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# Fisher effect

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Fisher effect

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### Fisher effect

1. 1. International Parity Conditions
2. 2. 2 Recollection  Introduction to Parity Conditions  Absolute & Relative Purchasing Power Parity  Real Exchange Rate  Fisher Effect (FE)  International Fisher Effect (IFE)  Unbiased Forward Rate (UFR)  Interest Rate Parity (IRP)  Covered Interest Arbitrage  Currency Forecasting => PROJECT
3. 3. 3 Introduction  Managers of multinational firms, international investors, importers and exporters, and government officials must deal with these fundamental issues:  Are changes in exchange rates predictable?  How are exchange rates related to interest rates?  What, at least theoretically, is the “proper” exchange rate?  To answer these questions we need to first understand the economic fundamentals of international finance, known as parity conditions.
4. 4. 4 Parity Conditions  Parity Conditions provide an intuitive explanation of the movement of prices and interest rates in different markets in relation to exchange rates.  The derivation of these conditions requires the assumption of Perfect Capital Markets (PCM).  no transaction costs  no taxes  complete certainty  NOTE – Parity Conditions are expected to hold in the long-run, but not always in the short term.
5. 5. 5 Purchasing Power Parity (PPP)  PPP is based on the notion of arbitrage across goods markets and the basic building block of PPP is the Law of One Price (LOP).  LOP states that the price of an identical good should be the same in all markets (assuming no transactions costs).  Otherwise, one could make profits by buying the good in the cheap market and reselling it in the expensive market.
6. 6. 6 The Law of One Price  LOP states that a product’s price may be stated in different currency terms, but the price of the product should remain the same. Comparison of prices would only require conversion from one currency to the other: Conversely, the exchange rate could be deduced from the relative local product prices: £ \$ £/\$ P P S = ££\$\$ PSP ×=
7. 7. 7 LOP Example  Pwheat,Aust = \$4/bushel and Pwheat,UK = £2.5/bushel  Spot rate (A\$/£) = 1.70  A\$ equivalent price of wheat in UK is A\$1.70/£ *£2.5 = \$4.25/bushel  Implication: The demand for Australian wheat will increase forcing up its price. The price of UK wheat will drop. wheat UK wheat Aust PSP ×= £/\$
8. 8. 8 The Big Mac Index  The most famous test is The Economist magazine’s Big Mac Hamburger standard.  First launched in 1986, updated ever since.  For example, see: http://www.oanda.com/products/bigmac/bigmac.shtml
9. 9. 9
10. 10. 10 Research on the Big Mac Index  Pakko and Pollard (1996) conclude that Big Mac PPP holds in the long-run, but currencies can deviate from it for lengthy periods. They note several reasons why the Big Mac index may be flawed:  It assumes that there are NO barriers to trade.  Prices are distorted by taxes.  Profit margins may vary according to competition.  Prices of non-traded goods (real estate, utilities, labor) are also inputs that affect production costs.
11. 11. 11 Working for a Big Mac Big Mac Price (US \$) Net Hourly Wage (US \$) Minutes of work to buy a Big Mac Big Mac Price (US \$) Net Hourly Wage (US \$) Minutes of work to buy a Big Mac Argentina 1.42 1.70 50 Mexico 2.18 2.00 65 Australia 1.86 7.80 14 New Zealand 2.22 6.80 20 Brazil 1.48 2.05 43 Peru 2.28 2.20 62 Britain 3.14 12.30 15 Philippines 2.24 1.20 112 Canada 2.21 9.35 14 Poland 1.62 2.20 44 Chile 1.96 2.80 42 Russia 1.32 2.60 30 China 1.20 2.40 30 Singapore 1.85 5.40 21 Colombia 2.13 1.90 67 South Africa 1.85 3.90 28 Czech Republic 1.96 2.40 49 South Korea 2.70 5.90 27 Denmark 4.09 14.40 17 Sweden 3.60 10.90 20 Euro area 2.98 9.59 19 Switzerland 4.60 17.80 16 Hong Kong 1.47 7.00 13 Taiwan 2.01 6.90 17 Hungary 2.19 3.00 44 Thailand 1.38 1.70 49 Indonesia 1.84 1.50 74 Turkey 2.34 3.20 44 Japan 2.18 13.60 10 United States 2.71 14.30 11 Malaysia 1.33 3.10 26 Venezuela 2.32 2.10 66
12. 12. 12 A New Index – Starbucks Index
13. 13. 13 Absolute PPP  A less extreme form of the Law of One Price is ABSOLUTE PPP which says that the price of a basket of goods should be the same in each market.  The PPP exchange rate between the two countries should then be: Absolute PPP: tF tDFD t PI PI S , ,/ = PID,t (PIF,t) is the domestic (foreign) price index (e.g., consumer price index) at time t.
14. 14. 14 Relative Purchasing Power Parity  Relative PPP claims that exchange rate movements should exactly offset any inflation differential between two countries: Relative PPP: F D π π + + =+ 1 1 S S D/F t D/F 1t  We can also write: F D π π + + ×=+ 1 1 SS D/F t PPP 1t Percentage change in domestic prices F FD π ππ + − = −+ 1S SS D/F t D/F t D/F 1t
15. 15. 15 Relative PPP  Relative PPP implies that the change in the exchange rate will offset the difference between the relative inflation of two countries.  The previous formula can be approximated as: where, πD and πF refers to the percentage change in domestic and foreign price levels respectively and ∆s to the percentage change in the exchange rate. If domestic inflation > (<) foreign inflation, PPP predicts the domestic currency should depreciate (appreciate). FDs ππ −=∆
16. 16. 16 Relative PPP Example  Given inflation rates of 5% and 10% in Australia and the UK respectively, what is the prediction of PPP with regards to \$A/GBP exchange rate? = (0.05 – 0.10)/(1 + 0.10) = - 0.045 = - 4.5% The general implication of relative PPP is that countries with high rates of inflation will see their currencies depreciate against those with low rates of inflation. F FD t tt S SS π ππ + − = − − − 11 1 Relative PPP
17. 17. 17 How well does PPP work?  We have seen that the strictest version of PPP – that all goods and financial assets obey the law of one price – is demonstrably false.  However, there is clearly a relationship between relative inflation rates and changes in exchange rates.  Currencies that have had the largest relative decline (gain) in purchasing power see the sharpest erosion (appreciation) in their foreign exchange values.
18. 18. 18 Relative Purchasing Power Parity Applications of Relative PPP: 1. Forecasting future spot exchange rates. 2. Calculating appreciation in “real” exchange rates. This will provide a measure of how expensive a country’s goods have become (relative to another country’s).
19. 19. 19 Forecasting Future Spot Rates  Suppose the spot exchange rate and expected inflation rates are:  What is the expected ¥/\$ exchange rate if relative PPP holds? 2%5%;\$;/¥90S ..t0¥/\$, === JapanSU ππ ( ) \$/¥43.87 05.1 02.1 \$/¥90 1 1 \$ ¥ 0,/¥1\$,/¥ =      ⋅=         + + ⋅= π π tS PPP t SS
20. 20. 20 Real Exchange Rate  By definition, the real exchange rate measures deviations from PPP.  That is, changes in the spot exchange rate that do not reflect differences in inflation rates between the two currencies in question. Real Exchange Rate: PPP 1t 1t S S E + + =
21. 21. 21 Real Exchange Rate  Appreciation/depreciation in the real exchange rate measures deviations from PPP.  When E = 1, the denominator currency is valued correctly. The competitiveness of this country is unaltered.  When E < 1, the denominator currency is undervalued. Products from the other country seem expensive relative to the base year. That is, the competitiveness of the denominator country improves.  When E > 1, the denominator currency is overvalued. Products from the other country seem cheap relative to the base year. That is, the competitiveness of the denominator country deteriorates.
22. 22. 22 The Fisher Effect  The international Fisher relation is inspired by the domestic relation postulated by Irving Fisher (1930).  The Fisher effect (also called Fisher-closed) states:  This relation is often presented as a linear approximation stating that the nominal interest rate is equal to a real interest rate plus expected inflation: ( ) ( )( ) πππ rriri ++=⇒++=+ 111 π+≈ ri
23. 23. Contd. • Fisher Effect • This equation tells us that, all things being equal, a rise in a country's expected inflation rate will eventually cause an equal rise in the interest rate (and vice versa). 23
24. 24. 24 The Fisher Effect  Applied to two different countries, like Australia and Japan, The Fisher Effect would be stated as:  It should be noted that this requires a forecast of the future rate of inflation, not what inflation has been in the past. \$ \$ \$ i r π≈ + ¥¥¥ π+≈ ri
25. 25. What Does International Fisher Effect - IFE Mean? An economic theory that states that an expected change in the current exchange rate between any two currencies is approximately equivalent to the difference between the two countries' nominal interest rates for that time. For example, if country A's interest rate is 10% and country B's interest rate is 5%, country B's currency should appreciate roughly 5% compared to country A's currency. The rational for the IFE is that a country with a higher interest rate will also tend to have a higher inflation rate. This increased amount of inflation should cause the currency in the country with the high interest rate to depreciate against a country with lower interest rates. 25
26. 26. 26 The International Fisher Effect  The International Fisher Effect (also called Fisher-open) states that the spot exchange rate should change to adjust for differences in interest rates between two countries: F D FD t FD t i i S S + + =+ 1 1 / / 1
27. 27. 27 The International Fisher Effect  The Fisher effect applied to two different countries like Australia and Japan would be: (1) (1+i\$ ) = (1+r\$ )(1+π\$ ) (2) (1+i¥ ) = (1+r¥ )(1+π¥ )  Dividing (1) by (2), we get: (3)       π+ π+       + + = + + ¥ \$ ¥ \$ ¥ \$ 1 1 r1 r1 i1 i1 = 1
28. 28. 28 The International Fisher Effect  If real interest rates are equalized across countries, then for equation (3) we get r\$ = r¥ : (4) ¥ \$ ¥ \$ 1 1 i1 i1 π+ π+ = + + (5) ¥ ¥\$ ¥ ¥\$ 11 π ππ + − = + − i ii Remember this? F FD t tt S SS π ππ + − = −+ 1 1 F FD t tt i ii S SS + − = −+ 1 1 International Fisher: E(St+1)
29. 29. 29 Tests of the International Fisher Effect  Empirical tests lend some support to the relationship postulated by the international Fisher effect (currencies with high interest rates tend to depreciate and currencies with low interest rates tend to appreciate), although considerable short-run deviations occur.
30. 30. 30 Unbiased Forward Rate (UFR)  Some forecasters believe that for the major floating currencies, foreign exchange markets are “efficient” and forward exchange rates are unbiased predictors of future exchange rates.  The unbiased forward rate (UFR) concept states that the forward exchange rate, quoted at time t for delivery at time t+1, is equal to the expected value of the spot exchange rate at time t+1.
31. 31. 31 Unbiased Forward Rate (UFR)  An unbiased predictor, however, does not mean the future spot rate will actually be equal to what the forward rate predicts.  Unbiased prediction means that the forward rate will, on average, overestimate and underestimate the actual future spot rate in equal frequency and degree.  UFR can be written as: Ft t+1 = Et[St+1]
32. 32. 32 Empirical Tests of UFR  A consensus is developing that rejects the efficient market hypothesis.  It appears that the forward rate is not an unbiased predictor of the future spot rate and that it does pay to use resources in an attempt to forecast exchange rates.  The existence and success of foreign exchange forecasting services suggest that managers are willing to pay a price for forecast information even though they can use the forward rate to forecast at no cost.
33. 33. 33 Interest Rate Parity  Interest rate parity (IRP) is an arbitrage condition that provides the linkage between the foreign exchange markets and the international money markets. f d t tt i i S F + + = + 1 11, where, Ft and St are the forward and spot rates and id and if are domestic and foreign interest rates respectively. Interest Rate Parity (IRP)
34. 34. 34 Interest Rate Parity  The approximate form of IRP says that the % forward premium equals the difference in interest rates. fd t tt ii S F −≈− + 1 1,  In general, the currency trading at a forward premium (discount) is the one from the country with the lower (higher) interest rate. Approximation of IRP fd t ttt ii S SF −≈ −+1,
35. 35. 35 Interest Rate Parity – An Example  Basic idea: Two alternative ways to invest funds over same time period should earn the same return.  Suppose the 3-month money market rate is 8% p.a. (2% for 3-months) in the U.S. and 4% p.a. (1% for 3- months) in Switzerland, and the spot exchange rate is SFr1.48/\$.  The 3-month forward rate must be SFr1.4655/\$ to prevent arbitrage opportunities (i.e., interest rate parity must hold).
36. 36. 36 The Example Continued 90 daysS = SF 1.4800/\$ SF 1,480,000 Dollar money market \$1,000,000 \$1,020,000× 1.02 Start End i \$ = 8.00 % per annum (2.00 % per 90 days) Swiss franc money market SF 1,494,800× 1.01 i SF = 4.00 % per annum (1.00 % per 90 days) F90 = SF 1.4655/\$ \$1,019,993* * Rounding error.
37. 37. 37 Interest Rate Parity: Why It Holds  This must hold by arbitrage. Otherwise riskless profits could be made. This is known as covered interest arbitrage (CIA) and occurs whenever IRP does not hold. CIA can involve the following steps: • Borrow the domestic currency; • Exchange the domestic currency for the foreign currency in the spot market; • Invest the foreign currency in an interest- bearing instrument; and then • Sign a forward contract to “lock in” a future exchange rate at which to convert the foreign currency proceeds back to the domestic currency.
38. 38. 38 Covered Interest Arbitrage: Example  The annual interest rate in the AUS and UK are 5% and 8% respectively. The current spot rate is \$1.50/£ and the 1 year forward rate is \$1.48/£. Can arbitrage profits be made? 1. Borrow \$1m (at 5%) 2. Purchase £666,667 using \$1m 3. Invest £ at 8% (will receive £720,000 in one year’s time) 4. Simultaneously sell £720,000 forward (\$1,065,600) 5. Repay loan + interest of \$1,050,000 6. ARBITRAGE PROFIT = \$15,600 )1(1 1, f t tt d i S F i +×=+ + 1.05 ≠ 1.0656 ??)08.1( 50.1 48.1 05.1 ×=
39. 39. 39 The Example Continued £666,667 for 1 year at i\$ = 5% <\$1,050,000> \$1,065,600 Borrow \$1,000,000 1 Convert Spot at \$1.50/£ 2 Invest for 1 year at i£ = 8% 3 Cover Forward at \$1.48/£ 4 Profit = \$15,600 £720,000
40. 40. 40 Covered Interest Arbitrage  Covered interest arbitrage should continue until interest rate parity is re-established, because the arbitrageurs are able to earn risk-free profits by repeating the cycle.  But their actions nudge the foreign exchange and money markets back toward equilibrium: 1. Purchase of Pounds in the spot market and sale of £ in the forward market narrow the premium on forward pounds. 2. The demand for pound-denominated securities causes pound interest rates to fall, while the higher level of borrowing in Australia causes dollar interest rates to rise.
41. 41. 41  A deviation from covered interest arbitrage is uncovered interest arbitrage (UIA).  In this case, investors borrow in countries and currencies exhibiting relatively low interest rates and convert the proceed into currencies that offer much higher interest rates.  The transaction is “uncovered” because the investor does no sell the higher yielding currency proceeds forward, choosing to remain uncovered and accept the currency risk of exchanging the higher yield currency into the lower yielding currency at the end of the period. Uncovered Interest Arbitrage
42. 42. 42 Currency Forecasting  What have we learnt about currency forecasting this week?  Unbiased forward rate  Long-term equilibrium relationships (RPPP and IFE)  More methodologies next week.