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**Multinational business finance course 723g33**

International Parity Conditions ESM chapter 7 Multinational business finance course 723g33 PhD in Finance

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**International Parity Conditions**

International Parity Conditions Managers of multinational firms, international investors, importers and exporters, and government officials must deal with these fundamental issues: What are the relationship between exchange rate, interest rate and inflation? Are changes in exchange rates predictable? PhD in Finance

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**International Parity Conditions**

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. PhD in Finance

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**International Parity Conditions**

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 run.

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**The Law of one price: If the identical product or service can be:**

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; and transportation costs of moving the product between markets do not exist, then the product’s price should be the same in both markets. This is called the law of one price. Arbitrage principle

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**Recall: Exchange Rates, th elaw of one price**

A primary principle of competitive markets is that prices will equalize across markets if frictions (transportation costs) do not exist. That is: P$ x S = P¥ or S= P¥ / P$ Where the product price in US dollars is (P$), the spot exchange rate is (S) and the price in Yen is (P¥). S here is dollar price in ters of Yen. PhD in Finance

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**Exhibit 7.1 Selected Rates from the Big Mac Index**

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Absolute PPP theory Law of one price should hold for a basket of identical goods and services in different currencies. By comparing the prices of identical products denominated in different currencies, we could determine the PPP exchange rate that should exist if markets were efficient. S ¥/$= ∑P¥/ ∑P$ Note that Big Mac index is potentially misleading but fun to know. PhD in Finance

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**RPPP: relative Purchasing Power Parity**

If the exchange rate between two currencies starts in equilibrium, then, we have what is termed Relative purchasing power parity (RPPP). The relative change in prices between two countries over a period of time determines the change in the exchange rate over that period. PhD in Finance

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**Prices and Exchange Rates**

More specifically, with regard to RPPP: “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.” PhD in Finance

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**Exhibit 7.2 Relative Purchasing Power Parity (RPPP)**

%∆S %∆P PhD in Finance

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**Prices and Exchange Rates**

RPPP is not accurate in predicting future exchange rates. Two general conclusions can be made from empirical tests: RPPP 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. PhD in Finance

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**Prices and Exchange Rates**

The objective is to discover whether a nation’s exchange rate is “overvalued” or “undervalued” in terms of RPPP. This problem is often dealt with through the calculation of exchange rate indices such as the nominal effective exchange rate index. Weighted average purchasing power of the currency relative to some base period. PhD in Finance

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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/£ exchange rate? = (0.05 – 0.10)/( ) = = - 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. Relative PPP

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**Forecasting Future Spot Rates**

Suppose the spot exchange rate and expected inflation rates are: What is the expected ¥/$ exchange rate if relative PPP holds? Answer:

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Exhibit 7.3 IMF’s Real Effective Exchange Rate Indexes for the United States, Japan, and the Euro Area

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**Prices and Exchange Rates**

Incomplete exchange rate pass-through is one of the reasons that a country’s Real effective exchange rate index can deviate from the exchange rate 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. The degree to which the prices of imported and exported goods change as a result of exchange rate changes is termed pass-through. PhD in Finance

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**Prices and Exchange Rates**

Price elasticity of demand is an important factor when determining pass-through levels. The price elasticity of demand for any good is the percentage change in quantity of the good demanded as a result of the percentage change in the goods price. Pass-through can also be partial as there are many mechanisms by which companies can absorb the impact of exchange rate changes. PhD in Finance

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**Exhibit 7.4 Exchange Rate Pass-Through**

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**Fisher Effect This equation reduces to: i = r +**

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: i = r + Where i is nominal interest rate, r is real interest rate and is expected inflation. Empirical tests (using ex-post) national inflation rates have shown the Fisher effect usually exists for short-maturity government securities (treasury bills and notes). PhD in Finance

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**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. Also called “Fisher-open”. The spot exchange rate should change in an equal amount but in the opposite direction to the difference in interest rates between two countries. PhD in Finance

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**International Fisher effect**

approximately: Where i$ and i¥ are the respective national interest rates and S1 is the spot exchange rate (¥/$) at t=1, S2 is the expected future spot rate at t=2. Justification for the International Fisher effect is that investors must offset the expected change in exchange rates. S2 = i$ - i¥ S1 – S2 PhD in Finance

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Interest Rates Parity A forward exchange agreement between currencies states the rate of exchange at which a foreign currency will be bought or sold forward at a specific date in the future. A forward rate is an exchange rate quoted for settlement at some future date. For 1, 2, 3, 6, 12 month. Forward rate over 2 years is called swap rate. PhD in Finance

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Interest Rates Parity 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. For example, the 90-day forward rate for the Swiss Franc/US dollar exchange rate (FSF/$90) = the current spot rate (SSF/$) times the ratio of the 90-day euro-Swiss franc deposit rate (iSF) over the 90-day Eurodollar deposit rate (i$). PhD in Finance

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**Interest Rates and Exchange Rates**

Formal representation of the forward rate: FSF/$90 = SSF/$ x [1 + (iSF x 90/360)] [1 + (i$ x 90/360)] PhD in Finance

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The forward premium The forward premium or discount (of SF) is the percentage difference between forward exchange rate and spot rate, stated in annual percentage terms. f SF = Spot – Forward Note that here SF/$ is used. If use $/SF, then it is (F-S)/S instead. Forward 360 days 100 x PhD in Finance

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**Interest Rates and Exchange Rates**

The theory of Interest Rate Parity (IRP) provides the linkage between the foreign exchange markets and the international money markets. The theory states: The difference in the national interest rates for securities of similar risk and maturity (i$ -i€) should be equal to, but with an opposite sign, the forward rate discount or premium for the foreign currency (F-S)/S. we use the quotation $/€ here. (i$ -i€) = (F-S)/S PhD in Finance

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**Exhibit 7.5 Currency Yield Curves and the Forward Premium**

i$ isf PhD in Finance

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**Exhibit 7.6 Interest Rate Parity (IRP)**

Exchange market Exchange market PhD in Finance

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**Arbitrage opportunities**

The spot and forward exchange rates are not constantly in the state of equilibrium described by interest rate parity. When the market is not in equilibrium, the potential for risk-free arbitrage profit exists. The arbitrager will exploit the imbalance by investing in the currency that offers higher return and sell forward and realize a risk free arbitrage profit. This is known as covered interest arbitrage (CIA). PhD in Finance

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**Exhibit 7.7 Covered Interest Arbitrage (CIA)**

PhD in Finance

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**Uncovered interest arbitrage**

Uncovered interest arbitrage (UIA) is a deviation from covered interest arbitrage . In UIA, investors borrow in currencies that have relatively low interest rates and convert the proceed into currencies that offer higher interest rates. The transaction is “uncovered” because the investor does not sell the higher yielding currency proceeds forward, choosing to remain uncovered and accept the exchange rate risk at the end of the period. PhD in Finance

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**Exhibit 7.8 Uncovered Interest Arbitrage (UIA): The Yen Carry Trade**

In the yen carry trade, the investor borrows Japanese yen at relatively low interest rates, converts the proceeds to another currency such as the U.S. dollar where the funds are invested at a higher interest rate for a term period. At the end of the period, the investor exchanges the dollars back to yen to repay the loan, pocketing the difference as arbitrage profit. If the spot rate at the end of the period is roughly the same as at the start, or the yen has fallen in value against the dollar, the investor profits. If, however, the yen were to appreciate versus the dollar over the period, the investment may result in significant loss. PhD in Finance

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**Interest Rates and Exchange Rates**

The following exhibit (7,9) illustrates the equilibrium conditions 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 will close this gap in no time. PhD in Finance

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**Exhibit 7.9 Interest Rate Parity (IRP) and Equilibrium**

Exhibit 7.9 Interest Rate Parity (IRP) and Equilibrium PhD in Finance

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**Interest Rates and Exchange Rates**

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. PhD in Finance

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**Exhibit 7.10 Forward Rate as an Unbiased Predictor for Future Spot Rate**

PhD in Finance

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**Ex: International Parity Conditions**

Fundamental parity conditions (using dollar and yen). The forcasted inflation for Japan and US are 1% and 5% respectively. A 4% differential. The US interest rate is 8%, Japan 4%. The spot rate S1 is 104￥/$. The one-year forward is S1 100￥/$. The Spot rate one year from now is S2 a) Purchasing Power Parity (PPP) S2 /S1= (1+∏￥)/(1+∏$) S2=104*1,01/1,05=100￥/$ PhD in Finance

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**International Parity Conditions**

b) the Fisher Effect The nominal interest rate differential =difference in expected rate of inflation 8%-4%=-(1%-5%) c) International Fisher Effect The forcasted change in spot rate =the differential between nominal interest rates (S1-S2 ) /S2 =i$ -i￥ d) Interest Rate Parity (S1-F ) /F=i$ -i￥ PhD in Finance

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**International Parity Conditions**

e) Forward rate as an unbiased predictor . This is also called expectations theory. Combining d) and c), we have F=S2 where S2 is expected spot rate in the future. See exhibit 7.11 for the 5 parity conditions in the exchange market. PhD in Finance

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**Exhibit 7.11 International Parity Conditions in Equilibrium (Approximate Form)**

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**Exchange Rate Pass-Through**

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**Mini-Case Questions: Currency Pass-Through at Porsche**

Which do you believe is most important for sustaining the sale of the new Carrera model, maintaining a profit margin or maintaining the U.S. dollar price? Given the change in exchange rates and the strategy employed by Porsche, would you say that the purchasing power of the U.S. dollar customer has grown stronger or weaker? In the long run, what do most automobile manufacturers do to avoid these large exchange rate squeezes? PhD in Finance

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**Exhibit 1 Pass-Through Analysis for the 911 Carrera 4S Cabriolet, 2003**

PhD in Finance

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International Parity Conditions

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