# international parity parity objectives to explain the concept of interest rate parity (irp), and how

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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) – 1 premium (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, then 6-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

Forward Premium of FC(%)

Forward Discount 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

Forward Premium of FC (%)

Forward Discount 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 Rate Premiums and Interest Rate

Differentials for Seven 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 year Pf1 Pf0 (1 + If ) (1 + ef )

where Pf = foreign country’s price index If = foreign country’s inflation rate ef = foreign currency’s % ∆ in value

6B. 23

Derivation of PPP If 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 appreciates Ih < 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