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
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,% 6 11 / 16 - 6 9 / 16 Belgian franc 1.4 5 5 / 16 - 5 3 / 16 Deutschmark 2.2 7 5 / 8 - 7 1 / 2 Sterling 2.7 4 - 3 7 / 8 Swiss franc 1.9 6 11 / 16 - 6 9 / 16 US dollar 3.2 11 3 / 4 - 11 5 / 8 Italian lira 5.5 2 1 / 16 - 2 Japanese yen -0.2 5-29 Rx
World Interest Rates Table Major Central Banks Overview Current Central Bank Next Meeting Last Change Interest Rate Bank of Jul 15 2008 Apr 22 2008 3% Canada Bank of Jul 10 2008 Apr 10 2008 5% England Bank of Japan Jul 15 2008 Feb 21 2007 0.5% European Aug 07 2008 Jul 03 2008 4.25% Central Bank Federal Aug 05 2008 Apr 30 2008 2% Reserve Swiss National Sep 18 2008 Sep 13 2007 2.75% Bank The Reserve Bank of Aug 05 2008 Mar 04 2008 7.25% Australia http://www.fxstreet.com/fundamental/interest-rates-table/ 5-30
5-31
http://finance.mapsofworld.com/financial-market/world-inflation.html http://inflationdata.com/inflation/Inflation_Rate/InternationalSites.asp 5-32
5-33 Exchange Rates Table
July 2007 5-34
• 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 Rx
5-36 Korean Won: Depreciation versus Interest Rate Differential (in % per year) Solnik 2.3
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 1991-97 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 1997. 5-37 Solnik 2.3
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
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
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 $1 into (1/ S t ) £ at the current spot rate S t ($/£), 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 1.0 = $1 x x (1 + i £ ) x F t, 1 wealth S t 5-40
Interest Rate Parity in a Perfect Capital Market Equating the two: 1.0 $1 x x (1 + i £ ) x F t, 1 = $1 x (1 + i $ ) S t Rearranging terms: F t, 1 1 + i $ = S t 1 + i £ Subtracting 1 from each side: F t, 1 - S t i $ - i £ (5.1) = S t 1 + i £ 5-41
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 S i i = , 1 t t $ £ (5.1) + 1 S i £ t Tips -- Intuition Check from Professor Levich 5-42
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 $1 into (1/ S t ) £ at the current spot rate S t ($/£), 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 . 5-43
Ending Wealth (assuming that capital gains taxes apply to foreign exchange earnings) = $1 x (1.0/ S t ) x (1 + i £ ) x F t, 1 - Capital Gains Tax - Income Tax F ( ) = + t , 1 1 i - Capital Gains Tax - Income Tax £ S t = {Capital Gains - Capital Gains Tax} + {(Interest) Income - Income Tax} + 1 5-44
− − ⎧ ⎫ { } F S F S ( ) ( ) = + − τ + + − τ + t , 1 t t , 1 t ⎨ ⎬ 1 i 1 i i i 1 £ k £ £ y £ S S ⎩ ⎭ t t − ⎧ ⎫ { ( ) } 1 F S ( ) ( ) = − τ + + − τ + t , 1 t ⎨ ⎬ i i 1 1 1 k £ y £ ⎩ S ⎭ t − F S ( ) + t , 1 t i 1 Note that the term £ S t is the hedged foreign exchange earnings. τ i on We have used the income tax rate y £ since all interest, whatever the currency or country of source, is subject to that rate. 5-45
Interest Rate Parity US Capital Gains Tax τ k < US Income Tax τ y Equating the two: − ⎧ ⎫ { ( ) } ( ) $ F S ( ) ( ) − τ + + + − τ = + − τ t , 1 t ⎨ ⎬ 1 1 i 1 1 i $ 1 1 i k £ y £ y ⎩ S ⎭ t Rearranging terms: − − ( ) F S i i ( ) − τ = − τ t , t 1 $ £ 1 1 + k y S i 1 t £ So: − τ − − 1 F S i i = × y t , 1 t $ £ + − τ S 1 i 1 t £ k 5-46
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
For example, suppose interest rates and exchange rates are such that interest parity holds precisely − on a before-tax basis: − F S i i = , 1 t t $ £ + 1 i S £ t 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 S ( ) ( ) − τ + + + − τ − t , 1 t ⎨ ⎬ 1 1 i 1 1 i 1 k £ y £ S ⎩ ⎭ = t 9 . 6 % 1 => The pound investment will be preferred on an after-tax basis. 5-48
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
Here are some prices in the international money markets: Spot rate = $0.75/A$ Forward rate (one year) = $0.77/A$ Interest rate (A$) = 7% per year Interest rate ($) = 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$, final $ = S x (1 + r $ ) Buy $ in the spot market final $ = (1 + r A$ ) x F Buy $ in the forward market 5-50
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
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 .50 - .07 x .50) / (1 + .07 x .50) = (.045 - .035) / 1.035 = 0.97%, while the after-tax forward premium on the A$ is (.77 - .75) 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
With i $ = 9%, i A$ = 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 S ( ) ( ) − τ + + + − τ − t , 1 t ⎨ ⎬ 1 1 1 1 1 i i A$ A$ k y ⎩ ⎭ S = t 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
Interest Rate Parity in a Perfect Capital Market % forward % interest = premium differential F - S The term 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 < 0. 5-54
Interest Rate Parity in a Perfect Capital Market Example A: i $,3month = 5.96%p.a. S t = $1.5000/£ i £,3month = 8.00%p.a. F t, 3month = $1.4925/£ Investor has $100. Invested in US$ security: Ending wealth = $100x(1+0.0596/4) = $101.49 Invested in UK£ security: Ending wealth = $100x(1+0.08/4)x1.4925/1.50 = $101.49 i.e. The 2 investments produce the same results. 5-55
Interest Rate Parity in a Perfect Capital Market Example A continued: Forward discount on UK: (F-S)/S = (1.4925-1.5)/1.5 = -0.50% Interest differential between the US$ and the UK£: ( i $ - i £ )/(1 + i £ ) = (0.0596/4-0.08/4)/(1+0.08/4) = -0.005 With £ at a forward discount, UK interest rates are higher than US interest rates to preserve IRP. 5-56
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
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
The Interest Rate Parity Line Equilibrium and Disequilibrium Points 0.04 Forward Premium: ( F - S ) / S Capital Outflows 0.03 $ to Foreign Currency 0.02 B’ A’ B 0.01 0 A - 0.01 B” A” - 0.02 Capital Inflows - 0.03 Foreign Currency to $ - 0.04 - 0.04 - 0.03 - 0.02 - 0.01 0 0.01 0.02 0.03 0.04 ( i $ - i foreign ) / (1 + i foreign ) 5-59 Levich Fig 5.1
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
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
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 $1. 5-62
Example of Covered Interest Arbitrage to Exploit Deviations from Interest Rate Parity time dimension Jan 1 Jul 1 currency dimension US$ B A interest rate spot forward £ C D interest rate 5-63
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 - S t i $ - i £ d t = - S t 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
Empirical Evidence on Interest Rate Parity (Levich 2E, pp. 152-55) 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 S i i = α + β + ε , 1 $, ? t t t t (5.1) + t 1 S i ? t t 5-65
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
• 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 long- term covered interest parity are only slightly higher (about 10 bp or 0.1%) than deviations from short-term covered interest parity. 5-67
• 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
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: forward = (1 + home interest rate) _ 1 premium (1 + foreign interest rate) 5-69 Extra
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 _ .009434) = $.09906/peso 5-70 Extra
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. 5-71 Extra
Graphic Analysis of Interest Rate Parity Interest Rate Differential (%) home interest rate - foreign interest rate 4 IRP line 2 -3 -1 1 Forward 3 Forward Discount (%) Premium (%) -2 -4 5-72 Extra
Graphic Analysis of Interest Rate Parity Home Interest Rate - Foreign Interest Rate (%) IRP line 4 Zone of potential covered interest arbitrage by 2 foreign investors Forward Discount (%) -1 -3 1 3 Forward Premium (%) Zone where covered Zone of potential interest -2 covered interest arbitrage is arbitrage by not feasible local investors -4 5-73 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 Extra
Correlation Between Spot and Forward Rates Interest Rates i A Because of i U.S. interest rate parity, a forward rate will normally move in tandem t 0 t 1 t 2 time with the spot rate. Forward Rates This correlation Spot and Spot A depends on interest rate Forward A. movements. t 0 t 1 t 2 time 5-75 Extra
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. ( ) ~ = + Δ i r E P $ $ US Driven by desire to insulate the real interest against expected inflation, and arbitrage between real and nominal assets. 5-76
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. ( ) ~ − = Δ S pot i i E $ £ Driven by arbitrage in bonds denominated in two currencies. 5-77
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
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
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 ) + r E ( p ) Since in most developed countries, inflation and real interest rates are low, the Fisher Effect is approximately: ~ i = r + E ( p ) 5-80
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
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
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 ~ 1.0 $1 x x (1 + i £ ) x E ( S t+ 1 ) S t 5-83
The International Fisher Effect Under PCM assumptions, both investments share the same maturity, risk, and final currency denomination, and hence the same ending wealth: ~ 1.0 $1 x x (1 + i £ ) x E ( S t+ 1 ) = $1 x (1 + i $ ) S t Rearranging terms: ~ E ( S t+ 1 ) 1 + i $ = S t 1 + i £ 5-84
The International Fisher Effect Subtracting 1 from each side: ~ E ( S t+ 1 ) - S t i $ - i £ (5.5) = S t 1 + i £ % expected exchange % interest = rate change differential Note that the RHS of (5.5) is approximately i $ - i £ when i £ is small. 5-85
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$. ~ − − ( ) i i E S S = + $ £ 1 t t (5.5) + 1 S i £ t Tips -- Intuition Check from Professor Levich 5-86
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
Empirical Evidence on the International Fisher Effect (Levich 2E, pp. 160-63) Under the assumption of rational expectations, S t+1 = E(S t+1 ) + ε t+1 , we can rewrite the International ~ Fisher Effect as: − − i i S S = + ε + $, ? t t 1 t t + + 1 t 1 S i ? t t 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. − − i i S S = α + β + ε + $, ? t t 1 t t + + 1 t 1 S i ? t t 5-88
Figure 5.5 presents a graph of the interest differential on Euro-$ 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 = 0.007 (0.008), β = -0.070 (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
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
The International Fisher Effect • According to the Fisher effect , nominal risk- free 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 Extra
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 _ i f , provides reasonable estimates when the interest rate differential is small. 5-92 Extra
The International Fisher Effect Investors Attempt Return Real Residing to in Home Return i h e f I h i f in Invest in Currency Earned Japan Japan 5 % 5 % 0 % 5 % 3 % % 2 5 U.S. 5 8 - 3 3 2 5 Canada 5 13 - 8 3 2 8 U.S. Japan 8 5 3 6 2 8 U.S. 8 8 0 6 2 Canada 13 - 5 8 8 6 2 Japan 5 8 13 Canada 13 11 2 U.S. 13 8 5 13 11 2 13 Canada 13 13 0 11 2 Old Data, Old Data, Old Data Old data, Old data, Old data 5-93 Extra
The International Fisher Effect Investors Attempt Return Real Residing to in Home Return i h i f e f I h in Invest in Currency Earned 5 Britain 5 % 5 % 0 % % 3 % 2 % Britain 5 New Z. 5 8 - 3 3 2 I h =2.5 % Brazil 13 - 8 5 5 3 2 New Britain 5 3 8 8 6 2 Zealand New Z. 8 8 0 8 6 2 I h =3.4 % 8 Brazil 8 13 - 5 6 2 Britain 13 5 8 13 11 2 Brazil 13 New Z. 13 8 5 11 2 I h =4.8 % 13 Brazil 13 13 0 11 2 5-94 Extra
July 2007 5-95
June 24, 2008 5-96
Feb 04, 2009 5-97
Graphic Analysis of the International Fisher Effect Interest Rate Differential (%) home interest rate - foreign interest rate 4 IFE line Lower returns from investing in 2 foreign deposits % Δ in the -3 -1 1 3 foreign currency’s Higher spot rate -2 returns from investing in foreign deposits -4 5-98 Extra
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: e f = a 0 + a 1 { (1+ i h )/(1+ i f ) - 1 } + μ The appropriate t -tests are then applied to a 0 and a 1 , whose hypothesized values are 0 and 1 respectively. 5-99 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. 5-100 Extra
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