yinghong.chen@liu.se PhD in Finance

Multinational business financecourse 723g33

International Parity Conditions

ESM chapter 7

7-1

List of CONCEPTS Introduction to Parity Conditions Absolute & Relative Purchasing Power Parity Real Exchange Rate Fisher Effect (FE) International Fisher Effect (IFE) Unbiased Forward Rate (UFR) Interest Rate Parity (IRP) Covered Interest Arbitrage

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International Parity ConditionsManagers of multinational firms, international investors, importers and exporters, and government officials must deal with these fundamental issues:

What are the relationship between exchange rate, interest rate and inflation?

Are changes in exchange rates predictable?

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International Parity ConditionsThe economic theories that link

exchange rates, price levels, and interest rates together are called international parity conditions.

These international parity conditions form the core of the exchange rate theory.

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International Parity Conditions

The derivation of these conditions requires the assumption of Perfect Capital Markets (PCM). no transaction costs no taxes complete certainty in interest rate

NOTE – Parity Conditions are expected to hold in the long-run, but not always in the short term. Interest rate parity generally holds where forward differential equals to the interest rate differential of two currencies.

The Law of one price:

If the identical product or service can be:sold in two different markets; and

no restrictions exist on the sale; and

transportation costs of moving the product between markets do not exist, or trivial, then

the product’s price should be the same in both markets.

This is called the law of one price.

Prices and Exchange RatesA primary principle of competitive markets is

that prices will equalize across markets if frictions (transportation costs) do not exist.

That is:P$ x S = P¥ or S= P¥ / P$

Where the product price in US dollars is (P$), the spot exchange rate is (S) and the price in Yen is (P¥).

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Exhibit 7.1 Selected Rates from the Big Mac Index

Absolute PPP theory Law of one price should hold for a basket of

identical goods and services in different currencies.

By comparing the prices of identical products denominated in different currencies, we could determine the PPP exchange rate that should exist if markets were efficient.

S ¥/$= ∑P¥/ ∑P$

Note that Big Mac index is potentially misleading but fun to know.

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Relative purchasing power parity If the exchange rate between two

currencies starts in equilibrium, then, we have what is termed Relative purchasing power parity (RPPP).

Definition of RPPP:

the relative change in prices between two countries over a period of time determines the change in the exchange rate over that period. This is RPPP.

Note: πD is demestic price change (inflation), πF is foreign price change. We use sometimes P for price level changes!

St is future spot rate. St-1 is the spot rate. 7-10

F

FD

t

tt

S

SS

11

1

Prices and Exchange RatesMore specifically, with regard to RPPP:

“If the spot exchange rate between two countries starts in equilibrium, any change in the differential rate of inflation between them tends to be offset over the long run by an equal but opposite change in the spot exchange rate.”

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Exhibit 7.2 Relative Purchasing Power Parity (RPPP)

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%∆S

%∆P

Relative PPP Example Given yearly inflation rates of 5% and 10% in

Australia and the UK respectively, what is the prediction of PPP with regards to $A/£ exchange rate?

= (0.05 – 0.10)/(1 + 0.10) = - 0.045 = - 4.5%We expect £ to trade at a discount of 4,5% at the end of 1

year.The general implication of relative PPP is that countries with high rates of inflation will see their currencies depreciate against those with low rates of inflation.

F

FD

t

tt

S

SS

11

1Relative PPP

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Relative PPP Relative PPP implies that the change in the

exchange rate will offset the difference between the relative inflation of two countries.

The previous formula can be approximated as:

where, πD and πF refers to the percentage change in domestic and foreign price levels respectively and s % to the percentage change in the exchange rate.

If domestic inflation > foreign inflation, PPP predicts the domestic currency should depreciate. Ceteris paribus.

FDs %

15

Relative Purchasing Power Parity

Applications of Relative PPP:

1. Forecasting future spot exchange rates.

2. Calculating appreciation in “real” exchange rates. This will provide a measure of how expensive a country’s goods have become (relative to another country’s).

Prices and Exchange Rates RPPP is not accurate in predicting future

exchange rates. Two general conclusions can be made from

empirical tests: RPPP holds well over the very long run but

poorly for shorter time periods; the theory holds better for countries with

relatively high rates of inflation and underdeveloped capital markets.

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Relative Purchasing Power Parity

Relative PPP claims that exchange rate movements should exactly offset any inflation differential between two countries:

Relative PPP:F

D

1

1

S

SD/Ft

D/F1t

We can also write:F

D

1

1SS D/F

tPPP

1t

Percentage change in domestic prices

F

FD

1S

SSD/Ft

D/Ft

D/F1t

Forecasting Future Spot Rates Suppose the spot exchange rate and

expected inflation rates are:

What is the expected ¥/$ exchange rate if relative PPP holds?

Answer:

2% 5%;$;/¥90S ..t0¥/$, JapanSU

$/¥43.8705.1

02.1$/¥90

1

1

$

¥0,/¥1$,/¥

tSPPP

t SS

Relative Purchasing Power Parity The objective is to discover whether a

nation’s exchange rate is “overvalued” or “undervalued” in terms of RPPP.

This problem is often dealt with through the calculation of exchange rate indices such as the nominal effective exchange rate index.

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Exhibit 7.3 IMF’s Real Effective Exchange Rate Indexes for the United States, Japan, and the Euro Area

Prices and Exchange RatesIncomplete exchange rate pass-through

is one of the reasons that a country’s Real effective exchange rate index can deviate from the exchange rate

For example, a car manufacturer may or may not adjust pricing of its cars sold in a foreign country if exchange rates alter the manufacturer’s cost structure in comparison to the foreign market.

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Prices and Exchange RatesPrice elasticity of demand is an

important factor when determining pass-through levels.

The price elasticity of demand for a good is the percentage change in quantity of the good demanded as a result of the percentage change in the goods price.

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PPQQ

Elasticity

Exhibit 7.4 Exchange Rate Pass-Through

24

The Fisher Effect The international Fisher relation is inspired

by the domestic relation postulated by Irving Fisher (1930).

The Fisher effect states:

It can be reduced to:

the nominal interest rate is equal to a real interest rate plus expected inflation:

rriri 111

ri

25

The Fisher Effect

Applied to two different countries, USA and Japan, The Fisher Effect would be stated as:

Note that the inflation term π is expected rate of inflation, not what inflation has been in the past.

$ $ $i r ¥¥¥ ri

International Fisher effect

Definition: if real interest rates r across countries are the same, thenthe percentage change in the spot exchange rate over time is equal to the interest rates differential of the two countries. Also called “Fisher-open”.

it states that the spot exchange rate should change in an equal amount but in the opposite direction to the difference in interest rates between two countries.

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Interest Rates Parity

A forward exchange agreement between currencies states the rate of exchange at which a foreign currency will be bought or sold forward at a specific date in the future.

A forward rate is an exchange rate quoted for settlement at some future date. For 1, 2, 3, 6, 12 month.

Forward rate over 2 years is called swap rate.

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Interest Rate Parity

Interest rate parity (IRP) is an arbitrage condition that provides the linkage between the foreign exchange markets and the international money markets.

f

d

t

tt

i

i

S

F

1

11,

where, Ft and St are the forward and spot rates and id and if are domestic and foreign interest rates respectively.

Interest Rate Parity (IRP)

29

Interest Rate Parity

The approximate form of IRP says that the % forward premium equals the difference in interest rates.

fdt

tt iiS

F 11,

In general, the currency trading at a forward premium (discount) is the one from the country with the lower (higher) interest rate.

Approximation of IRP

fdt

ttt iiS

SF

1,

Interest Rates ParityThe forward rate is calculated for any specific maturity by

adjusting the current spot exchange rate by the ratio of Eurocurrency interest rates of the same maturity for the two subject currencies.

For example, the 90-day forward rate for the Swiss Franc/US dollar exchange rate

(FSF/$90) = the current spot rate (SSF/$) times the ratio of the 90-day euro-Swiss franc deposit rate (iSF) over the 90-day Eurodollar deposit rate (i$).

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Caculating Forward RatesCalculation of the 90 day forward rate:

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)360/90(1

90/360) (i 1 S F

$

SFSF/$

90$/SF

i

Note, to use the same time period on both sides

Interest Rates and Exchange RatesThe theory of Interest Rate Parity (IRP) provides the linkage between the foreign exchange markets and the international money markets.

The theory states: The difference in the national interest rates for

securities of similar risk and maturity (i$ -i€)

should be equal to, but with an opposite sign, the forward rate discount or premium for the foreign currency (F-S)/S. we use the quotation $/€ here. (i$ -i€) = (F-S)/S

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Exhibit 7.5 Currency Yield Curves and the Forward Premium

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i$

isf

34

Interest Rate Parity – An Example

Basic idea: Two alternative ways to invest funds over same time period should earn the same return.

Ex: Suppose the 3-month money market rate is 8% p.a. (2% for 3-months) in the U.S. and 4% p.a. (1% for 3-months) in Switzerland, and the spot exchange rate is SFr1.48/$.

Calculate the 3 month forward rate.

The 3-month forward rate must be SFr1.4655/$ to prevent arbitrage opportunities (i.e., interest rate parity must hold).

Exhibit 7.6 Interest Rate Parity (IRP)

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Exchange m

arket

Exchange m

arket

36

Covered interest arbitrage (CIA) it involves 4 steps: if IRP does not hold

(check which way to arbitrage) Borrow the domestic currency; Exchange the domestic currency for the

foreign currency in the spot market; Invest the foreign currency in an interest-

bearing instrument; and then Sign a forward contract to “lock in” a future

exchange rate at which to convert the foreign currency proceeds back to the domestic currency.

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Covered Interest Arbitrage: Example

The annual interest rate in the AUS and UK are 5% and 8% respectively. The current spot rate is $1.50/£ and the 1 year forward rate is $1.48/£. Can arbitrage profits be made?

Forward pound is overvalued 1. Borrow $1m (at 5%)2. Purchase £666,667 using $1m3. Invest £ at 8% (will receive £720,000 in one year’s

time)4. Simultaneously sell £720,000 forward ($1,065,600)5. Repay loan + interest of $1,050,0006. ARBITRAGE PROFIT = $15,600

)1(1 1,f

t

ttd i

S

Fi

1.05 ≠ 1.0656

)08.1(50.1

48.105.1

?

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The Example Continued

£666,667

for 1 year

at i$ = 5%<$1,050,000>$1,065,60

0

Borrow$1,000,000

1

ConvertSpot at $1.50/£

2

Invest for 1 year

at i£ = 8%

3

Cover Forward at $1.48/£

4Profit = $15,600

£720,000

Exhibit 7.7 Covered Interest Arbitrage (CIA)

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Covered Interest Arbitrage

Covered interest arbitrage should continue until interest rate parity is re-established, because the arbitrageurs are able to earn risk-free profits by repeating the cycle.

But their actions nudge the foreign exchange and money markets back toward equilibrium:

1. Purchase of Pounds in the spot market and sale of £ in the forward market narrow the premium on forward pounds.

2. The demand for pound-denominated securities causes pound interest rates to fall, while the higher level of borrowing in US causes dollar interest rates to rise.

Uncovered interest arbitrageUncovered interest arbitrage (UIA) is a deviation from covered interest arbitrage .In UIA, investors borrow in currencies that have relatively low interest rates and convert the proceed into currencies that offer higher interest rates.

The transaction is “uncovered” because the investor does not sell the higher yielding currency proceeds forward, choosing to remain uncovered and accept the exchange rate risk at the end of the period.

yinghong.chen@liu.se PhD in Finance 7-41

Exhibit 7.8 Uncovered Interest Arbitrage (UIA): The Yen Carry Trade

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In the yen carry trade, the investor borrows Japanese yen at relatively low interest rates, converts the proceeds to another currency such as the U.S. dollar where the funds are invested at a higher interest rate for a term period. At the end of the period, the investor exchanges the dollars back to yen to repay the loan, pocketing the difference as arbitrage profit. If the spot rate at the end of the period is roughly the same as at the start, or the yen has fallen in value against the dollar, the investor profits. If, however, the yen were to appreciate versus the dollar over the period, the investment may result in significant loss.

Interest Rates and Exchange RatesThe following exhibit (7,9) illustrates the

equilibrium conditions between interest rates and exchange rates.

The disequilibrium situation, denoted by point U, is located off the interest rate parity line.

However, the situation represented by point U is unstable because all investors have an incentive to execute the same covered interest arbitrage, which will close this gap in no time.

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Exhibit 7.9 Interest Rate Parity (IRP) and Equilibrium

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EXPECTATIONS THEORY: Unbiased Forward Rate (UFR)

This hypothesis states that for the major floating currencies, foreign exchange markets are “efficient” and forward exchange rates are unbiased predictors of future exchange rates.

The unbiased forward rate (UFR) concept states that the forward exchange rate, quoted at time t for delivery at time t+1, is equal to the expected value of the spot exchange rate at time t+1.

46

Unbiased Forward Rate (UFR)

An unbiased predictor, however, does not mean the future spot rate will actually be equal to what the forward rate predicts.

Unbiased prediction means that the forward rate will, on average, overestimate and underestimate the actual future spot rate in equal frequency and degree.

Ft t+1 = Et[St+1]

Exhibit 7.10 Forward Rate as an Unbiased Predictor for Future Spot Rate

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Empirical Tests of unbiased predictor of future spot rate

A consensus is developing that rejects the efficient market hypothesis.

It appears that the forward rate is not an unbiased predictor of the future spot rate and that

it does pay to use resources in an attempt to forecast exchange rates.

Ex: International Parity ConditionsThe forcasted inflation for Japan and US are 1% and 5% respectively. A 4% differential. The US interest rate is 8%, Japan 4%. The spot rate S1 is 104￥ /$. The one-year forward is S1 100￥ /$. The Spot rate one year from now is S2

a) Purchasing Power Parity (PPP)S2 /S1= (1+π ￥ )/(1+π$) S2=104*1,01/1,05=100￥ /$

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International Parity Conditions

b) the Fisher Effect

The nominal interest rate differential =difference in expected rate of inflation

8%-4%=-(1%-5%)

c) International Fisher EffectThe forcasted change in spot rate =the

differential between nominal interest rates

d) Interest Rate Parity

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International Parity Conditionse) Forward rate as an unbiased predictor .

This is also called expectations theory.

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Exhibit 7.11 International Parity Conditions in Equilibrium (Approximate Form)

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Mini-Case Questions: Currency Pass-Through at PorscheWhich do you believe is most important for

sustaining the sale of the new Carrera model, maintaining a profit margin or maintaining the U.S. dollar price?

Given the change in exchange rates and the strategy employed by Porsche, would you say that the purchasing power of the U.S. dollar customer has grown stronger or weaker?

In the long run, what do most automobile manufacturers do to avoid these large exchange rate squeezes?

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Exhibit 1 Pass-Through Analysis for the 911 Carrera 4S Cabriolet, 2003