t,

44 Ending Wealth (assuming that capital gains taxes apply to foreign exchange earnings) = $1 x (1.0/St) x (1 + i ) x F t, 1 - Capital Gains Tax - Income Tax F ( i ) t, 1 = 1 + S t - Capital Gains Tax - Income Tax = {Capital Gains - Capital Gains Tax} + {(Interest) Income - Income Tax}

45 5-45 ( ) ( ) { } ( ) ( ) ( ) { } = =,,, i i S S F i i i S S F i S S F y t t t k y t t t k t t t τ τ τ τ ( ), i S S F t t t is the hedged foreign exchange earnings. Note that the term We have used the income tax rate on i since all interest, whatever the currency or country of source, is subject to that rate. τ y

46 5-46 Equating the two: Rearranging terms: So: Interest Rate Parity US Capital Gains Tax τ k < US Income Tax τ y ( ) ( ) ( ) { } ( ) $, $ i i i S S F y y t t t k τ τ τ + = ( ) ( ) y k t t t i i i S S F τ τ + = $, k y t t t i i i S S F τ τ + = $,

47 While some investors may enjoy a lower tax rate on foreign exchange than on interest earnings, banks and other major players do not; such investors, for whom international investment is a normal business, pay the same tax on interest and foreign exchange earnings. However, investors who do pay lower taxes on foreign exchange earnings than on interest income may find valuable tax arbitrage opportunities. 5-47

48 For example, suppose interest rates and exchange rates are such that interest parity holds precisely on a before-tax basis: Ft,1 St i$ i = S 1+ i With i $ = 12%, i = 8%, US Capital Gains Tax Rate τ k = 10%, US Income Tax Rate τ y = 25% U.S. dollar investments yield {$1 + (1 - τ y )i $ - 1}/1 = 9% after tax, while investments yield after tax: F ( ) t, 1 St 1 τ ( ) { ( ) } k 1 + i τ y i 1 St = 9. 6% 1 => The pound investment will be preferred on an after-tax basis. t 5-48

49 More generally, if covered interest parity holds on a before-tax basis, investors with favorable capital gains treatment will prefer investments denominated in currencies trading at a forward premium. It is a natural extension of our argument to show that in the same tax situation, borrowers will prefer to denominate borrowing in currencies at a forward discount. 5-49

50 Here are some prices in the international money markets: Spot rate Forward rate (one year) Interest rate (A$) Interest rate ($) = $0.75/A$ = $0.77/A$ = 7% per year = 9% per year Assuming that no transaction costs or taxes exist, do covered arbitrage profits exist in the above situation? Describe the flows. Beginning with 1 A$, Buy $ in the spot market Buy $ in the forward market final $ = S x (1 + r $ ) final $ = (1 + r A$ ) x F 5-50

51 0.75 X (1+0.09) < (1+0.07) X 0.77 Therefore, investing in A$ is more profitable. Hence (1) borrow in US$, (2) purchase A$ on the spot market, (3) sell A$ forward and make a profit. The annual dollar return on dollars invested in Australia is (1.07 x.77)/.75 1 = 9.85%. The return exceeds the 9% return on dollars invested in the United States by 0.85% per annum. Hence arbitrage profits can be earned by borrowing dollars or selling dollar assets, buying A$ in the spot market, investing the A$ at 7%, and simultaneously selling the A$ interest and principal forward for one year for dollars. 5-51

52 Suppose no transaction costs exist. Let the capital gains tax on currency profits equal 25%, and the ordinary income tax on interest income equal 50%. In this situation, do covered arbitrage profits exist? How large are they? Describe the transactions required to exploit these profits. [Answer to Question 3c, 10 points] [Previous exam question] In this case, the after-tax interest differential in favor of the U.S. is (.90 x x.50) / ( x.50) = ( ) / = 0.97%, while the after-tax forward premium on the A$ is ( ) x.75/.75 = 2%. Since the after-tax forward premium exceeds the after-tax interest differential, dollars will continue to flow to Australia as before. 5-52

53 With i $ = 9%, ia$ = 7%, US Capital Gains Tax Rate τ k = 25%, US Income Tax Rate τ y = 50% U.S. dollar investments yield {$1 + (1 - τ y )i $ - 1}/1 = 4.5% after tax, while A$ investments yield after tax: F ( ) t,1 St 1 τ ( 1 ) { 1 ( 1 ) } k + ia$ + + τ y ia$ 1 St = 5.64% 1 where Spot rate = $0.75/A$ Forward rate (one year) = $0.77/A$ Since U.S. dollar investments yield (4.5% after tax) is less than the A$ investments yield (5.64% after tax), dollars will continue to flow to Australia as before. 5-53

54 Interest Rate Parity in a Perfect Capital Market % forward premium = % interest differential The term F - S is called the forward premium. S When F > S, is more expensive in the forward market. When F < S, is cheaper in the forward market. Thus the term forward discount is often used when (F-S)/S <

55 Interest Rate Parity in a Perfect Capital Market Example A: i$,3month = 5.96%p.a. i,3month = 8.00%p.a. Investor has $100. Invested in US$ security: S t = $1.5000/ F t,3month = $1.4925/ Ending wealth = $100x( /4) = $ Invested in UK security: Ending wealth = $100x(1+0.08/4)x1.4925/1.50 = $ i.e. The 2 investments produce the same results. 5-55

56 Interest Rate Parity in a Perfect Capital Market Example A continued: Forward discount on UK: (F-S)/S = ( )/1.5 = -0.50% Interest differential between the US$ and the UK : (i $ - i )/(1 + i ) = (0.0596/4-0.08/4)/(1+0.08/4) = With at a forward discount, UK interest rates are higher than US interest rates to preserve IRP. 5-56

57 Example of Covered Interest Arbitrage to Exploit Deviations from Interest Rate Parity Suppose in example A, F = $1.52/ > F = $1.4925/. So, investors favor UK over US$ investments. This results in point A in Figure 5.1. The location of A => the incentive for risk-free covered arbitrage flows out of US$ and into UK. For an investor who held US$ securities initially: 1. Sell US$ security at 5.96% => i $ rises 2. Buy spot at $1.50 => S t rises 3. Buy UK security at 8.00% => i falls 4. Sell forward at $1.52 => F t falls 5. (i $ - i ) rises and (F t -S t ) falls => move rightward and downward to parity line! 5-57

58 Example of Covered Interest Arbitrage to Exploit Deviations from Interest Rate Parity Suppose in example A, F = $1.52/ > F = $1.4925/. So, investors favor UK over US$ investments. This results in point A in Figure 5.1. The location of A => the incentive for risk-free covered arbitrage flows out of US$ and into UK. For an investor who held US$ securities initially: 1. Sell US$ security at 5.96% => $bond price down, yield up 2. Buy spot at $1.50 => price up 3. Buy UK security at 8.00% => bond price up, yield down 4. Sell forward at $1.52 => future price down 5. (i $ - i ) rises and (F t -S t ) falls => move rightward and downward to parity line! 5-58

59 Forward Premium: (F - S) / S Levich Fig 5.1 The Interest Rate Parity Line Equilibrium and Disequilibrium Points Capital Outflows $ to Foreign Currency A A A B B B Capital Inflows Foreign Currency to $ (i $ - i foreign ) / (1 + i foreign )

60 Relaxing the Perfect Capital Market Assumptions Transaction costs has the effect of creating a neutral band within which covered interest arbitrage transactions will not occur. Forward Premium neutral band Interest Differential 5-60

61 Relaxing the Perfect Capital Market Assumptions Differential capital gains and ordinary income tax rates can tilt the 45 slope of the IRP line. However, the actual impact depends on the exact tax rates, the number of people who are subject to those rates, and transactions costs which may dominate the role of taxes. There are also uncertainty risks. Placing orders takes time and market prices may change. The foreign investment may present country risks. 5-61

62 Example of Covered Interest Arbitrage to Exploit Deviations from Interest Rate Parity The 4 transactions describe covered interest arbitrage. We also could call it round-trip arbitrage, during which a person can begin with $1, conduct 4 transactions, and wind up with more than $

63 Example of Covered Interest Arbitrage to Exploit Deviations from Interest Rate Parity currency dimension US$ time dimension Jan 1 Jul 1 B C interest rate A spot forward interest rate D 5-63

64 Example of Covered Interest Arbitrage to Exploit Deviations from Interest Rate Parity The profit from making these transactions is approximately the % deviation from IRP, defined as F t, 1 - St i $ - i d t = - St 1 + i Notice in Figure 5.1 that the marginal impact of each of the 4 transactions has the effect of pushing the configuration of the rates back towards IRP. 5-64

65 Empirical Evidence on Interest Rate Parity (Levich 2E, pp ) Testing whether α=0 and β=1 in the following simple linear regression would not be appropriate even though the IRP line is a 45 o line passing through the origin -- given the role played by transaction costs, it is clear that observations could cluster inside the neutral band in any number of ways. F t,1 S t S t = i α + β $, t? t + 1+ i? t i ε t (5.1) 5-65

66 Empirical Evidence on Interest Rate Parity Empirical Evidence on the Neutral Band (Levich 2E, page 153) The Eurocurrency markets made it possible to examine two securities that differed only in terms of their currency of denomination. The general result is that IRP holds in the short-term Eurocurrency market after accounting for transaction costs. For longer-term securities, a study found significant deviations from parity that represent profit opportunities even after adjusting for transaction costs. 5-66

67 More recently, Helen Popper (1993) analyzed long-term covered interest parity using five-year and seven-year securities and the interest differential implied by currency swaps of matching maturities. For her sample of major countries in the mid- 1980s, Popper found that deviations from longterm covered interest parity are only slightly higher (about 10 bp or 0.1%) than deviations from short-term covered interest parity. 5-67

68 In a related study, however, Donna Fletcher and Larry Taylor (1994) examined 5-, 7-, and 10-year securities for deviations from long-term covered interest parity. They reported that in every test market, there are significant deviations from parity that represent profit opportunities even after adjusting for transaction costs. Deviation from parity open a window of opportunity for firms and may partly explain the rapid growth in long-term currency swaps. 5-68

69 Interest Rate Parity When market forces cause interest rates and exchange rates to be such that covered interest arbitrage is no longer feasible, the equilibrium state achieved is referred to as interest rate parity (IRP). When IRP exists, the rate of return achieved from covered interest arbitrage should equal the rate available in the home country. By simplifying and rearranging terms: Extra forward = (1 + home interest rate) _ 1 premium (1 + foreign interest rate) 5-69

70 Interest Rate Parity If the 6-month Mexican peso interest rate = 6%, 6-month U.S. dollar interest rate = 5%, then from the U.S. investor s perspective, forward = (1 +.05) _ 1 = _.9434% premium (1 +.06) (not annualized) If the peso s spot rate is $.10/peso, then the 6-month forward rate = spot rate x (1 + premium) =.10 x (1 _ ) = $.09906/peso Extra 5-70

71 Interest Rate Parity The relationship between the forward rate and the interest rate differential can be simplified and approximated as follows: forward = forward rate - spot rate premium spot rate home _ foreign interest rate interest rate This approximated form provides a reasonable estimate when the interest rate differential is small. Extra 5-71

72 Graphic Analysis of Interest Rate Parity Interest Rate Differential (%) home interest rate - foreign interest rate 4 IRP line 2 Forward Discount (%) Forward Premium (%) -2 Extra

73 Graphic Analysis of Interest Rate Parity Home Interest Rate - Foreign Interest Rate (%) Zone of potential covered interest arbitrage by foreign investors 4 2 IRP line Forward Discount (%) Zone where covered interest arbitrage is not feasible Zone of potential covered interest arbitrage by local investors Forward Premium (%) Extra

74 Extra Interest Rate Parity IRP generally holds. Where it does not hold, covered interest arbitrage may still not be worthwhile due to transaction costs, currency restrictions, differential tax laws, political risk, etc. When IRP exists, it does not mean that both local and foreign investors will earn the same returns. What it means is that investors cannot use covered interest arbitrage to achieve higher returns than those achievable in their respective home countries. 5-74

75 Correlation Between Spot and Forward Rates Extra Because of interest rate parity, a forward rate will normally move in tandem with the spot rate. This correlation depends on interest rate movements. Interest Rates Spot and Forward Rates t 0 t 1 time t 2 t 0 t 1 time t 2 i A i U.S. Spot A Forward A. 5-75

76 The Fisher Parities Fisher Effect (Fisher Closed) For a single economy, the nominal interest rate equals the real interest rate plus the expected rate of inflation. i $ = r $ + E ( ~ ) ΔPUS Driven by desire to insulate the real interest against expected inflation, and arbitrage between real and nominal assets. 5-76

77 The Fisher Parities International Fisher Effect (Fisher Open) or uncovered interest parity For two economies, the U.S. interest rate minus the foreign interest rate equals the expected percentage change in the exchange rate. i i = E Δ $ ( ~ ) Spot Driven by arbitrage in bonds denominated in two currencies. 5-77

78 The Fisher Parities The Fisher parities describe how information regarding expected inflation and expected exchange rates are captured in current interest rates. (In financial markets, prices tend to reflect information.) The Fisher Effect represents another example of arbitrage between real assets and nominal (financial) assets within a single economy. If inflation is 0, $1 spend today yields the same utility as $1 invested at (1+r) and spent in the future. 5-78

79 The Fisher Effect Assume PCM, expected inflation E(p), ~ investor hold $1 in cash. => can buy commodity with $1 and sell the commodity for $1[1 + E(p)] ~ at the end of one period. To be indifferent between this commodity purchase and an interest-bearing security, the latter needs an end-of-period value of $1(1+r)[1+E(p)]. ~ 5-79

80 The Fisher Effect Since the return on security is normally quoted in nominal terms to yield $1(1+i), (1+i) = (1+r)[1+ E(p)] ~ or i = r + E(p) ~ + re(p) ~ Since in most developed countries, inflation and real interest rates are low, the Fisher Effect is approximately: i = r + E(p) ~ 5-80

81 Fisher Closed Parity Example: If I grow a tree in an inflation era (invest in a real asset), I will benefit from two sources of revenue growth: the cubic inches increases of 2.9% of the volume of the tree, plus the price increase of 2.5% of the timber. Therefore, if a finance company hopes to attract my investment (in a nominal or financial asset), the company will have to pay me (1+2.9%) x (1+2.5%) 1, or roughly 2.9%+2.5%, to make me indifferent of two investments (one in real asset (e.g., tree) and one in nominal asset (e.g., bonds or certificate of deposits)). Therefore, financial interest rate (nominal rate of return) = real interest rate (muscle growth rate) + expected inflation (fat growth rate). 5-81

82 The Fisher Effect % nominal % real % expected = + interest rate interest rate inflation To execute the arbitrage implied by the Fisher Effect, individuals will move out of financial assets into commodities when inflation is high. When inflation is receding, individuals will prefer financial assets to lock in higher returns. When the Fisher Effect holds, nominal / financial assets fully reflect expected inflation and preserve the real rate of return. 5-82

83 The International Fisher Effect interest rates across countries must be set with an eye toward expected exchange rate changes. Assume PCM and investor holds $1 in US$ security with i $ => ends up with $1 x (1 + i $ ). Alternatively, the investor could take $1, convert into UK at S t, and invest the entire proceeds in a UK security with i. => ends up with $1 x 1.0 ~ x (1 + i ) x E(S t+1 ) St 5-83

84 The International Fisher Effect Under PCM assumptions, both investments share the same maturity, risk, and final currency denomination, and hence the same ending wealth: $1 x 1.0 ~ x (1 + i ) x E(S t+1 ) = $1 x (1 + i $ ) St Rearranging terms: ~ E(S t+1 ) St = 1 + i $ 1 + i 5-84

85 The International Fisher Effect Subtracting 1 from each side: ~ E(S t+1 )-St St = i $ - i 1 + i (5.5) % expected exchange % interest rate change = differential Note that the RHS of (5.5) is approximately i $ - i when i is small. 5-85

86 Subject: The Intuition of Covered and Uncovered Interest Parity (2) In equation 5.5 on uncovered interest parity (the international Fisher effect), if we expect the US$ to be weaker in the future (meaning more $ per foreign currency) how would we get investors to willingly hold US$ assets? The answer is, we offer them an added bonus in the form of a higher $ interest rate - just high enough to offset the loss of a weaker US$. So the market is working by setting a high $ interest rate to offset an expected depreciation of the US$. ~ E( S t+ 1 t Tips -- Intuition Check from Professor Levich S ) S t = i $ i 1+ i (5.5) 5-86

87 Relaxing the Perfect Capital Market Assumptions Transaction costs result in a neutral band around the parity line, while differential taxes can possibly tilt the parity line. Since the ending value of the foreign investment depends on an uncertain future spot rate, an exchange-risk premium may be required. 5-87

88 Empirical Evidence on the International Fisher Effect (Levich 2E, pp ) Under the assumption of rational expectations, S t+1 = E(S t+1 ) + ε t+1, we can rewrite the International ~ Fisher Effect as: S S t+ 1 t $, t? t = + St 1+ i? t i Testing whether α=0 and β=1 in the following simple linear regression would reveal whether the interest differential provides a good forecast of the future spot rate change. S S i ε t+ 1 t+ 1 t $, t? t = α + β + St 1+ i? t i i ε t

89 Figure 5.5 presents a graph of the interest differential on Euro-$ and Euro-DM deposits at quarter t and the spot exchange rate change ($/DM) one quarter in the future. The graph shows that exchange rate changes from a volatile series that switches between sizable positive and negative values. In comparison, the interest differential is a relatively smooth and calm series that takes on positive values over most of the sample period. Figure 5.5 suggests little relationship between the current interest differential and the future realized exchange rate change. In a formal regression test of equation (5.12), we find coefficients with standard errors in parentheses: α = (0.008), β = (0.827), R 2 = 0.001, N = 108, D-W (Durbin-Watson statistic) = 1.75 These results clearly reject the α = 0 and β = 1 hypothesis. Note: Please refer to Chapter 12 Serial Correlation and Heteroskedasticity in Time Series Regressions of Wooldridge s Introductory Econometrics for details about D-W. 5-89

90 Empirical Evidence on the International Fisher Effect Empirical tests indicate that the International Fisher Effect condition performs poorly in individual periods. However, over extended periods of time, it appears that currencies with high interest rates tend to depreciate, and vice versa, as predicted. 5-90

91 Extra The International Fisher Effect According to the Fisher effect, nominal riskfree interest rates contain a real rate of return and an anticipated inflation. If the same real return is required across countries, differentials in interest rates may be due to differentials in expected inflation. According to PPP, exchange rate movements are caused by inflation rate differentials. The international Fisher effect (IFE) theory suggests that currencies with higher interest rates will depreciate because the higher rates reflect higher expected inflation. 5-91

92 The International Fisher Effect According to the IFE, the expected effective return on a foreign investment should equal the effective return on a domestic investment: (1 + i f ) (1 + e f ) _ 1 = i h where i h = interest rate in the home country i f = interest rate in the foreign country e f = % change in the foreign currency s value Solving for e f : e f = (1 + i h ) _ 1 (1 + i f ) The simplified form, e f i _ h if, provides reasonable estimates when the interest rate Extra differential is small. 5-92

93 The International Fisher Effect Investors Residing in Attempt to in Home Currency i f e f I h Invest in i h Return Real Return Earned Extra Japan U.S. Canada Japan U.S. Canada Japan U.S. Canada Japan U.S. Canada 5% 5% 0% 5% 3% 2% Old data, Data, Old Old data, Data, Old data Old Data

94 The International Fisher Effect Investors Residing in Attempt to in Home Currency i f e f I h Invest in i h Return Real Return Earned Britain I h =2.5% New Zealand I h =3.4% Brazil I h =4.8% Extra Britain New Z. Brazil Britain New Z. Brazil Britain New Z. Brazil 5% 5% 0% 5% 3% 2%

95 July

96 June 24,

97 Feb 04,

98 Graphic Analysis of the International Fisher Effect Interest Rate Differential (%) home interest rate - foreign interest rate 4 Lower returns from investing in foreign 2 deposits IFE line Extra Higher returns from investing in foreign deposits %Δ in the foreign currency s spot rate 5-98

99 The International Fisher Effect While the IFE theory may hold during some time frames, there is evidence that it does not consistently hold. A statistical test can be developed by applying regression analysis to the historical exchange rates and nominal interest rate differentials: = a + 0 a 1 { (1+i h )/(1+i f ) - 1 } + μ e f The appropriate t-tests are then applied to a 0 and a 1, whose hypothesized values are 0 and 1 respectively. Extra 5-99

100 Extra The International Fisher Effect Since the IFE is based on PPP, it will not hold when PPP does not hold. According to the IFE, the high interest rates in southeast Asian countries before the Asian crisis should not attract foreign investment because of exchange rate expectations. However, since narrow bands were being maintained by some central banks, some foreign investors were motivated. Unfortunately for these investors, the efforts made to stabilize the currencies were overwhelmed by market forces

101 Comparison of IRP, PPP, and IFE Theories Interest Rate Parity (IRP) Forward Rate Discount or Premium Interest Rate Differential Fisher Effect Purchasing Power Parity Inflation Rate Differential (PPP) International Fisher Effect (IFE) Exchange Rate Expectations Extra 5-101

102 The Forward Rate Unbiased Condition Forward Rate Unbiased Today s forward premium (for delivery in n days) equals the expected percentage change in the spot rate (over the next n days). ( ) ( ( ~ ) ) F S S = E S S S t t t t+ n t t Driving force: Market players monitor the difference between today s forward rate (for delivery in n days) and their expectation of the future spot rate (n days from today)

103 5-103 Given the PCM assumptions, the interest rate parity condition, $,1 1 i i i S S F t t t + = and the International Fisher Effect, $ 1 1 ) ~ ( i i i S S S E t t t + = + (5.1) (5.5) The Forward Rate Unbiased Condition

104 The Forward Rate Unbiased Condition ~ E( S 1) S S t+ t t, 1 t = F S S t t (5.16) % Expected exchange rate change = % Forward premium If the average deviation between today s forward rate F t,1 and the actual future spot exchange rate is near zero, then the forward rate is an unbiased predictor of the spot rate. S t 5-104

105 The Forward Rate Unbiased Condition A forward rate bias may imply market inefficiency, or it may reflect a risk premium. Empirical data reveals that the forward rate and future spot rate track along a very similar path, though F tracks below the future S when the spot rate is rising, and vice versa. On the other hand, actual exchange rate changes form a volatile series, while the forward premium is relatively smooth and calm

106 The Forward Rate Unbiased Condition The forward rate unbiased condition is monitored by speculators, who in the PCM setting, trade in the forward contract only at prices equal to the expected future spot rate. When we relax the PCM assumptions, it is clear that the forward rate unbiased condition depends on 2 further assumptions

107 The Forward Rate Unbiased Condition (1) Market Efficiency: ( S t + = S t + 1 Speculators are able to form unbiased expectations of future spot rates; and (2) Forward Rate Pricing: F E S ) E ~ 1) ~ t, 1 = ( t+ 1 Speculators choose to trade forward contracts at prices equal to their expectations. Forward rates will be biased if either assumption fail

108 Empirical Evidence on the Forward Rate Unbiased Condition (Levich 2E, pp ) A test of the forward rate unbiased condition requires a series of forward rates and expected future spot rates. As discussed, measurements on the market s expected future spot rate are difficult to obtain. So again we start by assuming rational or unbiased expectations whereby the actual future spot rate is equal to the expected future spot rate augmented by an error term. With this assumption, we can rewrite the forward rate unbiased condition as: S S t+ 1 t = t,1 t + S t F S t S ε (5.17) t

109 Empirical Evidence on the Forward Rate Unbiased Condition (Levich 2E, pp ) Tests Using the Level of Spot and Forward Exchange Rates Figure 5.7A One-Month Forward and Future Spot Rates, and Figure 5.7B Three-Month Forward and Future Spot Rates reveal that the forward rate and the future spot rate track along a very similar path. Therefore, we expect that a regression of the level of the future spot rate against the level of the present forward rate, such as: S + F + t+ t = α β ε (5.18) 1,1 t+ 1 would produce coefficients α and β near 0 and 1, respectively, and a high R 2 for the regression

110 Tests Using the Level of Spot and Forward Exchange Rates Inspection of Figure 5.7 reveals another interesting pattern. It appears as if the forward rate tracks below the future spot rate when the spot rate is rising, and above the future spot rate when the spot rate is falling. As a result, the forward rate misses all of the turning points in the spot rate series

111 Forecast Bias Using the Forward Rate as a Forecast for the British Pound $2.60 $2.40 Forward Rate $2.20 $2.00 $1.80 $1.60 $1.40 $1.20 Realized Spot Rate $ Madura 5-111

112 Graphic Evaluation of Forecast Performance Using the Forward Rate as a Forecast for the British Pound Realized Spot Rate $2.50 $2.00 $1.50 $1.00 $1.00 $1.50 $2.00 $2.50 Forecast (Forward Rate) Perfect Forecast Line Madura 5-112

113 Empirical Evidence on the Forward Rate Unbiased Condition (Levich 2E, pp ) Tests Using Forward Premiums and Exchange Rate Changes Our perception of the forward rate as a predictor changes when we examine percentage changes in exchange rates rather than the levels. In percentage rate form, the forward rate unbiased condition of equation (5.15) requires us to compare the present forward premium with the expected future exchange rate change. d S S i t 1 t $, t? t t 1 = + + (5.15) St 1+ i? t i 5-113

114 Tests Using Forward Premiums and Exchange Rate Changes Figure 5.8 shows a graph of the present forward premium and the actual future exchange rate change for the $/DM rate at one-month and three-month maturities. The graphs show that actual exchange rate changes form a volatile series while the forward premium is a relatively smooth and calm series. Testing the joint hypothesis α=0 and β=1 in a regression such as: S S F S α ε (5.19) t+ 1 t t,1 t = + β + St St t+ 1 tests whether the current forward rate premium is an unbiased predictor of the future exchange rate change

115 Tests Using Forward Premiums and Exchange Rate Changes In table 5.1, we see that the α=0 and β=1 hypothesis is rejected for the DM and every other currency in the sample; the data indicate that β is negative and significant for several currencies. Thus, the analysis of exchange rate changes suggests that the forward premiums are poor predictor of the future exchange rate change, and often times a biased predictor. As we will see in Chapters 7 and 8, this empirical finding may offer good news through the hope it offers forecasters to beat the forward rate at forecasting exchange rate changes

116 Policy Matters - Private Enterprises We have referred to the parity conditions as benchmark or break-even points. When interest rate parity (IRP) holds, the covered cost of funds is identical across all currencies; there are neither bargains nor bad deals on a covered basis. When the International Fisher Effect holds, the expected cost of borrowed funds is identical across currencies and the expected return on invested funds is identical across currencies on an uncovered basis

117 Policy Matters - Private Enterprises When the forward rate unbiased condition holds, the expected cash flows associated with hedging or not hedging a currency exposure are identical. If all of the parity conditions are valid at each and every moment in time, then all financial choices would be fairly priced compared with the alternatives

118 Policy Matters - Private Enterprises But empirical evidence shows that while many of the parity conditions may hold in most cases or on average, at times the parity conditions are violated. As a result, managers may have an opportunity to make profit maximizing decisions by exploiting deviations from the parity conditions

119 Application : Interest Rate Parity & One-Way Arbitrage Example of one-way arbitrage in foreign exchange and security markets: A manager who holds US$ can obtain in the future by following two alternative paths. By taking the low cost path, the manager is engaging in one-way arbitrage

120 currency dimension One-Way Arbitrage A manager who holds US$ now wants in the future. US$ Buy spot at S time dimension Jan 1 Jul 1 B C Invest US$ at i $ Path 1 By taking the lower cost path, the manager is engaging in one-way arbitrage. Path 2 Invest at i A D Buy forward at F 5-120

121 One-Way Arbitrage Suppose that an investor holds US$ cash and wishes to make a payment in 6 months. The investor has 2 alternatives to choose between: Path 1: Invest US$ for 6 months, buy forward on Jan 1 for July 1 delivery Cost = F 1+ i ) ( Jan1, July1 $, 6months Path 2: Buy spot on Jan 1, invest for 6 months Cost = S ( 1+ i Jan euro, 6 1 months ) 5-121

122 One-Way Arbitrage In the absence of transaction costs, the two alternatives will be identical. But when transaction costs are present, an investor may favor one alternative over another, even though no round-trip arbitrage profits are possible. One-way arbitrage then is simply picking the lowest-priced (highestpriced) alternative when buying (selling) for a transaction between 2 corners of the box in Figure

123 Example of Round-Trip Arbitrage Profits Spot A$: $ $ month Forward A$: $ $ month Euro A$: % p.a. 1-month Euro $: % p.a. Note: Euro$ are US$ on deposit in non-us banks. counter-clockwise: Borrowing $ for 30 days, buying A$ spot, investing A$ for 30 days, and selling A$ forward will result in a cost of ( ) ( ) =

124 Example of Round-Trip Arbitrage Profits clockwise: Borrowing A$, selling A$ spot, investing $, and buying A$ forward will result in a cost of ( ) ( ) = In both cases, borrowing one unit of currency costs more than the unit of currency => no round-trip arbitrage profits 5-124

125 Example of Round-Trip Arbitrage Profits Assuming that your firm has a payment of A$ 1 million due in 30 days and you want to lock in the price today, how should you transact? Path 1 (clockwise): Investing US$ for 30 days, buying A$ spot, investing A$ for 30 days, and selling A$ at the forward rate. The cost of path 1 is: $ A$ = $ A$ /12 < $ A$ = The _ Cost _ of Counter Clockwise _ 5-125

126 Example of Round-Trip Arbitrage Profits Path 2 (counter-clockwise): Selling US$ for A$ at the spot rate and then investing A$ for 30 days. The cost of path 2 is: $ A$ /12 = $ A$ Path 1 is preferred since the cost is lower

127 Policy Matters - Private Enterprises Managers may make profit maximizing decisions by exploiting deviations from the parity conditions, or they may want to avoid or hedge the risks of such deviations. Application 1: IRP & One-Way Arbitrage One-way arbitrage is picking the better-priced alternative for a transaction in the presence of transaction costs

128 Policy Matters - Private Enterprises Application 2: Credit Risk & Forward Contracts The costs of using an outright forward versus a synthetic forward for hedging may differ for firms because credit risk is usually priced in bank loans but not in forward contracts. Application 3: IRP & the Country Risk Premium The deviations of government securities from IRP provides a measure of the political risk differences among countries

129 Policy Matters - Private Enterprises Appln 4: Are Deviations from IFE Predictable? Even if the deviations are zero on average, a nonrandom pattern can present a profit opportunity. Appln 5: Are Deviations from IFE Excessive? Under a system of pegged exchange rates, any interest rate differential represents a deviation. A speculator may (1) invest in the high interest rate currency when the peg is expected to hold, or (2) borrow the high interest rate currency when the peg is expected to change by more than the interest differential

130 Strategy 1: Investing in the High-Interest-Rate Currency A current application of this principle was the surge of U.S. investment into Mexican government securities. During 1992, peso-denominated, short-term securities had yields of 7-16 percentage points greater than US$ government securities. With the foreign exchange value of peso depreciating gradually, at about 5 percent per year, the realized International Fisher Effect deviations were substantial, enough to draw large sums to U.S. investment into Mexico. For example, in late 1992 the Fidelity Short- Term World Income Fund, a $631 million fund managed by Fidelity Investments of Boston, held almost 17 percent of its assets in peso-denominated securities. This strategy failed in late 1994, when the peso suffered a maxi-devaluation and took back more than the excess interest paid on peso securities

131 A slightly more complex application of the same principle involved currencies within the European Exchange Rate Mechanism (ERM). As we described in Chapter 2, currencies within the ERM were pegged to one another, but within bands of 2.25 percent for most currencies and 6.0 percent for the British pound and Italian lira. Suppose, as was the case in early 1991, that three-month Euro- interest rates were 14 percent while comparable Euro-DM interest rate was 9 percent. By borrowing Euro-DM and investing in Euro-, the speculator would earn 5 percent per annum. As long as the DM/ rate did not depreciate by more than 5 percent per annum, the strategy would add incremental profits to a short-term investment portfolio. The strategy worked reasonably well through the early 1990s, as the ERM held up and interest rate differentials persisted

132 Strategy 2: Borrowing the High-Interest-Rate Currency In September 1992, the European Exchange Rate Mechanism (ERM) came under stress and fears mounted that several currencies would have to devalue or exit the ERM. Anticipating this, speculators had an opportunity to invoke an alternative strategy -- borrowing the high-interest-rate currency while owning the low-interest-rate currency and betting against the preservation of the ERM. In early September 1992, three-month Euro- rates were only 0.50 percent higher than Euro-DM rates. Euro-lira rates, however, were some 6.00 percent higher than Euro-DM rates. Still, paying this interest differential for a few weeks was a modest cost relative to the exchange rate changes that occurred -- a 14 percent depreciation of the pound (from 2.78 DM/ to 2.40 DM/ ) and a 13 percent depreciation of the lira (762 lira/dm to 863 lira/dm)