INTERNATIONAL PARITY CONDITIONS CHAPTER FIVE PARITY CONDITION IN INTERNATIONAL FINANCE & CURRENCY FORECASTING • Some fundamental questions that managers of MNEs, international portfolio investors, importers, exporters, and government officials must deal with every day are: – What are the determinants of exchange rates? – Are changes in exchange rates predictable? • The financial theories that link exchange rates, price levels, and interest rates together are called international parity conditions • These theories not always work out to be “true” when compared to what you observe in the real world, but they are still fundamental to understand exchange rates and thus the risk of international investments – The mistake is sometimes not with the theory itself, but in the way it is interpreted or applied in practice THE GOALS OF CHAPTER • Describes the core financial theories surrounding the determination of exchange • More specifically, four international parity conditions will be introduced among the exchanges rates, price levels, and interest rates – – – – Purchasing power parity Fisher effect International Fisher effect Interest rate parity • Introduce the relationship between the (future) spot exchange rate and the forward exchange rate ARBITRAGE AND THE LAW OF ONE PRICE FIVE KEY THEORETICAL RELATIONSHIPS AMONG SPOT RATE, FORWARD RATES, INFLATION RATES, AND INTEREST RATES Expected percentage change of spot exchange rate of foreign currency - 3% Forward discount or premium on foreign currency - 3% UFR IFE IRP Interest rate differential + 3% PPP FE Expected inflation rate differential + 3% LAW OF ONE PRICE • If the identical product or service can be: – Sold in two different markets (perfect substitutability of goods and services) – No restrictions exist on the sale (free trade) – No transportation costs of moving the product between markets (costless transportation) ※Then the product or service prices should be the same in both markets • In a word, perfectly tradable goods or services are subject to the law of one price • A primary principle of competitively efficient markets is that prices of identical products or services will equalize across them if frictions or transportation costs not exist THE LAW OF ONE PRICE PPP - PURCHASING POWER PARITY • If the two markets are in two different countries, the product’s price may be stated in different currency terms – Price comparison in different markets (countries) would require a conversion from one currency to the other, e.g., P $ × S = P¥ ? is P$, the spot exchange rate where the product price in US dollars is S (yen per US$), and the price in Japanese yen is P¥ • If these two markets are competitively efficient, i.e., the law of one price holds, the purchasing power parity (PPP) exchange rate could be deduced from the relative local product prices: S = P¥ / P$ – If the price level in the U.S P$ ↑, then S ↓, which means that the US$ depreciates PPP - PURCHASING POWER PARITY • The absolute version of the PPP theory – By comparing the prices of identical products denominated in different competitively efficient currencies, we could determine the PPP exchange rate • Example: Price of wheat in France per bushel (p€) = €3.45 Price of wheat in U.S per bushel (p$) = $4.15 S€/$ = 0.83215 (s$/€ = 1.2017) • The hamburger standard or said the Big Mac index is calculated regularly by The Economist since 1986 Country Dollar equivalent price of wheat in France = S$/€ x P€ = 1.2017 $/€ x 3.45 € = $4.15 U.S Euro area Big Mac price in US$ Implied PPP exchange rate Under (-) / over(+) valuation (FC vs US$) relative to the Big Mac index $3.57 – – $5.34 = €3.37×$1.5846/€ $3.57/€3.37= $1.0593/€ +49.58% =($1.5846/€ - $1.0593/€) / $1.0593/€  When law of one price does not hold, supply and demand forces help restore the equality ※ A Big Mac in the Euro area cost €2.92, and the actual exchange rate is $1.5846/€ ※ An alternative to the hamburger standard is the “Starbucks tall-latte index” introduced by The Economist in 2004 http://www.economist.com/content/big-mac-index IN-CLASS EXERCISE #1 BIG MAC PRICE IN LOCAL CURRENCY COUNTRY United State BIG MAC PRICE IN $ IMPPLIED PPP OF $ ACTUAL ER $2.49 Argentina Ps2.5 3.13 A$3.00 1.86 Real3.60 2.34 Britain £1.99 0.69 Canada C$3.33 1.57 Chile Ps1,400 655 China Yuan 10.50 8.28 Australia Brazil UNDER/OVER VALUATION OF LOCAL CURRENCY Euro Area €2.67 0.89 Indonesia Rupi 16,000 9,430 ¥262 130 Japan Chapter -57% = (3.59 - 8.28):8.28 Local price $ Food for thought # May 27th 2004 From The Economist print edition PPP - PURCHASING POWER PARITY • Why is the Big Mac a good candidate for the application of the law of one price? – The product is nearly identical in each market – The product is a result of predominantly local materials and input costs, i.e., its price in each country represents domestic costs and prices rather than imported ones • Only a price of single product is not objective enough to decide the exchange rate – Replacing the price of a single product with a price index of a basket of goods, the absolute PPP exchange rate between two countries can be stated as S = PI¥ / PI$ 7-12 PPP - PURCHASING POWER PARITY EXHIBIT: PPP - PURCHASING POWER PARITY • Based on the absolute version of the PPP theory, we can derive relative purchasing power parity (RPPP) • RPPP is not particularly helpful in determining what the spot exchange rate today, but that the relative change in prices between two countries over a period of time determines the change in the exchange rate over that period • More specifically, the spot exchange rate should change in an equal amount but in the opposite direction to the difference in inflation rates between two countries – Thus, the currency with higher (lower) inflation rate will depreciate (appreciate) PPP - PURCHASING POWER PARITY • Given the exchange rate St = Pt¥ / Pt$ (yen per US$) at time t, ¥ ¥ ¥  St+1  Pt (1   ) (1   )  St Pt$ (1   $ ) (1   $ ) • For the indirection quotation of Japanese ¥ for the U.S., the change of the exchange rate is as follows ¥ St  St+1  St+1  (1   ) (1   $ ) (1   $ )  (1   ¥ )  (1   ¥ ) 1  ¥ St $ (1   ) S t  St St  St+1  (1   $ )  (1   ¥ )   $   ¥ St+1 ※ For instance, point P represents an equilibrium point where the inflation rate in the foreign country, Japan, is 4% lower than that in the home country, the U.S ※ Therefore, RPPP would predict that the Japanese yen would appreciate by 4% per annum with respect to the U.S dollars ※ If the domestic country is with a higher inflation rate  prices of domestic products become relatively expensive  export ↓, import ↑  deficit on current account (and on BOP)  supply of domestic currency > demand of domestic currency  domestic currency depreciates PPP - PURCHASING POWER PARITY • Empirical testing of PPP and the law of one price has been done, but has not proved PPP to be accurate in predicting future exchange rates • Possible reasons for the poor performance of PPP – Transportation costs of goods and services are not zero – Many services are not tradable, e.g., legal services – Many goods and services are not of the same quality across countries, reflecting different tastes of consumers in different countries – Different tax rules in different countries +: FC appreciates against DC –: FC depreciates against DC ※ If π¥ is smaller than π$ (the U.S is with a higher inflation rate), St+1 is smaller than St, which indicates the appreciation of Japanese ¥ (depreciation of US$) ※ Furthermore, the percentage change of the PPP exchange rate is proportional to the difference of the inflation rate (see Exhibit on the next slide) PPP - PURCHASING POWER PARITY ADJUSTED RER • Two general conclusions from these studies: – PPP or RPPP hold well over the very long run but poorly for shorter time periods – The theory holds better for countries with relatively high rates of inflation and underdeveloped capital markets • A higher inflation rate generates a strong enough pressure to affect the currency to depreciate • For countries with underdeveloped capital markets, the effect of the current account dominates BOP (comparing to the financial and capital accounts), so there is a closer relationship between price levels and exchange rates CPI-VN CPI-US NER 1992 100 100.0 10.800 1993 105.2 102.9 1994 114.4 101.8 1995 112.9 102.5 1996 105.5 102.5 1997 103.6 102.7 CPI-VN CPI-US RER 1992 100 100.0 10.800 1993 105.2 102.9 1994 114.4 101.8 1995 112.9 102.5 1996 105.5 102.5 1997 103.6 102.7 NOMINAL AND REAL EXCHANGE RATES ADJUSTED NER NAÊM NAÊM • According to the RPPP, the change of the (nominal) exchange rate is to offset the change in the differential growths of price levels between two countries – For the country with a higher inflation rate, the prices of products increase inside the country, but due to the depreciation of the currency of that country, the prices of products in foreign currency remain the same • So, the change of the nominal exchange rate will not affect the relatively competitive power for different countries • Only the change of the real exchange rate, which measures the purchasing power of a currency, will affect the price competitiveness of a country 18 NOMINAL AND REAL EXCHANGE RATES • The real exchange rate is defined as follows SR,t = SN,t  Pf,t Pd,t – SR,t: real exchange rate at time t – SN,t: nominal exchange rate at time t (1 foreign dollar = SN,t domestic dollars) – Pf,t: foreign price level at time t relative to the base period at time (Pf,0=100) – Pd,t: domestic price level at time t relative to the base period at time (Pd,0=100) ※ If RPPP holds, the magnitude of the increase of the foreign price level (Pf,t ↑) and the magnitude of the depreciation of the foreign currency (SN,t ↓) will be the same and offset for each other, so the real exchange rate will not change NOMINAL AND REAL EFFECTIVE EXCHANGE RATE INDICES • Nominal effective exchange rate index (NEERI) uses nominal exchange rates to create an index, on a weighted average basis, of the value of the main trading currencies over a period of time, which is defined as follows n NEERI t =  Wi  ( i=1 (1/SN,i,t ) (1/SN,i,0 )  100) – n: number of major trading currencies for the domestic country – Wi: weight of a foreign currency, depending on the trading volume between the domestic country and that foreign country – SN,i,t: nominal exchange rates for the i-th foreign currency at time t (1/SN,i,t measures the domestic currency value in terms of foreign currencies) NOMINAL AND REAL EFFECTIVE EXCHANGE RATE INDICES NOMINAL AND REAL EFFECTIVE EXCHANGE RATE INDICES • Individual national currencies often need to be evaluated against all other currency values to determine relative purchasing power • The objective is to discover whether a nation’s exchange rate is “overvalued” or “undervalued” in terms of PPP • This problem is often dealt with through the calculation of exchange rate indices such as the nominal effective exchange rate index and the real effective exchange rate index • Example to calculate NEERI for NT$ against the US$ and Japanese yen (Year 2000 is the base period) SN,i,2000 SN,i,2008 Trading volume U.S (i=1) 1US$=30NT$ 1US$=32NT$ NT$ 600 billion Japan (i=2) 1¥=0.25NT$ 1¥=0.2NT$ NT$ 400 billion NEERI2008 =W1  ( (1/SN,1,2008 ) (1/SN,1,2000 )  0.6  ( 100)  W2  ( (1/SN,2,2008 ) (1/SN,2,2000 ) 100) (1/32) (1/0.2) 100)  0.4  ( 100)  106.25 (1/30) (1/0.25) ※ From 2000 to 2008, NT$ depreciates against US$ (by 6.25%) and appreciates against Japanese ¥ (by 25%) ※ From the analysis of NEERI, overall speaking, the nominal exchange rate of NT$ appreciates by 6.25% against the US$ and Japanese ¥ NOMINAL AND REAL EFFECTIVE EXCHANGE RATE INDICES • Real effective exchange rate index (REERI) indicates how the weighted average purchasing power of the domestic currency has changed relative to some arbitrarily selected base period, which is defined as follows n REERI t =  Wi  ( i=1 (1/SR,i,t ) (1/SR,i,0 ) NOMINAL AND REAL EFFECTIVE EXCHANGE RATE INDICES REERI2008 =W1  ( (1/SR,1,2008 ) (1/SR,1,2000 )  0.6  ( 100)  W2  ( (1/SR,2,2008 ) (1/SR,2,2000 ) 100) (1/36.3636) (1/0.1727) 100)  0.4  ( 100)  107.40 (1/30) (1/0.25) 100) – SR,i,t: real exchange rates for the i-th foreign currency at time t ※ Overall speaking, the real exchange rate of NT$ appreciates by 7.40% against the US$ and Japanese ¥ ※ In other words, the purchasing power of NT$ increases by 7.40% against the US$ and Japanese ¥ from 2000 to 2008 NOMINAL AND REAL EFFECTIVE EXCHANGE RATE INDICES • Example to calculate REERI for NT$ against the US$ and Japanese yen (Year 2000 is the base period) U.S (i=1) SN,i,2000 SN,i,2008 Price level in 2000 Price level in 2008 Trading volume 1US$=30NT$ 1US$=32NT$ 100 125 NT$ 600 billion Japan (i=2) 1¥=0.25NT$ 1¥=0.2NT$ 100 95 NT$ 400 billion Taiwan 100 110 Pf,1,2000 100 SR,1,2000 = SN,1,2000  =30   30 Pd,2000 100 SR,2,2000 =SN,2,2000  Pf,2,2000 Pd,2000 SR,1,2008 = SN,1,2008  SR,2,2008 =SN,2,2008  Pf,1,2008 Pd,2008 Pf,2,2008 Pd,2008 =0.25  =32  100  0.25 100 NOMINAL AND REAL EFFECTIVE EXCHANGE RATE INDICES • The meaning of real effective exchange rate index (REERI): – REERIt > REERI0: Real exchange rate of the domestic currency against foreign currencies appreciates relative to the base period, so the competitive power of domestic products decreases relative to the base period – REERIt < REERI0: Real exchange rate of the domestic currency against foreign currencies depreciates relative to the base period, so the competitive power of domestic products increases relative to the base period 125  36.3636 110 =0.20  95  0.1727 110 EXHIBIT REAL EFFECTIVE EXCHANGE RATE INDEXES FOR SOME SELECTED CURRENCIES (Y2000 = 100) EXCHANGE RATE PASS-THROUGH ※ From 1981 to 1995, the real exchange rate of Japanese ¥ against foreign currencies appreciates, so the competitive power of the Japanese products declines ※ From 1995 to 2008, the real exchange rate of Japanese ¥ against foreign currencies depreciates generally, so the competitive power of the Japanese products increases ※ If the RPPP is true for the long term, i.e., the real exchange rate remains stable due to the offset of the effects of the changes in nominal exchange rates and inflation rates, the REERI should fluctuate around 100 EXCHANGE RATE PASS-THROUGH • The degree to which the prices of imported and exported goods change as a result of exchange rate changes is termed exchange rate pass-through • Although PPP implies that all exchange rate changes are passed through by equivalent changes in prices to trading partners, empirical researches in the 1980s questioned this long-held assumption • For example, a car manufacturer may or may not adjust pricing of its cars sold in a foreign country if exchange rates alter the manufacturer’s cost structure in comparison to the foreign market • Pass-through can also be partial as there are many mechanisms by which companies can absorb the impact of exchange rate changes ※The reason for absorption is trying not to affect the selling volume too much ※The absorption could result from reducing profit margins, cost reductions, or both ※Cost reductions arises from the lower imported price for components and raw materials to Germany when the euro appreciates FISHER EFFECT • The Fisher effect states that nominal interest rates in each country are equal to the required real rate of return plus compensation for expected inflation • Because investors concern about the real returns (i.e., the growth of their purchasing power), we would expect that as inflation increases, investors will demand higher nominal rates of returns on their investment • The nominal interest rate is derived from (1+r) × (1+ π) – 1, and can be reduced to: i = r + π + rπ  r + π where i = nominal interest rate, r = real interest rate, and π = expected inflation FISHER EFFECT • Because of the arbitrage investment activities among countries, the real interest rates were to be held constant among countries, e.g., if the r$ is larger than the r¥, the capital will flow from Japan to the U.S continuously until the r$ equals the r¥ • So, according to the Fisher effect, the nominal interest rate and the inflation rate have to be adjusted on a one-for-one basis • Empirical tests using ex post national inflation rates and the nominal rates of return of fixed-income securities have shown the Fisher effect usually exists for short-maturity government securities (see the next slide) FISHER EFFECT INT’L FISHER EFFECT • The relationship between the percentage change in the spot exchange rate over time and the differential between comparable interest rates in different national capital markets is known as the international Fisher effect • Fisher found that the spot exchange rate should change in an equal amount but in the opposite direction to the difference in interest rates between two countries – The opposite direction means for a country with lower (higher) interest rates, its currency will appreciate (depreciate) INT’L FISHER EFFECT • The equation of the international Fisher effect: i$ – i¥ (1+i$) – (1+i¥) St  St+1    i$ – i¥ ¥ 1+i + i¥ St+1 ※ According to the above figure, it is obvious that investors indeed require higher nominal risk-free rates (T-bill rates) with the increase of higher inflation rates ※However, studies about longer-term government bonds and private sector bonds not support the Fisher effect where i$ and i¥ are the respective nominal interest rates of the investing period, and St and St+1 are the spot exchange rates using indirect quotes at the beginning and the end of that period (¥/$) (if St+1 < St, it means that the Japanese ¥ appreciates) • According to the above equation, the currency with lower interest rate will appreciate – If i$ =6% and i¥ =4%, St+1 is expected to be smaller than St by 2%, which means that the Japanese ¥ should appreciate about 2% per year CURRENCY FORECATING INT’L FISHER EFFECT • The unrestricted capital flows will see the opportunity around the world and make the international Fisher effect to be true • For example, if i$ =6% and i¥ =5%, and the Japanese ¥ is expected to appreciate 2%, the unrestricted capital will flow from the U.S to Japan to earn 7% (=5% + 2%) return This activity will increase the money supply in the Japanese economy and thus reduce the i¥ until it becomes 4% (thus the international Fisher effect holds again) • Currency forecasting can lead to consistent profits only if the forecaster meets at least one of the following four criteria – Has exclusive use of a superior forecasting model – Has consistent access to information before other investors – Exploits small, temporary deviations from equilibrium – can predict the nature of government intervention in the foreign exchange • As a general rule, in a fixed rate system, the forecaster must focus on the governmental decision-making structure because the decision to devalue or revalue at a given time is clearly political • In case of floating system, currency forecasting have the choice of using either market or model-based forecasts, neither of which guarantees success INT’L FISHER EFFECT # • The international Fisher effect vs the Relative Purchase Power Parity (RPPP) St  St+1 $ ¥ ¥  i  i  (r $   $ )  (r ¥   ) St+1   $  ¥ By force of the international arbitrage, real rates of return between markets should be equal, i.e., r$=r¥ ※ The international Fisher effect and the RPPP is consistent if the Fisher effect is valid ※ The only difference is that in the international Fisher effect, the interest rate, i, is applied to a future time period and thus the inflation rate, π, is the expected inflation rate FORECASTING EXCHANGE RATES: EFFICIENT MARKETS APPROACH • Financial markets are efficient if prices reflect all available and relevant information • The efficient market hypothesis (Prof Eugene Fama) • If this is true, exchange rates will only change when new information arrives, thus: St = E[St+1] The random walk hypothesis suggest that today’s ER is the best predictor of tomorrow’s ER Ft = E[St+1| It] • Predicting exchange rates using the efficient markets approach is affordable and is hard to beat ※ In the RPPP, however, the inflation rate, π, is ex post, i.e., only at the end of the period, the inflation rate for that period is known, and thus the exchange rate should 7-38 change in response to the realized inflation rate 10 FORECASTING EXCHANGE RATES: FUNDAMENTAL APPROACH • Involves econometrics to develop models that use a variety of explanatory variables This involves three steps: – Step 1: Estimate the structural model – Step 2: Estimate future parameter values – Step 3: Use the model to develop forecasts FORECASTING EXCHANGE RATES: TECHNICAL APPROACH • Technical analysis looks for patterns in the past behavior of exchange rates • Clearly it is based upon the premise that history repeats itself • The downside is that fundamental models not work any better than the forward rate model or the random walk model FORECASTING EXCHANGE RATES: FUNDAMENTAL APPROACH # MOVING AVERAGE CROSSOVER RULE: GOLDEN CROSS vs DEATH CROSS s    1 (m  m* )   (  * )   ( y *  y )   • • • • • • S: natural logarithm of spot ER m-m*: natural logarithm of domestic/foreign money supply  - *: natural logarithm of domestic/foreign velocity of money y-y*: natural logarithm of domestic/foreign output : random error term, with zero mean , : model parameter LMA: Long-term Moving Average SMA: Short-term Moving Average 11 HEAD AND SHOULDERS PATTERN: A REVERSAL SIGNAL R MAE ( S ) MAE ( F ) 1 MAE   i Pi  Ai N MAE(S): mean absolute forecast error of a forecasting service MAE(F): mean absolute forecast error of the forward exchange rate as a predictor PERFORMANCE OF THE FORECASTERS • Forecasting is difficult, especially with regard to the future • As a whole, forecasters cannot a better job of forecasting future exchange rates than the forecast implied by the forward rate • The founder of Forbes Magazine once said, “You can make more money selling financial advice than following it.” R MSE ( B ) MSE ( S ) MSE(B)[...]...FORECASTING EXCHANGE RATES: FUNDAMENTAL APPROACH • Involves econometrics to develop models that use a variety of explanatory variables This involves three steps: – Step 1: Estimate the structural model – Step 2: Estimate future parameter values – Step 3: Use the model to develop forecasts FORECASTING EXCHANGE RATES: TECHNICAL APPROACH... whole, forecasters cannot do a better job of forecasting future exchange rates than the forecast implied by the forward rate • The founder of Forbes Magazine once said, “You can make more money selling financial advice than following it.” R MSE ( B ) MSE ( S ) MSE(B) ... 114.4 101.8 19 95 112.9 102 .5 1996 1 05. 5 102 .5 1997 103.6 102.7 CPI-VN CPI-US RER 1992 100 100.0 10.800 1993 1 05. 2 102.9 1994 114.4 101.8 19 95 112.9 102 .5 1996 1 05. 5 102 .5 1997 103.6 102.7 NOMINAL... x 3. 45 € = $4. 15 U.S Euro area Big Mac price in US$ Implied PPP exchange rate Under (-) / over(+) valuation (FC vs US$) relative to the Big Mac index $3 .57 – – $5. 34 = €3.37×$1 .58 46/€ $3 .57 /€3.37=... IMPPLIED PPP OF $ ACTUAL ER $2.49 Argentina Ps2 .5 3.13 A$3.00 1.86 Real3.60 2.34 Britain £1.99 0.69 Canada C$3.33 1 .57 Chile Ps1,400 655 China Yuan 10 .50 8.28 Australia Brazil UNDER/OVER VALUATION