International Parity Conditions

8Chapter

6B. 1

Major International Finance Theories

The objective of International Finance theories is to understand how and why, in a system of free markets and flexible exchange rates, currencies strive to move toward equilibrium.

These theories define the relationship between exchange rates (current spot, future spot, and forward), inflation, and nominal interest rate movements.

6B. 2

Parity Objectives

To explain the concept of interest rate parity (IRP), and how parity condition prevents foreign exchange arbitrage opportunities.

To explain Purchasing Power Parity (PPP) and International Fisher Effect (IFE) theories, and their implications on exchange rate changes; and

To compare and show linkage between PPP, IFE, and Interest Rate Parity (IRP) theories.

6B. 3

1. Interest Rate Parity (IRP) Theorem

According to IRP, at equilibrium, the forward rate of a foreign currency will differ (in %) from the current spot rate by an amount that will equal the interest rate differential (in%) between the home and foreign country.

6B. 4

Interest Rate Parity (IRP)

• As a result of market forces, the forward rate differs from the spot rate by an amount that sufficiently offsets the interest rate differential between two currencies.

• Then, covered interest arbitrage is no longer feasible, and the equilibrium state achieved is referred to as interest rate parity (IRP).

6B. 5

Derivation of IRP

• When IRP exists, the rate of return achieved from covered interest arbitrage should equal the rate of return available in the home country.

• End-value of a $1 investment in covered interest arbitrage = (1/S)× (1+iF)×F

= (1/S)× (1+iF)× [S× (1+p)]= (1+iF)× (1+p)

where p is the forward premium.

6B. 6

Derivation of IRP

• End-value of a $1 investment in the home country = 1 + iH

• Equating the two and rearranging terms:

(1+iF)× (1+p) = 1 + iH

p = (1+iH) – 1(1+iF)

i.e.

forward = (1 + home interest rate) – 1premium (1 + foreign interest rate)

6B. 7

Determining the Forward Premium

Example

• Suppose 6-month ipeso = 6%, i$ = 5%.

• From the U.S. investor’s perspective,forward premium = (1.05/1.06) – 1 ≈ - .0094

• If spot rate, S = $.10/peso, then6-month forward rate = S × (1 + p)

≈ .10 × (1 _

.0094)

≈ $.09906/peso

6B. 8

Determining the Forward Premium

• The IRP relationship can be rewritten as follows:

F – S = S(1+p) – S = p = (1+iH) – 1 = (iH–iF)

S S (1+iF) (1+iF)

• The approximated form, p ≈ iH – iF, provides a reasonable estimate when the interest rate differential is small.

6B. 9

Graphic Analysis of Interest Rate Parity

IRP line

Interest Rate Differential (%)home interest rate – foreign interest rate

ForwardPremium of FC(%)

ForwardDiscount of FC (%)

-2

-4

2

4

1 3-1-3

A

B

W

X

Y

Z

6B. 10

Graphic Analysis of Interest Rate Parity

Interest Rate Differential (%)home interest rate – foreign interest rate

ForwardPremium of FC (%)

ForwardDiscount of FC (%)

-2

-4

2

4

1 3-1-3

IRP line

Zone of potential covered interest

arbitrage by local investors

Zone of potential covered interest

arbitrage by foreign investors

6B. 11

Test for the Existence of IRP

• To test whether IRP exists, collect actual interest rate differentials (assets of similar risk and maturity) and forward premiums/discounts for various currencies, and plot them on a graph.

• IRP holds when covered interest arbitrage is not possible or worthwhile.

6B. 12

Interpretation of IRP

• When IRP exists, it does not mean that both local and foreign investors will earn the same returns.

• What it means is that investors cannot use covered interest arbitrage to achieve higher returns than those achievable in their respective home countries.

6B. 13

Does IRP Hold?

Forward RatePremiums andInterest Rate

Differentials forSeven Currencies

6B. 14

Does IRP Hold?

• Various empirical studies indicate that IRP generally holds.

• While there are deviations from IRP, they are often not large enough to make covered interest arbitrage worthwhile.

• This is due to the characteristics of foreign investments, such as transaction costs, political risk, and differential tax laws.

6B. 15

Considerations When Assessing IRP

Transaction Costs

iH – iF

p

Zone of potential covered interest

arbitrage by foreign investors Zone of

potential covered interest

arbitrage by local

investors

IRP line

Zone where covered interest arbitrage is not feasible due to

transaction costs

6B. 16

Considerations When Assessing IRP

Political Risk• A crisis in a country could cause its government to

restrict capital outflow and impose exchange controls (exchange of the local currency for reserve currencies).

• Investors may also perceive a higher default risk on foreign investments.

Differential Tax Laws• If tax laws vary, after-tax returns should be

considered instead of before-tax returns.

6B. 17

Changes in Forward Premiums

6B. 18

PPP and IFE Theories

• Purchasing Power Parity (PPP): At equilibrium, the future spot rate of a foreign currency will differ (in %) from the current spot rate by an amount that equals (in %) the inflation differential between the home and foreign countries.

• International Fisher Effect (IFE): At equilibrium, the future spot rate of a foreign currency will differ (in %) from the current spot rate by an amount that equals (in %) the nominal interest rate differential between the home and foreign countries

6B. 19

2. Purchasing Power Parity (PPP)

• When a country’s inflation rate rises relative to that of another country, decreased exports and increased imports depress the high-inflation country’s currency because of worsening trade and current account balances.

• Purchasing Power Parity (PPP) theory attempts to quantify this inflation – exchange rate relationship.

6B. 20

Interpretations of PPP

• The absolute form of PPP is an extension of the law of one price. It suggests that the prices of the same products in different countries should be equal when measured in a common currency.

• The relative form of PPP accounts for market distortions like transportation costs, labor costs, tariffs, taxes, and quotas. It states that the rate of price changes should be similar.

6B. 21

Rationale behind PPP Theory

Suppose U.S. inflation > U.K. inflation.⇒ ↑ U.S. imports from U.K. and

↓ U.S. exports to U.K., and U.S. current account ↓⇒ Downward pressure (depreciation) is placed on the $

This shift in consumption and the $’s depreciation will continue until

in the U.S.: priceU.K. goods ≥ priceU.S. goods

in the U.K.: priceU.S. goods ≤ priceU.K. goods

6B. 22

Derivation of PPP

Assume that PPP holds. Over time, as inflation occurs exchange rates adjusts to maintain PPP:Ph1 Ph0 (1 + Ih )Where Ph1=home country’s price index, year-1 end

Ih =home country’s inflation rate for the yearPf1 Pf0 (1 + If ) (1 + ef )

where Pf = foreign country’s price indexIf = foreign country’s inflation rateef = foreign currency’s % ∆ in value

6B. 23

Derivation of PPPIf PPP holds ⇒ Ph1 = Pf1 and

Ph0 (1 + Ih ) = Pf0 (1 + If ) (1 + ef )

Solving for ef = (1 + Ih ) – 1(1 + If )

Ih > If ⇒ ef > 0 i.e. foreign currency appreciatesIh < If ⇒ ef < 0 i.e. foreign currency depreciates

Example: Suppose IU.S. = 9% and IU.K. = 5% .

Then e£ = (1 + .09 ) – 1 = 3.81%(1 + .05 )

6B. 24

Simplified PPP Relationship

When the inflation differential is small, the PPP relationship can be simplified as

ef ≅ Ih – If

Example: Suppose IU.S. = 9% and IU.K. = 5% . Then e£ ≅ 9 – 5 = 4%

U.S. consumers: ∆ PU.S. = IU.S. = 9%∆ PU.K. = IU.K. + e£ = 9%

U.K. consumers: ∆ PU.K. = IU.K. = 5%∆ PU.S. = IU.S. – e£ = 5%

6B. 25

Graphic Analysis of Purchasing Power Parity

PPP line

Inflation Rate Differential (%)home inflation rate – foreign inflation rate

% ∆ in the foreign

currency’s spot rate-2

-4

2

4

1 3-1-3

Increased purchasing

power of foreign goods

Decreased purchasing

power of foreign goods

A

B

C

D

6B. 26

Testing the PPP Theory

Conceptual Test

• Plot actual inflation differentials and spot exchange rate changes for two or more countries on a graph.

• If the points deviate significantly from the PPP line over time, then PPP does not hold.

6B. 27

Testing the PPP Theory

Statistical Test

• Apply regression analysis to historical exchange rates and inflation differentials:

ef = a0 + a1 [ (1+Ih)/(1+If) – 1 ] + µ• Then apply t-tests to the regression coefficients. (Test

for a0 = 0 and a1 = 1.)

• If any coefficient differs significantly from what was expected, PPP does not hold.

6B. 28

Testing the PPP Theory

• Empirical studies indicate that the relationship between inflation differentials and exchange rates is not perfect even in the long run.

• However, the use of inflation differentials to forecast long-run movements in exchange rates is supported.

A limitation in the tests is that the choice of the base period will affect the result.

6B. 29

Why PPP Does Not Occur

PPP does not occur consistently due to:

confounding effects• Exchange rates are also affected by differences in

inflation, interest rates, income levels, government controls and expectations of future rates.

a lack of substitutes for some non traded goods

6B. 30

PPP in the Long Run

• PPP can be tested by assessing a “real” exchange rate over time (e.g., crawling pegs).

• The real exchange rate is the actual exchange rate adjusted for inflationary effects in the two countries of concern.

• If the real exchange rate follows a random walk, it cannot be viewed as being a constant in the long run. Then PPP does not hold.

6B. 31

The Big Mac Index

The Big Mac Index was invented by The Economist in 1986 as a lighthearted guide to whether currencies are at their “correct” level. It is based on the theory of purchasing-power parity (PPP), the notion that in the long run exchange rates should move towards the rate that would equalize the prices of an identical basket of goods and services (in this case, a burger) in any two countries. For example, the average price of a Big Mac in America in July 2017 was $5.30; in China it was only $2.92 at market exchange rates. So the "raw" Big Mac index says that the yuan was undervalued by some 45% at that time. http://www.economist.com/content/big-mac-index

6B. 32

3. International Fisher Effect (IFE)

• According to the Fisher Effect, nominal risk-free interest rates contain a real rate of return and anticipated inflation

in = ir + inflation• If all investors require the same real return on

assets of similar risk and maturity, then differentials in interest rates may be due to differentials in expected inflation.

• Recall that PPP theory suggests that exchange rate movements are caused by inflation rate differentials.

6B. 33

International Fisher Effect (IFE)

• The International Fisher Effect (IFE) theory suggests that currencies with higher interest rates will depreciate because the higher nominal rates reflect higher expected inflation.

• Hence, investors hoping to capitalize on a higher foreign interest rate should earn a return no higher than what they would have earned domestically.

6B. 34

International Fisher Effect (IFE)

InvestorsResiding in

Japan

U.S.

Canada

JapanU.S.Canada

JapanU.S.Canada

JapanU.S.Canada

Attempt toInvest in Ih

333

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111111

%

If

36

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%

ef

0– 3– 8

30

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850

%

if

58

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%

Return inHome

Currency

555

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131313

%

Ih

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RealReturnEarned

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6B. 35

Derivation of the IFE

• According to the IFE, E(rf ), the expected effective return on a foreign money market investment, should equal rh , the effective return on a domestic investment.

• rf = (1 + if ) (1 + ef ) – 1if = interest rate in the foreign countryef = % change in the foreign currency’s

value

• rh =ih = interest rate in the home country

6B. 36

Derivation of the IFE

• Setting rf = rh : (1 + if ) (1 + ef ) – 1 = ih

• Solving for ef : ef = (1 + ih ) _ 1(1 + if )

• ih > if ⇒ ef > 0 i.e. foreign currency appreciates ih < if ⇒ ef< 0 i.e. foreign currency depreciates

Example: Suppose iU.S. = 11% and iU.K. = 12% .

Then eU.K. = (1 + .11 ) – 1 = –.89% .(1 + .12 )

This will make rf = rh .

6B. 37

Derivation of the IFE

• When the interest rate differential is small, the IFE relationship can be simplified as

ef ≅ ih _ if• If the British rate on 6-month deposits were

2% above the U.S. interest rate, the £ should depreciate by approximately 2% over 6 months. Then U.S. investors would earn about the same return on British deposits as they would on U.S. deposits.

6B. 38

Graphic Analysis of the International Fisher Effect

6B. 39

Tests of the IFE

• If actual interest rates and exchange rate changes are plotted over time on a graph, we can see whether the points are evenly scattered on both sides of the IFE line.

• Empirical studies indicate that the IFE theory holds during some time frames. However, there is also evidence that it does not hold consistently.

6B. 40

Tests of the International Fisher Effect

6B. 41

Tests of the IFE

• To test the IFE statistically, apply regression analysis to historical exchange rates and nominal interest rate differentials:

• ef = a0 + a1 [ (1+ih)/(1+if) – 1 ] + µ• Then apply t-tests to the regression coefficients.

(Test for a0 = 0 and a1 = 1.)

• IFE does not hold if any coefficient differs significantly from what was expected.

6B. 42

Why the IFE Does Not Occur

• Since the IFE is based on PPP, it will not hold when PPP does not hold.

• In particular, if there are factors other than inflation that affect exchange rates, exchange rates may not adjust in accordance with the inflation differential.

6B. 43

Comparison of the IRP, PPP, and IFE Theories

Exchange RateExpectations

Inflation RateDifferential

Forward RateDiscount or Premium

Interest RateDifferential

PurchasingPower Parity (PPP)

Interest Rate Parity(IRP)

FisherEffect

InternationalFisher Effect (IFE)

6B. 44

Comparison of the IRP, PPP, and IFE Theories

Interest rate parityForward rate premium pInterest rate differential ih – if

( )( ) fh

f

h iiiip −≅−

++

= 111

Purchasing power parity% ∆ in spot exchange rate efInflation rate differential Ih – If

( )( ) fh

f

hf II

IIe −≅−

++

= 111

International Fisher effect% ∆ in spot exchange rate efInterest rate differential ih – if

( )( ) fh

f

hf ii

iie −≅−

++

= 111

6B. 45