International International Parity Conditions Parity Conditions

By : Madam Zakiah Hassan By : Madam Zakiah Hassan

9 February 20109 February 2010

IntroductionIntroduction

Exchange rates are influenced by interest rates and inflation rates Exchange rates are influenced by interest rates and inflation rates and together, they influence markets for exchange rates in the and together, they influence markets for exchange rates in the future, known as forward rates. future, known as forward rates.

Means that, the main determinants of exchange rates are relative Means that, the main determinants of exchange rates are relative inflation rate, interest rates, national income and political inflation rate, interest rates, national income and political stability.stability.

The linkages among these variables are called ‘parity conditions’ The linkages among these variables are called ‘parity conditions’

Parity conditions are key relationship used to predict movements in Parity conditions are key relationship used to predict movements in exchange rates. exchange rates.

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

Objective Objective

Learn how to predict foreign Learn how to predict foreign exchange rates using arbitrage exchange rates using arbitrage

arguments. arguments.

What is arbitrage What is arbitrage

Business operation involving the purchase of foreign Business operation involving the purchase of foreign exchange gold, financial securities or commodities in exchange gold, financial securities or commodities in

one market and their almost simultaneous sale in one market and their almost simultaneous sale in another market, in order to profit from price another market, in order to profit from price differentials existing between the markets. differentials existing between the markets.

Arbitrage generally tends to eliminate price differentials Arbitrage generally tends to eliminate price differentials between markets.between markets.

So, So,

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

making certain profit. making certain profit.

Structure of IPCStructure of IPC Purchasing power parity (PPP) and Law of one price Purchasing power parity (PPP) and Law of one price

(LOP)(LOP)

International Fisher Effect (IFE) International Fisher Effect (IFE)

Fisher Effect (FE)Fisher Effect (FE)

Interest Rate Parity (IRP) Interest Rate Parity (IRP)

Forward rates as unbiased predictors of future spot Forward rates as unbiased predictors of future spot rates (UFR) rates (UFR)

Diagram of Parity Conditions

Exchange Rate Forecasts

Differences in Interest Rates

InternationalFischer Effect

Differences in Inflation Rates

Forward RatePremium or

Discount

Interest Rate Parity

Fisher Effect

Purchasing Power Parity

Unbiased ForwardRate

Interrelationship between Parity Interrelationship between Parity

ConditionsConditions The four parity conditions are all inter linked. The four parity conditions are all inter linked.

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

A change in the market interest rate will then, in turn, A change in the market interest rate will then, in turn, affect the future spot rate (IFE) and the forward affect the future spot rate (IFE) and the forward market through IRP. market through IRP.

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

Purchasing power parity (PPP) and Law of one pricePurchasing power parity (PPP) and Law of one price

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

LOP states : identical goods sell for the same price worldwideLOP states : identical goods sell for the same price worldwide

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

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

Since the product is sold in different countries, the product’s Since the product is sold in different countries, the product’s price must be stated in different currency terms, but the price must be stated in different currency terms, but the price of the product should still be the same when expressed price of the product should still be the same when expressed in one common currency. in one common currency.

So, PPP states : the exchange rate So, PPP states : the exchange rate between two countries’ currencies between two countries’ currencies should be equal to the ratio of their should be equal to the ratio of their price levels. price levels.

PPP is a manifestation of the LOP PPP is a manifestation of the LOP applied internationally to a standard applied internationally to a standard commodity basket. commodity basket.

Purchasing power parity (PPP)Purchasing power parity (PPP)

(1) Absolute PPP(1) Absolute PPPGoods and services should cost the same regardless of Goods and services should cost the same regardless of

the country the country

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

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

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

Problem : difficult of getting similar basket goods for both Problem : difficult of getting similar basket goods for both countries, because due to each country’s different countries, because due to each country’s different consumption patterns. consumption patterns.

Purchasing power parity (PPP)Purchasing power parity (PPP)

(2) Relative PPP(2) Relative PPP

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

-----the exchange between HC and any FC will adjust of -----the exchange between HC and any FC will adjust of reflect changes in the price levels ( inflation) of two reflect changes in the price levels ( inflation) of two countries. countries.

PURCHASING POWER PARITYPURCHASING POWER PARITY

1.1. In mathematical terms:In mathematical terms:

wherewhere e ett = future spot rate= future spot rate

ee00 = spot rate= spot rate

iihh = home inflation= home inflation

iif f = foreign inflation= foreign inflation

tt = the time period= the time period

tf

tht

i

i

e

e

1

1

0

PURCHASING POWER PARITYPURCHASING POWER PARITY

2.2. If purchasing power parity is If purchasing power parity is expected to hold, then the expected to hold, then the

bestbestprediction for the one-periodprediction for the one-periodspot rate should bespot rate should be

tf

th

ti

iee

1

10

Example PPPExample PPPUS inflation 4%US inflation 4%

Australia inflation 8%Australia inflation 8%

Current spot is USD 0.8034 per AUD Current spot is USD 0.8034 per AUD

Answer : Answer :

Spot rate Spot rate = (1 + 0.04) / ( 1 + 0.08 ) * 0.8034 = (1 + 0.04) / ( 1 + 0.08 ) * 0.8034

= USD 0.7736 per AUD = USD 0.7736 per AUD

THE INTERNATIONAL FISHER EFFECT (IFE)THE INTERNATIONAL FISHER EFFECT (IFE)

IFE STATES:IFE STATES:

the spot rate adjusts to the interest rate the spot rate adjusts to the interest rate differential between two countries.differential between two countries.

THE INTERNATIONAL FISHER THE INTERNATIONAL FISHER EFFECTEFFECT

IFE = PPP + FEIFE = PPP + FE

tf

tht

r

r

e

e

)1(

)1(

0

EXAMPLE IFE EXAMPLE IFE

► Malaysia interest rate for 6-month Malaysia interest rate for 6-month 4%4%► Australia interest rate for 6 month Australia interest rate for 6 month 8%8%► Current spot rate is MYR2.8735/AUD Current spot rate is MYR2.8735/AUD ► What is forecast future spot rate of the MYR/AUD if What is forecast future spot rate of the MYR/AUD if

the interest rate in Australia were rise to 10% p.a? the interest rate in Australia were rise to 10% p.a?

► Future spot rate = 2.8735 [ 1 + 0.04/20] / [1 + Future spot rate = 2.8735 [ 1 + 0.04/20] / [1 + (0.1/2)] = 2.7914(0.1/2)] = 2.7914

Interest Rate Parity (IRP) Interest Rate Parity (IRP) TheoryTheory

► IRP focuses on the IRP focuses on the spotspot and and forwardforward (expected) exchange rates (expected) exchange rates withwith international international money and bond marketsmoney and bond markets..

► The parity condition implied by this theory The parity condition implied by this theory establishes the break-even condition where establishes the break-even condition where the the return on a domestic currency return on a domestic currency investment is identical with the return investment is identical with the return on a foreign currencyon a foreign currency investment covered investment covered against exchange rate riskagainst exchange rate risk

EXAMPLE OF IRP EXAMPLE OF IRP

Example : Example :

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

Spot rate USD 1.68/GBPSpot rate USD 1.68/GBP

Forward rate USD 1.6066/GBPForward rate USD 1.6066/GBP

UK interest rate 13 % p.aUK interest rate 13 % p.a

USA interest rate 8.0625% p.aUSA interest rate 8.0625% p.a

Two alternative :Two alternative :

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

Alternative 2 : Alternative 2 :

Take advantage of the higher interest rate Take advantage of the higher interest rate by investing in UK by investing in UK

Alternative 2: Alternative 2: ► Take advantage of the higher interest rate by investing Take advantage of the higher interest rate by investing

in UK in UK ► IF INVESTOR CHOOSE AT ALTERNATIVE 2, HE MUST IF INVESTOR CHOOSE AT ALTERNATIVE 2, HE MUST

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

because bankers only accept pounds. because bankers only accept pounds. USD 1 Million / 1.68 = GBP 595,238.USD 1 Million / 1.68 = GBP 595,238.

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

► Step 3 :Step 3 : Sell immediately one year forward at forward rate to Sell immediately one year forward at forward rate to get back USDget back USDGBP 672,619 X 1.6066 = USD 1,080,630.GBP 672,619 X 1.6066 = USD 1,080,630.

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

Why doing covered interest rate Why doing covered interest rate because to protect against risk that because to protect against risk that pound will depreciate in one year.pound will depreciate in one year.

UNCOVERED INTEREST RATE PARITY UNCOVERED INTEREST RATE PARITY

Example : Example : Suppose that the current one year Suppose that the current one year interest rate in the US is 9.4% and interest rate in the US is 9.4% and the UK interest rate is 11%. The spot the UK interest rate is 11%. The spot rate is USD1.5 per GBP. rate is USD1.5 per GBP.

►What is expected one year forward What is expected one year forward rate for USD/GBP? rate for USD/GBP?

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

EXPECTATION THEORY OF THE EXCHANGE EXPECTATION THEORY OF THE EXCHANGE RATE. RATE.

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

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

► The expectation theory state that The expectation theory state that forward rate forward rate approximately = the expected future spotapproximately = the expected future spot but does not means they same, because forward but does not means they same, because forward rate will, on average, over estimate and under rate will, on average, over estimate and under estimate the actual future spot rate. estimate the actual future spot rate.

► The rationale behind that is the foreign exchange The rationale behind that is the foreign exchange is reasonable efficient. is reasonable efficient.

Conclusion Conclusion

In this chapter, we learned about five parity conditions or In this chapter, we learned about five parity conditions or relationship apply to spot rates, inflation rates and interest relationship apply to spot rates, inflation rates and interest rates in different currencies: PPP, FE, IFE,IRP and forward rates in different currencies: PPP, FE, IFE,IRP and forward rates as an unbiased forecast of the future spot rate or UFR. rates as an unbiased forecast of the future spot rate or UFR.

International trade or exchange of goods and services across International trade or exchange of goods and services across borders gives rise to international settlement with borders gives rise to international settlement with payments being made in different currencies. payments being made in different currencies.

Discrepancies may arise as a consequences when the Discrepancies may arise as a consequences when the settlement is executed in one currency as against the other settlement is executed in one currency as against the other currency. Moreover, economic conditions and changes in currency. Moreover, economic conditions and changes in economic conditions in different countries may take effect economic conditions in different countries may take effect on the value of goods measured in different currencies and on the value of goods measured in different currencies and the relative values and opportunity costs of these the relative values and opportunity costs of these currencies. currencies.

International parities are important since they establish International parities are important since they establish relative currency values and their evolution in terms of relative currency values and their evolution in terms of economic circumstances and cross broader arbitrage economic circumstances and cross broader arbitrage may be possible when they are violated. may be possible when they are violated.