FINANCE Chapter.03

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AJAFIN 6605-03

Parity Conditions In International Finance

Outline:* International Arbitrage and the Law of One Price

* Excess Money Supply Growth and Inflation

* The Neutrality of Money* Inflation and Domestic Currency Depreciation

Nominal Interest Rates and Real Interest Rates

International Arbitrage: The Covered Interest Arbitrage Parity Conditions: IRP, FRP, PPP, FE & GFE, and IFE.

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Parity Conditions in International Finance

These are economic theories linking exchange

rates, price levels, and interest rates.

International Arbitrage and the Law of One Price

In a competitive market characterized by:

i. Many buyers

ii. Many sellers

iii. Cost-less access to information

iv. Lack of government controls

v. Free transportation 2


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The price of an identical tradable good and

financial asset must be equalized.

This is the law of one price

All goods and financial assets obey the law of one

price or, equivalently, free trade will equalize the

price of an identical product in all countries.

This law is enforced by the international

arbitragers who follow the dictum of buy low"and "sell high" to generate profits forthemselves.

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Certain key theoretical economic relationships

result from arbitrage activities, namely:

Interest Rate Parity (IRP)

Forward Rate Parity (FRP)

Purchasing Power Parity (PPP)

Fisher Equation (FE) & GFE

International Fisher Equation (IFE)

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These relationships explain the links between prices, spot

exchange rates, interest rates, and forward exchange rates.

Underlying these parity conditions is the adjustment of

various rates and prices to inflation.

Modern monetary theory posits that an expansion of the

money supply in excess of real output results in a logical

outcome of inflation.

While this view is not universally subscribed to, it has a

solid microeconomic foundation.

The basic precept of price theory is that as the supply

of product A increases relative to others, the price of

product A must decrease relative to others.

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Extraordinary verifications of this theory abound.

The German hyperinflation (1920-23) and thelessons thereof.Inflation peaked at 200 billion percent in 1923.

In 1922, Germanys highest currency denominationwas 50,000 mark.

By 1923, the highest denomination was100,000,000,000,000 mark.

In December of 1923 one US dollar was equal to

4,000,000,000,000 marks!.

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The Bolivian hyperinflation (1985).

In the spring 1985 Bolivian hyperinflation was

running at over 100,000% per year.The government revenue covered only 15% ofspending while the rest was paid for by printing pesocurrency notes.

The government fell.Spending cuts were introduced.Excessive Peso printing stopped.Inflation returned to 0% that same year.

Greece, in the mid 1940s with 8.55 billionpercent per month.

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Yugoslavia, 1993 (500 billion dinar for a gallon of milk!)

Yugoslavias Central Bank introduced a 500 billion

dinar bank note around Christmas 1993.

It marked another milestone in the countrys descent

into economic chaos.

In November 1993, inflation topped 600,000 %.

In 1992, the U.S dollar was worth 1,000 dinar.By Christmas 1993, it took 180 trillion of the same

1,000 dinar notes to equal one dollar!

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Hungary about the 1940s at 4.19 quintillion

(1 plus 18 zeros) percent per month.

Zimbabwe (Aug. 2008). Facing inflation of about 50million percent per year, Zimbabwe's Reserve Bank

knocked 10 zeros off its hyper-inflated currency.

10 billion old Z$ note becomes one new Z$1 note.

100 billion new Z$ note introduced (still not enough to

buy a loaf of bread!). Gasoline coupon used for currency.

In Jan 09, Zimbabwe rolled out Z$100tr note $33

The widespread use of fiat money created the possibility

of hyperinflation as governments often print large

amounts of money, without actual market demand, to

finance spending. 9


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Inflation causes a transfer of wealth: It benefits:

-- the asset-rich at the expense of the asset-poor

-- debtors at the expense of creditors-- non-savers at the expense of savers

It results in less total wealth within the economy than

would have been in its absence.

Deflation is a decrease in the general price level over

a period of time.

It is the opposite of inflation.With deflation, the demand for liquidity goes up, in

preference to goods or interest.

The purchasing power of money increases.10


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For consumers, deflation is a delight because the purchasing

power of money increases with time.

Consumers are encouraged to delay their purchases until the

future when the goods they wish to buy will be cheaper.

Deflation depresses consumption, leading to lower national

income which further decreases consumptionthe vicious

cycle continues. Depressed profits for firms translates to less income for

households and this in turn means less income to spend on

goods and services and decline in investment by firms.

Deflation is bad for borrowers. The debt continues to growthe real value of money owed increases.

Nominal interest rate may be zero, but real rate may be

several percentage points higher since inflation is negative.11


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Economic values measured in current dollars are

termed nominal while those measured in constant

(adjusted) dollars are termed real.

The relationship between real and nominal is given

by: Real = nominal/deflator.

The deflator adjusts for inflation.Common deflators are:

CPI = Consumer price index based on market

basket of consumer goods. PPI = Producer price index based on prices of

inputs (labor and capital)

GDP deflator: takes into account all components of GDP.

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Another link in the money supply growth, inflation,

interest rates, and exchange rates, is the notion of the

neutrality of money" i.e., money should have no

impact on real variables, such as output, employment

and interest rates.

For example, if money supply (Ms) should increaseby 10% relative to money demand (Md), then prices

should increase by 10%.

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Inflation and Currency Depreciation

The international analogue to inflation is the

depreciation of domestic currency.

Inflation results in a change in the exchange rate

between domestic currency and domestic goods.

Whereas domestic currency depreciation results in a

change in the exchange rate between domestic

currency and foreign goods.

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If international arbitrage enforces the law of oneprice, then the change in the exchange ratebetween domestic currency and domestic goods

(inflation) must equal the change in the exchangerate between domestic currency and foreign goods.

Therefore if $1.00 buys a loaf of bread in the U.S.,

it should buy the same loaf in Japan, the U.K., orelsewhere.

For this to happen, foreign exchange rate must

change by the difference between domestic andforeign rates of inflation.

The theory of Purchasing Power Parity (PPP)espousesthis notion.

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Nominal and Real Interest Rates:

The nominal interest rate is the price quoted on

lending and borrowing transactions. It determines the exchange rate between current and

future dollars.But the Fisher Equation and International Fisher Equation

emphasize what really matters, i.e., the exchange ratebetween current and future purchasing power as measuredby the real interest rate.

Lenders are concerned about how many more goodscan be obtained in the future by foregoingconsumption today and borrowers are concernedabout how much of future consumption must be givenup, or sacrificed, for today's consumption to be paid

for with future earnings. 17


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Consequently, if exchange rate between current

and future goods (the real interest rate) varies from

one country to another, arbitrage activities (in theform of capital flows) will tend to equalize the real

interest rate across countries.

Arbitrage can be defined as "The process ofbuying or selling a good or an asset in order to

exploit a price differential so as to make a riskless

profit."

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Covered Interest Arbitrage (CIA):

CIA is a profit seeking activity that takes advantage

of differences in domestic and foreign interest rates inthe presence of forward exchange markets.

Suppose a U.S. investor decides to capitalize on a

relatively higher British interest rates.The spot exchange rate is known and there exists aforward market.

The only uncertainty is the future spot exchange rate.A forward sale can be used to lock-in the rate at whichpounds could be exchanged for dollars.

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Algebraically,

Let A = Amount to be invested, e.g. $1

S = Spot exchange rate (direct)ius = U.S. interest rate

F = Forward exchange rate

iuk= U.K. interest rate

Comparing what can be earned at home with

what is possible through CIA we have:

1(1+ius) vs 1/S(1+iuk)F Then arbitrage profit (AP) is given by:

AP = 1/S(1+iuk)F(1+ius)21


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CIA will be profitable if AP > 0. However, marketforces resulting from CIA will cause a pricerealignments so that excess profits from arbitrage are

no longer possible.

For example, as $s are used to purchase s in the spotmarket, S increases, netting fewer s.

The forward sale of s puts a downward pressure onthe forward rate F, netting fewer $s.

In addition, as U.S. investors transfer funds to the U.K.,there will be a decrease in iuk and an increase in ius

As a result of market forces from CIA a relationshipexists between the forward rate premium(discount) andthe interest rate differentials.

This is the subject matter ofInterest Rate Parity Theory.22


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Arbitrage between the two investments (the domestic and theforeign) results in parity so that,

or (1)

(2)

Subtracting 1 from both LHS and RHS gives:

(3)

where (1 + iUK) = 1 (approximately.), assuming small values of iUK.

Equation 3 indicates that the interest rate differential between acomparable U.S. and U.K. investment is equal to the forwardpremium (discount) on the pound.

S

)Fi+(1

=i+1

UK

US

1 + i

1 + i

=F

S

US

UK

S

S-Fi-i ukus

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Examples:

(1) Spot $/C$ = .80

90 day fwd $/C$ = .79

90 day iCan = 4%

90 day iUS = 2.5% .

(2) Spot $/ = 1.50

90- day fwd rate = 1.4550

90- day ius = 3%

90- day iuk= 4%.

Show whether or not IRP holds

Find the yield to a U.S. investor who executes a CIA.

Explain the direction of flow and compute arbitrage profits

Find the 90-day fwd rate on C$ () if IRP holds. 25


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Solution (1)

For parity, forward rate on C$ rate is given by:

from which F = .78846

The currency of the country with a lower interest rate shouldbe at a forward premium with respect to the currency of the

higher interest rate country.The interest rate differential should be approximately equal tothe forward rate differential (premium or discount) when

parity exists.

(SEE APPENDIX I)

77 .02=1-1.02=1-)(1.04)(.79.80

1=CIAYield

1

.80

(1.04)F = 1.025

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Interpret points A,B,X,Y.

In reality the IRP line is a band because transactioncosts arising from the spread on spot and forwardcontracts and brokerage fees on security purchasesand sales cause effective yields to be lower thannominal yields.

Note that if IRP exists, it does not mean that domesticand foreign investors earn the same return.

Rather existence of IRP means that investors cannotuse covered interest arbitrage to achieve higherreturns than those possible at home.

Effective returns are equalized for domestic investors ifIRP holds regardless of where they invest - domestic or

foreign market. 27

i i i


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Empirical Evidence

It is difficult to get quotations that reflect the same pointin time for interest rates and the forward rates.

Nevertheless IRP theory is well supported empirically ininternational finance literature.

In the Euro-Currency markets the forward rate is

frequently calculated from interest rate differencialbetween two countries using the no arbitrage condition.

The Eurocurrency markets are relatively unregulated.Deviations from IRP occur due to capital controls,taxes, transaction costs, political risks etc.

Note that "default risks" could exit on loan contracts forwhich IRP is supposed to apply.

This would create deviation from parity. 28


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The forward exchange rate must be equal to theexpected future spot exchange rate at maturity otherwiserisk-less arbitrage will take place.

One may argue whether the forward rate should be equal

the expected future spot rate or whether there is apremium incorporated in the forward rate that serves asreward for bearing risk in which case the forward woulddiffer from the expected future spot by this premium.

Empirical work typically focuses on whether the fwdrate is an unbiased predicator of future spot rate.

An unbiased predictor is one that is correct on average:

it is equally likely to guess too high or guess too low.

Forward Rate Parity (FRP)(The forward rate is an unbiased predictor of future spot rate)

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Pressure from the forward market is transmitted into thespot market and vice-versa.

Equilibrium is achieved only when the forward differential

equals the expected change in the future exchange rate (Append II)

At I, parity prevails as an expected 2% depreciation of thePound is matched by a 2% discount on the Pound.

Point J is a position of dis-equilibrium because a 3%forward discount on the Pound is more than offset by a4% expected depreciation of the Pound.

Speculators are expected to sell pound forward and replenish or

cover their commitments with 4% fewer units of domesticcurrency (short sale). Points L, X, K are also in disequilibrium.

Formally we can state that the forward rate is an unbiasedpredictor of future spot or that the forward differential

equalsthe expected change in exchange rates as follows:30


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S0 Sn

|------------------------------------|

t = 0 t = nFn

Speculative efficiency hypothesis: Ft = E[St]

(4)

iscount)][Premium(D

al)Differenti(Forward

Rate)Exchangein

Change(Expected

S

S-F

S

S-SOR

F

S

o

on

o

on

nn

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Empirical Evidence There are pros and cons for the notion that the forward rate is

an unbiased predictor of the future spot.

It is probably unrealistic to expect a perfect correlationbetween forward rates and the realized future spot rates since

future spot rates are influenced by events that cannot be

perfectly forecast.

The rationale for the hypothesis that the fwd rate is unbiased is

that the foreign exchange market is reasonably efficient (semi-

strong form).

The forward market can be said to be efficient if the forwardrate ruling at anytime is equal to the rational expectation of the

future spot when the contract matures, plus the risk premium

that speculators require to in order to compensate them for the

additional risk that they bear in the forward market. 32


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Questions for Discussion.

Under what conditions would the forward rate be a

biased predictor of future spot?

What should be expected to happen?

Currencies trading at a forward premium are expected toappreciate while currencies trading at a forward discount

are expected to depreciate.

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Empirical Verifications (A method)

Consider,

Ft,n = forward rate at n+t

St+n = spot rate at time n+t

Then,

St+n = a0 + b0Ft,n + Ut (5)

The null hypothesis: a0 = 0 ; b0 = 1

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If th ll h th i t b j t d th f d t i


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If the null hypothesis cannot be rejected, the forward rate is anunbiased predictor of the future spot rate.However, movements in the spot are expected to be dominatedby a trend.

Therefore the above equation may produce high R2

, or low DWstatistic. There is also the danger of spurious regression if theseries are not stationary. The level of forward rate will explain ahigh percentage of the variations in the level of future spot. Thisrelationship may be spurious if the series are not stationary. Butchanges in the spot rate about its trend are likely to be nearlyrandom so that,

(6)

is likely to produce a low R2 - i.e., the forward premium (ordiscount) will explain a low percentage of the variation of thechanges in the spot rates.

If the null hypotheses a1 = 0, b1 = 1 cannot be rejected, we canconclude that the forward premium or discount is an unbiased

predictor of changes in the exchange rates.

t+n

t

1 1t,n

t

t

S

S= a + b

F

S+

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The Purchasing Power Parity (PPP)

The PPP was first stated by Gustav Cassel (1918).

He used it as a basis for a new set of official exchangerates at the end of World War I so that normal trade

relations might resume among nations.

The Absolute Form: The PPP states that equilibriumexchange rate between the domestic and the foreign

currencies equals the ratio between the domestic and

foreign price levels.

The absolute PPP postulates that perfect commodity

arbitrage [in the absence of transaction or information

cost of other restrictions] ensures that PPP relationship

holds at each point in time. 36


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Algebraically, given: St = et = exchange rate at time t

Pd, Pf= aggregate price level for domestic and foreign, then:

7(a)

OR

7(b)

t

d

fe =P

P

dt

fP = e P

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This means that:

The general level of prices, when converted to a

common currency will be the same in every country.

In other words, a unit of domestic currency shouldcommand the same purchasing power around the world.

This theory rests on the law of one price which states

that free trade will equalize the price of any good (or

asset) in all countries.

The theory however assumes away transportation

cost, tariffs, quotas, product differentiation, and other

restrictions. 38

Th R l i V i i f l d i l


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The Relative Version: more meaningful and practical.

It moves from levels to changes in exchange rates given

relative price innovations. It states that:

In comparison to a period when equilibrium rates

prevailed, changes in the ratio of domestic and foreign

prices will indicate the necessary adjustment between

domestic and the foreign currencies.

Given that: S0 = e0 and St = et

= domestic currency units per unit of a foreign currency at 0,t.

Pod, Pof = initial aggregate price levels respectively for

domestic and foreign.

Ptd, Pt

f = aggregate price levels at time t respectively for

domestic and foreign.39


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Formally:

(8)

where P0d, P0

f, Ptd, Pt

fare price indices.

Letting,

Ptd / Po

d = 1 + d ; d = Domestic inflation ratePt

f / Pof = 1 + f; f= Foreign inflation rate

P/P

P/P=P/P

P/P=e

ef0

d0

ft

dt

f0

ft

d0

dtt

o

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then,

So that,

and (9)

assuming that 1 + f 1, for low values off .

1-+1

+1=1-

e

e

+1

+1=

e

e

f

d

0

t

f

d

0

t

fdf

fd

0

0t -+1

-=e

e-e

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E i (9) h h l i ( d)


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Equation (9) states that the relative (expected)

exchange rate change for two currencies between

t1

and t2

should equal the relative change in price

indices of the two countries between t1 and t2.

For parity in the purchasing power of two

currencies to obtain over a period of time, the rateof change of the exchange rate must equal the rate

of change of relative prices. (See Appendix III)

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At A i fl ti diff ti l ff t b di


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At A or inflation differentials are offset by corresponding

foreign currency appreciation or depreciation.

At A, there exists a 3% more domestic inflation.

This is matched by a 3% increase in exchange rate (a 3%depreciation of domestic currency).

At B, 1% more f is matched by 1% reduction in ex (d/f).

At D, f> d by 3%, but exchange rate (d/f) has reduced by

only 1%. This means that domestic residents have a reduced

purchasing power on the foreign goods. They therefore reduce

their purchase of foreign goods but foreigners continue to

purchase domestic goods. Foreign currency depreciates in

value so that D approaches the PPP line.

Similarly at C, d > f by 2% but ex (d/f) has risen by only

1%. There is a higher PP on foreign goods for domestic

residents. 43

N t th t if h i i l h t f ll


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Note that if changes in nominal exchange rates are fully

offset by relative price level changes between two

countries, then the real exchange rates remains unchanged.

Alternatively, a change in the real exchange rate isequivalent to a deviation from PPP.

Algebraically:

Let Real Exchange Rate = RERt then,

= BP,

us

uk

uk

us

t

d

t+1

+1

BP

$=

)

+1

BP(

)+1

$(

+1

BP+1

$

=RER

)+(1

)+(1e=RER d

ft

t

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But by PPP,

(10)

This means that there are no real changes in e fromt = 0 to t = t, if PPP holds.

If PPP holds then real return on an identical asset isequalized for investors worldwide.

t0

d

fe =e (1 + )

(1 + )

RER =e (1 + )

(1 + )

(1 + )

(1 + )= et

0d

f

f

d 0

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Empirical Evidence


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Empirical Evidence

Relative PPP holds fairly in the long-run especially in highinflation countries. The PPP does not hold consistently for

many reasons:01. Other factors maybe at work

02. No substitute for traded goods

03. Existence of internationally non-traded goods in the national

price indexes.04. Changes in Taste

05. Technological Progress

06. Differently constructed price indexes

07. Different "Market Baskets"08. Different weighing formula for Market Basket

09. Relative price changes (vs. changes in general price level)

10. The "best" index cannot be a basis for a perfect representation

of theoretical parity. 46

E i i l V ifi ti


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Empirical Verifications

Recent empirical tests focus on the L-R behavior of theRER (regarded as a measure of deviations from PPP)

Examples:

Joseph Whilt [RWK (1991) article #24] reports thatinflation adjusted exchange rates (= RER) do not follow a

random, but instead returns, over time, to some L-Requilibrium level posited by PPP.

Richard Roll (1979), Jacob Frenkel (1981), Michael Adler& Bruce Lehmann (1983), and others are unable to rejectthe hypothesis that the RER follows a RW.

If RER follows a RW, no L-R equilibrium exists to whichthe rate tends to return, so that PPP can no longer serve as agauge of L-R exchange equilibrium. So PPP does not hold.

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Other studies Cumby & Obstfeld (1984) Jeffrey Frankel


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Other studies - Cumby & Obstfeld (1984), Jeffrey Frankel(1985), John Huizinga (1987) have been able to reject theRW hypothesis for RER in some instances. (equil. Level exists)

However, Hakkio (1984, 1986) is also unable to reject theRW hypothesis.He demonstrates that, if in fact, the RER differs modestlyfrom a RW, standard tests are very likely to favor the RW

even if it is false! So tests may be the problem.

Sims (1988) proposes a new statistical test that isespecially sensitive in determining whether a variable is a

true RW or whether the variable returns to its equilibriumlevel after a long-lag.

More recent developments: Cointegration and errorcorrection models.

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A Test of PPP


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A Test of PPP

The exchange rate can be expressed as:

et

= ao

+ a1

(Pt

- Pt

*) + Ut

where et , Pt , Pt* are in logs.

and a0, a1 can be estimated in a regression equation

with monthly, quarterly, or annual data on et, P

t, P

t*.

However problems exist here!

Direction of causality?

Estimated residuals, Ut, always exhibit severe positive

autocorrelation.

If residuals are autocorrelated, the estimated std. errors ofcoefficient will be biased downwards!

The usual fix is to difference the data. 49

That means: Construct Z = X - X thus shifting the


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That means: Construct Zt = Xt - Xt-1, thus shifting thefocus to changes in the (natural log of) original series Xtrather than (natural log of) the levels. Thus:

et - et -1 = a1 [(Pt - Pt-1) - (Pt* - Pt -1*)] + Ut - Ut-1or

et = a1 ( Pt - Pt *) + Zt ,where Zt is iid (inde. and identically distr.)

Another problem: PPP is an "equality"relationship not "causal".

Empirical evidence shows as much impact of exchangerates on prices as of prices on exchange rates.

The usefulness of PPP, however, depends on existenceof a lag between price level changes and exchange rateschanges.

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D d ll V C t P h I fl ti


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Demand-pull Vs Cost Push Inflation

The cost-push view of inflation relates inflation rate

to factors such as changes in wage rate, andproductivity gains (compared to Demand-pull which

views inflation as a monetary phenomenon).

A synthesis is possible so that,ex = f( in wage rates, in productivity gains,

in price levels)Economies with relatively stable wage rates andhigher productivity gains more than the US, for

example, will experience currency appreciation

against the US dollar.51

O h I Ab PPP


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Other Issues About PPP

Is the PPP expected to hold in the S-R and L-R?

Too many market imperfections exist in the S-R thatallow S-R deviations from parity.

In certain circumstances, the PPP might serve as an

indicator of L-R equilibrium relationship among

currencies.

New econometric designs may improve tests of PPP

e.g. Cointegration & error correction models.

The selection of the reference currency (country) maybe critical.

Differential speed of adjustment between financial

prices (very fast) and goods prices (relatively slow).52

In general a validity for PPP (the necessary


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In general, a validity for PPP (the necessary

condition) can be established by showing that the

series et, Ptd, Pt

f, share a common LR equilibrium

relationship - i.e. they are bound in a LR equalrelationship. (that means that the series are

cointergrated)

PPP is important because it is the centerpiece of manyexchange rate models and also because ofitspolicyimplications.

It provides a benchmark exchange rate for policy

makers and exchange rate arbitragers.

Check significance of coefficients, explanatory

power, and residuals. 53


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The U.S.

Dollar

Price of a

Big Mac

around the

world in

May 2004

54

Th Fi h E ti


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The Fisher Equation:

There is a distinction between the real and nominalinterest rates.

The nominal interest rate is the rate quoted or observedin the market.

The real rate measures the return after adjusting for

inflation.

The real rate is the rate at which current goods are beingconverted into future goods.

It is the net increase in wealth that people expect toachieve when they save and invest their current income.

It is the added future consumption promised by aborrower to a lender.

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Si i t ll ll fi i l t t t t d i


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Since virtually all financial contracts are stated innominal terms, nominal interest rates will tend toincorporate inflation expectation in order to provide

lenders with a real return.The Fisher Equation (named after Irving Fisher) statesthat the nominal interest rate, i, is made up of a realrequired rate of return, r and inflation premium (the

expected rate of inflation),This equation is given by (Approx)

(11)

+ri 56

The exact relationship is given by:


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The exact relationship is given by:

1 + i = (1 + r) ( 1 + )

= 1 + + r + r

and, i r + , if r 0

Thus an increase in will tend to increase i.

Example: If r = 3% and = 5%, find the:

exact nominal rate:

i = r + +r = .03+.05+ (.03)(.05) = .08+.0015 = 8.15%

approximate nominal rate

i r + =.03+.05 = 8%

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I h U S f l h h f ll i


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In the U.S. for example, we have the following

experiences:

In the 1950's and the 60's low inflation rates were

accompanied by low nominal rates.

In the 1970's and 80's high inflation rates wereaccompanied by high nominal rates.

In the 90's the experience was low inflation rates

with low interest rates!

So far in the 20s, the experience has been

historically low inflation with low interest rates!58

The Generalized Fisher Equation (GFE)


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The Generalized Fisher Equation (GFE)

This theory asserts that real returns are equalized across

countries through arbitrage.

If rd > rfcapital inflows will ensue and continue until rd = rf.

Hence if we express the FE for both domestic (d) and foreign (f)

countries, we have:

id rd + dif rf + f

And if rd = rf then,

(12)

This is the Generalized Fisher Equation.

It asserts that "the nominal interest rates, id and if , differ solely

by expected inflation differential.

(SEE APPENDIX IV)

fdfd -i-i

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At C there is equilibrium A 2% increase in f is offset by


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At C, there is equilibrium. A 2% increase in fis offset by

a 2% increase in if .

At D, there is a 5% increase in ifbut only 3% increase infwhich implies that real return is higher in foreign

country.

Funds should flow from domestic to foreign country to

take advantage of this real difference until expected realreturns are equalized.

Empirical evidence tends to support this hypothesis if we

ignore the effects of tax differences, government controls,political risks, and risk premia.

60

We can summarize the link between interest, inflation,


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We can summarize the link between interest, inflation,

and exchange rates by combining the Interest Rate Parity

and the Generalized Fisher Equation, so that,

(13)

i.e., real interest rates are equalized across countries when

the Fisher Equation and Interest Rate Parity hold andnominal interest rates differ by expected inflation

differential between domestic and foreign.

In the real world, the above inter-relationship are

determined simultaneously because interest rates,

inflation expectation, and exchange rates are jointly

affected by the arrival of new information (events).

S

S-F-i-ifd

fd

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Alternatively we can combine PPP and GFE as follows:


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Alternatively, we can combine PPP and GFE as follows:

(15)

(16)

Combining (15) and (16) we have:

(17)

(17) states that the spot exchange rates will change inaccordance with the difference in interest rates (on

comparable securities) between countries.Hence the return on foreign uncovered money marketsecurities will, on an average, be no higher than return ondomestic money market securities from the point of view of

a domestic resident (and vice versa).

fd

0

0t -e

e-e:PPP

fdfd -i-i:GFE

d ft 0

0i - i

e - e

e

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This notion can be expressed as:


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p

or

which reduces to (17). That is UIRP holds.

IFE states that arbitrage between financial markets in the form

of capital flows should ensure that id - if is an unbiased

predictor of the expected change in spot exchange rates

between domestic and foreign currencies; or that spot

exchange rate should change to adjust for differences in

nominal interest rates between two countries. (SEE APPENDIX V) NOTE: A carry trade (in which the investor borrows in low interest currency and invests in high

interest currency) is profitable on average. (e.g. Japanese carry trade) Most often, the estimated slope

coefficient is negative, meaning that the currency with the higher interest rate tends to appreciate.

This is a classic case of empirical rejection of UIRP.

1 + i =1

e(1 + i )ed

0

f t

t

0

d

f

e

e=

1 + i

1 + i

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At E, if > id by 3%, foreign currency depreciates by


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At E, if idby 3%, foreign currency depreciates by

3% to offset the interest difference so that parity holds.

At F parity also obtains as a 2% higher domesticinterest is offset by a 2% increase in exchange rates.

Points along IFE reflect exchange rates adjusting to offset

interest rate differentials.

Points below the IFE line implies an increase in return on

foreign assets owned by domestic investors.

Points above the IFE line implies a reduction in return on

foreign assets owned by domestic investors.

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When a parity condition fails to hold, the structure


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When a parity condition fails to hold, the structure

of international financial markets may influence

investors strategy of borrowing, investing, hedging,

speculating, or making investment location decisions.

If absolute PPP does not hold, sellers have the power

to price discriminate across countries and buyers have

incentives to overcome barriers to access lower costgoods.

If IRP does not hold, the cost of borrowing or return

on investment (with forward cover) differs depending

on which currency is used therefore it is possible

to find superior investment or lower cost funds

without incurring foreign exchange risk.

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FINANCE Chapter.03

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