# Chapter 6

International Parity Conditions

### International Parity Conditions

• Some fundamental questions 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 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.

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### Prices and Exchange Rates

• 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

.

### Prices and Exchange Rates

• 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 ¥ Where the product price in US dollars is (P \$ ), the spot exchange rate is (S) and the price in Yen is (P ¥ ).

### Prices and Exchange Rates

• If the law of one price were true for all goods and services, the purchasing power parity (PPP) exchange rate could be found from any individual set of prices.

• By comparing the prices of identical products denominated in different currencies, we could determine the “real” or PPP exchange rate that should exist if markets were efficient.

• This is the

absolute version

of the PPP theory.

Exhibit 6.2

P -6 -5 -4 -3 -2 -1 -1 -2 -3 -4

4 3 2 1

Percent change in the spot exchange rate for foreign currency

1 2 3 4 5 6

Percent difference in expected rates of inflation (foreign relative to home country)

6-6

### Prices and Exchange Rates

• If the assumptions of the absolute version of the PPP theory are relaxed a bit more, we observe what is termed

(RPPP).

• RPPP holds that PPP is not particularly helpful in determining what the spot rate is 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.

### 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

.

### Prices and Exchange Rates

• 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 6-9 Copyright © 2004 Pearson Addison-Wesley. All rights reserved.

### Prices and Exchange Rates

• Individual national currencies often need to be evaluated against 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

.

180 160 140 120 Exhibit 6.3

IMF’s Real Effective Exchange Rate Indexes for the United States & Japan (1995 = 100)

United States Japan 100 80 60 40 20 0 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 Source: International Financial Statistics, International Monetary Fund, monthly, 1995=100.

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### Prices and Exchange Rates

• The degree to which the prices of imported and exported goods change as a result of exchange rate changes is termed

pass-through

.

• Although PPP implies that all exchange rate changes are passed through by equivalent changes in prices to trading partners, empirical research 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 compartmentalize or absorb the impact of exchange rate changes.

• Price elasticity of demand is an important factor when determining pass-through levels.

### Interest Rates and Exchange Rates

• 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 = r + π Where i = nominal interest rate, r = real interest rate and π = 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).

### Interest Rates and Exchange Rates

• 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.

### Interest Rates and Exchange Rates

• More formally: S 1 – S 2 S 2 x 100 = i \$ - i ¥ • Where i \$ and i ¥ are the respective national interest rates and S is the spot exchange rate using indirect quotes (¥/\$) .

• Justification for the international Fisher effect is that investors must be rewarded or penalized to offset the expected change in exchange rates.

### Interest Rates and Exchange Rates

• A

forward rate

is an exchange rate quoted for settlement at some future date.

• A forward exchange agreement between currencies states the rate of exchange at which a foreign currency will be

bought forward

or

sold forward

at a specific date in the future.

### Interest Rates and Exchange Rates

• 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 (F (S SF franc deposit rate (i SF ) over the 90-day eurodollar deposit rate (i \$ ).

### Interest Rates and Exchange Rates

• Formulaic representation of the forward rate: F SF/\$ 90 = S SF/\$ x [1 + (i SF x 90/360)] [1 + (i \$ x 90/360)] 6-18 Copyright © 2004 Pearson Addison-Wesley. All rights reserved.

### Interest Rates and Exchange Rates

• 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 Forward x 360 days x 100 • This is the case when the foreign currency price of the home currency is used (SF/\$). Copyright © 2004 Pearson Addison-Wesley. All rights reserved.

6-19

### 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:

transaction costs.

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

Exhibit 6.5

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 % 30

60

Forward premium is the percentage difference of 3.96%

Euro Swiss franc yield curve 90 120

Days Forward

150 Eurodollar yield curve 180

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Exhibit 6.6

Interest Rate Parity (IRP)

i \$ = 8.00 % per annum (2.00 % per 90 days)

Start

\$1,000,000 x 1.02

Dollar money market End

\$1,020,000 \$1,019,993 * S = SF 1.4800/\$ 90 days F 90 = SF 1.4655/\$ SF 1,480,000

Swiss franc money market

x 1.01

SF 1,494,800 i SF = 4.00 % per annum (1.00 % per 90 days)

Note that the Swiss franc investment yields \$1,019,993, \$7 less on a \$1 million investment.

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### Interest Rates and Exchange Rates

• 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).

Exhibit 6.7

Covered Interest Arbitrage (CIA)

Start

\$1,000,000 Eurodollar rate = 8.00 % per annum x 1.04

Dollar money market End

\$1,040,000 \$1,044,638 Arbitrage Potential S =¥ 106.00/\$ 180 days F 180 = ¥ 103.50/\$ ¥ 106,000,000

Yen money market

x 1.02

Euroyen rate = 4.00 % per annum ¥ 108,120,000

6-24

### Interest Rates and Exchange Rates

• 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.

Exhibit 6.8

Uncovered Interest Arbitrage (UIA): The Yen Carry Trade

Start

¥ 10,000,000 Investors borrow yen at 0.40% per annum x 1.004

Japanese yen money market End

¥ 10,040,000 Repay ¥ 10,500,000 Earn ¥ 460,000 Profit S =¥ 120.00/\$ 360 days S 360 = ¥ 120.00/\$ \$ 83,333,333

US dollar money market

x 1.05

\$ 87,500,000 Invest dollars at 5.00% per annum 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. 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.

6-26

### Interest Rates and Exchange Rates

• 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.

Exhibit 6.9

Interest Rate Parity (IRP) and Equilibrium

-6 -5 -4 -3 -2 -1 -1 -2 -3

Percent difference between foreign (¥) and domestic (\$) interest rates

-4

4 3 2 1 1 2 3

Percentage premium on foreign currency (¥)

4.83

4 5 6 X Y Z U

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Exhibit 6.11

International Parity Conditions in Equilibrium (Approximate Form)

Forward rate as an unbiased predictor

( E ) Forecast change in spot exchange rate + 4 %

( A ) Forward premium on foreign currency + 4 %

(yen strengthens) Interest rate parity

( D )

International Fisher Effect

( C ) Difference in nominal interest rates - 4 %

(less in Japan)

Forecast difference in rates of inflation - 4 %

(less in Japan) Fisher effect

( B )

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### Interest Rates and Exchange Rates

• 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.