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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:

    PURCHASING POWER PARITY

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

    finds advertisements from both English and French car

    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?

     1

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.

II. ABSOLUTE PURCHASING POWER PARITY

     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.

     2

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.

All goods are traded goods.

Theory

     Formally, absolute PPP states that the nominal exchange

    rate adjusts to equate the internal purchasing power of a

    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?

     3

     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

    external purchasing power is less than its internal purchasing

    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.

     5

Noncompetitive markets

Lack of homogeneity

Nontraded goods

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.

     6

    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?

IV. RELATIVE PURCHASING POWER PARITY

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?

     7

RELATIVE PURCHASING POWER PARITY

     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

    relative cost of a consumption basket abroad versus at home:

    $/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

     8

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.

     9

     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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