international parity conditions 9 feb 2010

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International Parity

ConditionsBy : Madam Zakiah Hassan

9 February 2010


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Introduction

Exchange rates are influenced by interest rates and inflation rates

and together, they influence markets for exchange rates in thefuture, known as forward rates.

Means that, the main determinants of exchange rates are relativeinflation rate, interest rates, national income and political

stability.

The linkages among these variables are called parity conditions

Parity conditions are key relationship used to predict movements inexchange rates.

Since arbitrage plays a critical role in this discussion, we shoulddefine it upfront.


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Objective

Learn how to predict foreign exchangerates using arbitrage arguments.


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What is arbitrage

Business operation involving the purchase of foreign exchange

gold, financial securities or commodities in one market andtheir almost simultaneous sale in another market, in order toprofit from price differentials existing between the markets.

Arbitrage generally tends to eliminate price differentials betweenmarkets.

So,

the act of simultaneously buying and selling the same orequivalent assets or commodities for the purpose of making

certain profit.


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Structure of IPCPurchasing power parity (PPP) and Law of one price (LOP)

International Fisher Effect (IFE)

Fisher Effect (FE)

Interest Rate Parity (IRP)

Forward rates as unbiased predictors of future spot rates

(UFR)


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Diagram of Parity Conditions

Exchange Rate Forecasts

Differences in Interest Rates

InternationalFischer Effect

Differences inInflation Rates

Forward RatePremium or

Discount

Interest RateParity

Fisher Effect

Purchasing Power

Parity

Unbiased

Forward

Rate


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Interrelationship between Parity Conditions

The four parity conditions are all inter linked.

A change in price level ( inflation rate ) in the commoditymarket will affect the market interest rate.

A change in the market interest rate will then, in turn, affectthe future spot rate (IFE) and the forward market throughIRP.

The four main theoretical relationship among the S, F, P (inf),and I are shown in previous graph.


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Purchasing power parity (PPP) and Law of one price

PPP is based on law of one price (LOP) and the no arbitrage condition.

LOP states : identical goods sell for the same price worldwide

Stated that in the absence of transportation cost, taxes and otherrestrictions, meanwhile the price of a product stated in a commoncurrency such as USD should be the same in every country.

This means same product, same price in one common currency.

Since the product is sold in different countries, the products pricemust be stated in different currency terms, but the price of the

product should still be the same when expressed in one commoncurrency.


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So, PPP states : the exchange rate betweentwo countries currencies should be equal tothe ratio of their price levels.

PPP is a manifestation of the LOP appliedinternationally to a standard commoditybasket.


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Purchasing power parity (PPP)

(1) Absolute PPP

Goods and services should cost the same regardless of the

country

This simply requires replacing a single product with a price index.

Example : if the price index in USD is the price of basket of goodsin the US and a price index in AUD is the price of a similarbasket of goods in Australia, then :

Price index USD = Price index AUD ( spot USD/AUD)

Problem : difficult of getting similar basket goods for bothcountries, because due to each countrys different consumptionpatterns.


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Purchasing power parity (PPP)

(2) Relative PPP

The exchange rate is expected to adjust in order to reflectexpected relative differences in purchasing power.

-----the exchange between HC and any FC will adjust of reflect

changes in the price levels ( inflation) of two countries.


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PURCHASING POWER PARITY

1. In mathematical terms:

where et = future spot rate

e0 = spot rate

ih = home inflationif = foreign inflation

t = the time period

t

f

t

ht

i

i

e

e

1

1

0


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PURCHASING POWER PARITY

2. If purchasing power parity is

expected to hold, then the best

prediction for the one-periodspot rate should be

tf

t

ht

iiee

11

0


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THE INTERNATIONAL FISHER EFFECT (IFE)

IFE STATES:

the spot rate adjusts to the interest rate differentialbetween two countries.


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THE INTERNATIONAL FISHEREFFECT

IFE = PPP + FE

tf

t

ht

r

r

e

e

)1(

)1(

0


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EXAMPLE IFE

Malaysia interest rate for 6-month 4%

Australia interest rate for 6 month 8%

Current spot rate is MYR2.8735/AUD

What is forecast future spot rate of the MYR/AUD if theinterest rate in Australia were rise to 10% p.a?

Future spot rate = 2.8735 [ 1 + 0.04/20] / [1 + (0.1/2)] =

2.7914


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Interest Rate Parity (IRP)Theory

IRP focuses on the spotand forward(expected) exchange rates with internationalmoney and bond markets.

The parity condition implied by this theoryestablishes the break-even condition where thereturn on a domestic currency investment isidentical with the return on a foreign

currency investment covered against exchangerate risk


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EXAMPLE OF IRP

Example :

Assume that American has USD 1 M to invest either in the UKor USA given the following information:

Spot rate USD 1.68/GBP

Forward rate USD 1.6066/GBP

UK interest rate 13 % p.a

USA interest rate 8.0625% p.a


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Two alternative :

Alternative 1 : invest in USA & get USD1,080,625 after one year ( 1M X 1.080625)

Alternative 2 :

Take advantage of the higher interest rate byinvesting in UK


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Alternative 2:

Take advantage of the higher interest rate by investing in UK

IF INVESTOR CHOOSE AT ALTERNATIVE 2, HE MUST

PERFORM THE FOLLOWING STEPS: Step 1: Convert USD 1 Million into pounds at spot rate because

bankers only accept pounds.

USD 1 Million / 1.68 = GBP 595,238.

Step 2 : Invest GBP 595,238 at 13% after one year.GBP 595,238 X 1.13 = GBP 672,619

Step 3 :

Sell immediately one year forward at forward rate to get backUSD

GBP 672,619 X 1.6066 = USD 1,080,630.

Arbitrage profit = USD 1 M USD 1,080,630 = USD 80,630


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Why doing covered interest rate because toprotect against risk that pound will

depreciate in one year.


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UNCOVERED INTEREST RATE PARITY

Example :

Suppose that the current one year interestrate in the US is 9.4% and the UK interestrate is 11%. The spot rate is USD1.5 perGBP.

What is expected one year forward ratefor USD/GBP?

[ 1 + 0.094] / [1 + 0.11] = f / s

[ 1 + 0.094] / [1 + 0.11] = f / 1.5So one year USD/GBP = 1.478


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EXPECTATION THEORY OF THE EXCHANGE RATE.

Theory seeks to answer the question: is the forwardrate an accurate forecast of future spot rate?

Actually investor want to know whether the forwardrate is an unbiased predictor of the future spot rate.

The expectation theory state that forward rateapproximately = the expected future spot butdoes not means they same, because forward ratewill, on average, over estimate and under estimatethe actual future spot rate.

The rationale behind that is the foreign exchange isreasonable efficient.


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Conclusion

In this chapter, we learned about five parity conditions orrelationship apply to spot rates, inflation rates and interest

rates in different currencies: PPP, FE, IFE,IRP and forwardrates as an unbiased forecast of the future spot rate orUFR.

International trade or exchange of goods and services acrossborders gives rise to international settlement withpayments being made in different currencies.

Discrepancies may arise as a consequences when thesettlement is executed in one currency as against the othercurrency. Moreover, economic conditions and changes ineconomic conditions in different countries may take effecton the value of goods measured in different currencies andthe relative values and opportunity costs of thesecurrencies.

International parities are important since they establish relative


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International parities are important since they establish relativecurrency values and their evolution in terms of economiccircumstances and cross broader arbitrage may be possiblewhen they are violated.

international parity conditions 9 feb 2010

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