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# International Finance - HKUST HomePage Search

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International Finance - HKUST HomePage Search

International Finance Dr. Angela Ng

FINA 342 HKUST

Class Notes 5

INTERNATIONAL PARITY CONDITION I:

I. THE LAW OF ONE PRICE

Example: Cars in France and U.K.

Suppose that a student in Paris dreams of owning a red

convertible Mercedes. Flipping through the newspaper, he

dealers:

Cost of Mercedes in Paris = FF200,000

Cost of Mercedes in London = ?50,000

The currency paper of a French newspaper reveals:

FF/? spot rate = 3.00

He also spots an ad from the brand-new Chunnel company on

a special offer providing free rides from Paris to London for

university students.

Where should the student buy the car?

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The Law of One Price

In a perfect capital market (i.e. no transaction costs, no taxes,

and complete certainty) setting, homogeneous goods will sell

for the same price in two markets, taking the exchange rate

into account.

Thus, in perfect capital markets, two securities that have

identical cash flows must have the same price.

Does the law of one price hold in the above example for cars?

The law is enforced by speculation when prices are uncertain

and by arbitrage when prices are certain.

Pure or riskless arbitrage is defined as a profitable position

obtained with (1) no net investment and (2) no risk.

Purchasing Power Parity (PPP) is a simple model of the

determination of exchange rates based on the law of one price

applied to the general price level of the two countries. In

relatively efficient markets, the price of a basket of goods

should be the same in each market.

Motivations

Useful benchmark model to determine where the exchange

rate “ought to be” or where it may return in the “long run”.

PPP deviations (sometimes referred to as real exchange rate

fluctuations) affect the competitive position of most

companies.

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Example: Caterpillar an automobile company in the U.S.

Caterpillar Tractor’s main competitor in the domestic market during the 1980s was Komatsu of Japan, and its operating results were dramatically affected by fluctuations in the exchange rate. See Exhibit 5.1.

Note that the exchange rate fell from ?250/\$ in 1984 to ?123/\$ by the end of 1987. How did the competitive position of Komatsu evolve because of the exchange rate fluctuation?

Assumptions:

Free trade with no costs, tariffs, quotas, etc.

Theory

Formally, absolute PPP states that the nominal exchange

money to the external purchasing power of the money.

How do we measure the purchasing power of a dollar (i.e.

the value of the dollar in terms of general goods) internally

within the U.S.?

What is the external purchasing power of a dollar in

Britain?

Suppose that the internal purchasing power of the dollar is

less than its external purchasing power. What could you do

to make a profit?

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In symbols, absolute PPP states:

usfSP/PAmerican terms (S = \$/FC): ttt

fusSP/PEuropean terms (S = FC/\$): ttt

Example: The world price of gold

\$Suppose: P = \$500/oz in New York

DM P = DM800/oz in Berlin

What is the exchange rate implied by the absolute PPP?

An overvalued currency’s external purchasing power is greater

than its internal purchasing power. An undervalued currency’s

power.

If the Japanese yen is undervalued (on foreign exchange

markets) relative to the U.S. dollar, what prediction would you

make regarding the movement of the exchange rate of ?/\$ if a

correction back to PPP is imminent?

Empirical evidence: See Exhibits 5.2 & 5.3 for the DM/\$ and

\$/?.

A medium rare guide to whether exchange rates are trading at

the right exchange rates, can be found in the Economist’s Big

Mac index. (see Exhibit 5.4)

What is the result of the survey?

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Explanations for the failure of PPP

Transaction costs

When transaction costs are present, arbitrage will not take

place to take advantage of a deviation from parity unless the

absolute magnitude of the deviation is greater than the

transaction costs involved in undertaking the arbitrage.

Thus, with transaction costs, arbitrage only restricts the

deviation from PPP to with a band defined by the

transaction costs, and this band can be quite wide.

Example: The world price of gold

A New York dealer quotes: \$500/oz bid and \$501/oz ask.

Spot exchange rate: \$0.625/DM

What would be the comparable DM bid and ask prices of

gold that a dealer in Berlin would quote?

Taxes

Tariffs or duties reduce the effective amount of funds

available for arbitrage by an amount equal to one minus the

tariff rate. A tax of this type will widen the neutral band

within which no profitable arbitrage opportunities are

available.

Uncertainty

When uncertainty enters, the calculation of the incentive to

buy domestic or foreign goods is subject to errors and risks.

Risk-averse arbitrageurs will seek greater profit to

compensate for these risks, thus leading to a widen neutral

band around PPP exchange rates.

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Noncompetitive markets

Lack of homogeneity

III. TRIANGULAR ARBITRAGE

Example: Arbitrage between different quotes

Bank A’s quote: HK\$0.060/? – HK\$0.063/?

Bank B’s quote: HK\$0.064/? – HK\$0.066/?

How could one make an arbitrage profit?

d/ee/ff/d Cross-Rate or Triangular Equilibrium: SSS = 1

If this relation does not hold (within the bounds of transaction costs), then there is an opportunity to lock in a riskless arbitrage profit.

d/ee/ff/dd/ee/ff/dIf SSS < 1, then S, S and/or S must increase.

Buy the currency in the denominator with the currency in

the numerator of each spot rate.

d/ee/ff/dd/ee/ff/dIf SSS > 1, then S, S and/or S must fall.

Sell the currency in the denominator for the currency in the

numerator of each spot rate.

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HK\$/US\$ Example: S = HK\$7.75/US\$

US\$/? S = US\$0.01/?

?/HK\$ S = ?13.05/HK\$

How can one make a riskless arbitrage profit?

REAL EXCHANGE RATES

The real exchange rate is defined to be the nominal exchange

rate (here, in American terms as dollars per foreign currency)

adjusted for the price levels in the two countries. Hence, the

real exchange rate is given by

fP\$/FCtXStt usPt

What is the unit of the real exchange rate?

The real exchange rate would be equal to one if absolute PPP

held. Similarly, if absolute PPP is violated, the real exchange

rate fluctuates.

What are the real appreciations and real depreciations of

currencies? How do they relate to a country’s

competitiveness?

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What leads to a depreciation of the U.S. real exchange rate?

A change in the nominal exchange rate can be just offset by

differences in inflation rates leaving the real exchange rate

unchanged. This phenomenon is called Relative Purchasing

Power Parity. It is a weak version of purchasing power parity.

If the factors that cause deviation of the absolute PPP are

relatively constant over time, relative PPP should still hold.

In symbols, according to relative PPP:

Xt;11x0 t;1Xt

where the lowercase letter indicates “percentage change” of

the uppercase letter.

The change in the real exchange rate is the change in the

\$/FCfSPt;1t;1

us\$/FCfXP(1;s)(1;p)t;1t;1t;1t;1\$/FCfus SPX(1;p)tttt;1

usPt

where, for example, p = (P - P)/P. t+1t+1tt

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Definition: P = consumer price index at time t t

p(PP)/P Inflation: ttt1t1

Thus, consumer price at time t depends on inflation during the t intervening periods as: t?

;PP(1p)t0 ??1?

A simple version of Relative PPP

Relative PPP holds whenever inflation differentials get compensated by exchange rate changes, i.e.

\$/FCusfspp

This is only approximately correct, because s ( ln(1+s) and

p ( ln(1+p).

If PPP is true, then currencies with higher rates of inflation should devalue relative to currencies with lower rates of inflation.

This is because goods can flow from a low inflation country to a high inflation country through international trade. Thus the currency of a country with lower inflation should appreciate.

One can simply use logarithms to compute percentage changes in which case the above equation holds exactly:

FCfus\$/((((XSPPtttt~)~)~)~)ln0lnlnln; FCfus\$/~)~)~)~)XSPP0000????????

or

FCususust\$/SPP(1;p)tt0 FCffft\$/SPP(1;p)t00 usfwhere p and p are the geometric mean inflation rates.

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Example:

Assume that the real exchange rate between the U.S. and Japan is initially one. Now, the dollar appreciates relative to the yen by 5%. In addition, there is 10% inflation in Japan, 3% inflation in the U.S. Is there a real exchange rate appreciation or depreciation of the dollar? What is the percentage change in the real exchange rate of the dollar relative to the yen?

E[P] = expected consumer price index at time t t

Using the same equation, we can make forecasts of future exchange rates.

The expected change in the spot exchange rate should reflect the difference in inflation between two currencies, i.e.

\$/FC\$/FCusfusfE[P/P]/(P/P)E[S]/S = t0tt00

ususff(E[P]/P)/(E[P]/P) = t0t0

ttusf((1;E[p]))/((1;E[p])) = 11ustft(1;E[p])/(1;E[p]) =

usfwhere p and p are the geometric mean inflation rates.

The relative PPP states that the expected appreciation or depreciation of the spot exchange rate is determined by the mean expected inflation over the period.

This relation only holds over the long run. (See Exhibit 5.5)

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