International Parity Conditions. 1. The Law of One Price. 2. Absolute Purchasing Power Parity

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1 International Parity Conditions Some fundamental questions of international financial managers are: - What are the determinants of exchange rates? - Are changes in exchange rates predictable? The economic theories that link exchange rates, price levels, and interest rates together are called international parity conditions. These international parity conditions form the core of the financial theory that is unique to international finance The Law of One Price If the identical product or service can be sold in two different markets, and no restrictions exist on the sale or transportation costs of moving the product between markets, the products price should be the same in both markets. This is called the law of one price. 2 A primary principle of competitive markets is that prices will equalize across markets if frictions (transportation costs) do not exist. Comparing prices then, would require only a conversion from one currency to the other: P $ x S = P 2. Absolute Purchasing Power Parity If the law of one price were true for all goods and services, the purchasing power parity (PPP) states that exchange rate could be found from any set of prices. Where the product price in US dollars is (P $ ), and the price in Baht is (P ) the spot exchange rate is (S) (Direct Quote). 3 4

2 By comparing the prices of identical set of products denominated in different currencies, we could determine the real or PPP exchange rate that should exist if markets were efficient. PI $ x S = PI Where the prices of identical set of products in US dollars is (PI $ ), the prices of identical set of products in Baht is (PI ) and the spot exchange rate is (S) (Direct Quote). This is the absolute version of the PPP theory Relative Purchasing Power Parity If the assumptions of the absolute version of the PPP theory are relaxed a bit more, we observe what is termed relative purchasing power parity (RPPP). RPPP holds that the relative change in prices between two countries over a period of time determines the change in the exchange rate over that period. 6 More specifically, if the spot exchange rate between two countries starts in equilibrium, any change in the differential rate of inflation between them tends to be offset over the long run by an equal but opposite change in the spot exchange rate. S 1 = 1+I S 0 1+I $ S 1, S 0 = Spot Exchange Rate ( / $) at time 1, 0 I = Inflation Rate of Thailand I $ = Inflation Rate of U.S.A. 7 Purchasing Power Parity (PPP) Percent change in the spot exchange P rate for foreign currency Percent difference in expected rates of inflation (foreign relative to home country) 8

3 Empirical Test of PPP 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. Two general conclusions can be made from these tests: - PPP holds up 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. 4. The 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 This equation reduces to (in approximate form): i = (1+r)(1+ π)-1 = r + π + rπ = r + π Where i = nominal interest rate r = real interest rate π = expected inflation Currencies with high rates of inflation should bear higher interest rates than currencies with lower rates of inflation. 1+ π d = 1+i d 1+ π f 1+i f Empirical Tests of Fisher Effect 1. For short-term, the Fisher Effect holds. 2. For long-term, the Fisher Effect affected by increased financial risks. 3. For private securities, the comparison are influenced by unequal creditworthiness of the issuers The International 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-open, as it is termed, states 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. 12

4 More formally: S 0 S 1 S 1 x 100 = i $ -i Where i $ and i are the respective national interest rates and S is the spot exchange rate using direct quotes ( /$). Justification for the international Fisher effect is that investors must be rewarded or penalized to offset the expected change in exchange rates. 13 Currencies with lower interest rates are expected to appreciate relative to currencies with higher interest rates. S 1 = S 0 1+i 1+i $ Empirical Tests of International Fisher Effect 1. Lend some support to the International Fisher Effect. 2. Indicate the long-run tendency for interest differentials to offset exchange rate changes Interest Rate Parity The theory of Interest Rate Parity (IRP) provides the linkage between the foreign exchange markets and the international money markets. The forward rate is calculated for any specific maturity by adjusting the current spot exchange rate by the ratio of eurocurrency interest rates of the same maturity for the two subject currencies. The theory states: The difference in the national interest rates for securities of similar risk and maturity should be equal to, but opposite in sign to, the forward rate discount or premium for the foreign currency, except for transaction costs. 15 F = 1+i d S 1+i f 16

5 For example, the 90-day forward rate for the Swiss franc/us dollar exchange rate (F SF/$ 90) is found by multiplying the current spot rate (S SF / $ ) by the ratio of the 90-day euro-swiss franc deposit rate (i SF ) over the 90-day eurodollar deposit rate (i $ ). F = 1+i d S 1+i f Interest Rate Parity (IRP) 90 days Swiss franc money market i $ = 8.00 % per annum Start (2.00 % per 90 days) End $1,000,000 x 1.02 $1,020,000 $1,019,993 * Dollar money market S = SF /$ F 90 = SF /$ SF 1,480,000 x 1.01 SF 1,494,800 i SF = 4.00 % per annum (1.00 % per 90 days) 17 Note that the Swiss franc investment yields $1,019,993, $7 less on a $1 million investment. 18 The forward premium or discount is the percentage difference between the spot and forward exchange rate, stated in annual percentage terms. f SF = Spot Forward 360 x x 100 Forward days This is the case when currency SF/$ is used. 19 Currency Yield Curves & The Forward Premium Interest yield 10.0 % 9.0 % 8.0 % 7.0 % 6.0 % 5.0 % 4.0 % 3.0 % 2.0 % 1.0 % Eurodollar yield curve Forward premium is the percentage difference of 3.96% Euro Swiss franc yield curve Days Forward 20

6 7. Covered Interest Arbitrage The spot and forward exchange rates are not, however, constantly in the state of equilibrium described by interest rate parity. When the market is not in equilibrium, the potential for risk-less or arbitrage profit exists. The arbitrager will exploit the imbalance by investing in whichever currency offers the higher return on a covered basis. This is known as covered interest arbitrage (CIA). 21 Covered Interest Arbitrage (CIA) Start End $1,000,000 x 1.04 $1,040,000 $1,044,638 Dollar money market S = /$ Eurodollar rate = 8.00 % per annum 180 days Yen money market F 180 = /$ 106,000,000 x ,120,000 Euroyen rate = 4.00 % per annum Arbitrage Potential 22 The following exhibit illustrates the conditions necessary for equilibrium between interest rates and exchange rates. The disequilibrium situation, denoted by point U, is located off the interest rate parity line. However, the situation represented by point U is unstable because all investors have an incentive to execute the same covered interest arbitrage, which is virtually risk-free. 23 Interest Rates Parity (IRP) and Equilibrium Percent difference between foreign ( ) and domestic ($) interest rates Percentage premium on foreign currency ( ) 4.83 X Y Z U 24

7 8. Forward Rate as an Unbiased Predictor for Future Spot Rate Some forecasters believe that forward exchange rates are unbiased predictors of future spot exchange rates. Intuitively this means that the distribution of possible actual spot rates in the future is centered on the forward rate. Unbiased prediction simply means that the forward rate will, on average, overestimate and underestimate the actual future spot rate in equal frequency and degree. 25 Forward Rate as an Unbiased Predictor for Future Spot Rate Exchange rate t 1 S 1 S 2 F 1 t 2 t 3 t 4 Error F 2 S 3 Error F 3 S 4 Error Time t 1 t 2 t 3 t 4 The forward rate available today (F t,t+ 1), time t, for delivery at future time t+1, is used as a predictor of the spot rate that will exist at that day in the future. Therefore, the forecast spot rate for time S t2 is F 1 ; the actual spot rate turns out to be S 2. The vertical distance between the prediction and the actual spot rate is the forecast error. When the forward rate is termed an unbiased predictor of the future spot rate, it means that the forward rate over or underestimates the future spot rate with relatively equal frequency and amount. It therefore misses the mark in a regular and orderly manner. The sum of the errors equals zero International Parity Conditions in Equilibrium (Approximate Form) Forward rate as an unbiased predictor ( E ) Forecast change in spot exchange rate + 4 % (yen strengthens) Purchasing power parity ( A ) Forward premium on foreign currency + 4 % (yen strengthens) International Fisher Effect ( C ) Forecast difference in rates of inflation -4 % (less in Japan) Interest rate parity ( D ) Difference in nominal interest rates -4 % (less in Japan) Fisher effect ( B ) 27