1. International Parity Conditions
Chapter 6
International Parity Conditions

2. 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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3. 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.
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4. 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¥).
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5. 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.
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6. Exhibit 6.2 Purchasing Power Parity (PPP)
PPP line
Percent change in the spot exchange
rate for foreign currency 4 P 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1
Percent difference in
expected rates of inflation
(foreign relative to
home country) -2 -3 -4
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7. 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 relative purchasing power parity (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.
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8. 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.
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9. 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
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10. 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.
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11. Exhibit 6.3 IMF’s Real Effective Exchange Rate Indexes for the United States & Japan (1995 = 100)
Source: International Financial Statistics, International Monetary Fund, monthly, 1995=100.
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12. 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.
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13. 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).
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14. 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.
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15. Interest Rates and Exchange Rates
More formally:
S1 – S2
Where i$ and i¥ are the respective national interest rates and S is the spot exchange rate using indirect quotes (¥/$).
Justification for the international Fisher effect is that investors must be rewarded or penalized to offset the expected change in exchange rates. S2
x 100 = i$ - i¥
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16. 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.
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17. 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 (FSF/$90) is found by multiplying the current spot rate (SSF/$) by the ratio of the 90-day euro-Swiss franc deposit rate (iSF) over the 90-day eurodollar deposit rate (i$).
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18. Interest Rates and Exchange Rates
Formulaic representation of the forward rate:
FSF/$90 = SSF/$ x [1 + (iSF x 90/360)]
[1 + (i$ x 90/360)]
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19. 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
This is the case when the foreign currency price of the home currency is used (SF/$).
360 x x
100
Forward
days
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20. 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 should be equal to, but opposite in sign to, the forward rate discount or premium for the foreign currency, except for transaction costs.
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21. Exhibit 6.5 Currency Yield Curves & The Forward Premium
Interest
yield
Eurodollar
yield curve
10.0 %
9.0 %
8.0 %
7.0 %
Forward premium is the
percentage difference of 3.96%
6.0 %
5.0 %
Euro Swiss franc
yield curve
4.0 %
3.0 %
2.0 %
1.0 % 30 60 90
120
150
180
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Days Forward

22. Exhibit 6.6 Interest Rate Parity (IRP)
i $ = 8.00 % per annum
(2.00 % per 90 days)
Start
End
$1,000,000
x 1.02
$1,020,000
$1,019,993*
Dollar money market
90 days
S = SF /$
F90 = SF /$
Swiss franc money market
SF 1,480,000
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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23. 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).
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24. Eurodollar rate = 8.00 % per annum Euroyen rate = 4.00 % per annum
Exhibit 6.7 Covered Interest Arbitrage (CIA)
Eurodollar rate = 8.00 % per annum
Start
End
$1,000,000
x 1.04
$1,040,000
$1,044,638
Arbitrage
Potential
Dollar money market
180 days
S =¥ /$
F180 = ¥ /$
Yen money market
¥ 106,000,000
x 1.02
¥ 108,120,000
Euroyen rate = 4.00 % per annum
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25. 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.
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26. Exhibit 6.8 Uncovered Interest Arbitrage (UIA): The Yen Carry Trade
Investors borrow yen at 0.40% per annum
Start
End
¥ 10,000,000 x
¥ 10,040,000 Repay
¥ 10,500,000 Earn
¥ ,000 Profit
Japanese yen money market
360 days
S =¥ /$
S360 = ¥ /$
US dollar money market
$ 83,333,333
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.

27. 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.
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28. Exhibit 6.9 Interest Rate Parity (IRP) and Equilibrium4 3 2
Percentage premium on
foreign currency (¥) 1
4.83 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3
Percent difference between foreign (¥)
and domestic ($) interest rates X U -4 Y Z
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29. Exhibit 6.11 International Parity Conditions in Equilibrium (Approximate Form)
Forecast change in
spot exchange rate
+ 4 %
(yen strengthens)
Forward rate
as an unbiased
predictor
( E )
Purchasing
power
parity
( A )
Forward premium
on foreign currency
+ 4 %
(yen strengthens)
Forecast difference
in rates of inflation
- 4 %
(less in Japan)
International
Fisher Effect
( C )
Interest
rate
parity
( D )
Difference in nominal
interest rates
- 4 %
(less in Japan)
Fisher
effect
( B )

30. 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.
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31. Exhibit 6.10 Forward Rate as an Unbiased Predictor for Future Spot Rate
Exchange rate
t 2
t 3
t 4
t 1 S2 F2
Error F3 S1
Error
Error F1 S3 S4
Time
t 2
t 3
t 4
t 1
The forward rate available today (Ft,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 St2 is F1; the actual spot
rate turns out to be S2. 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.
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