International Parity Conditions

2

Introduction

Managers of multinational firms, international investors, importers and exporters, and government officials must deal with these fundamental issues: Are changes in exchange rates predictable? How are exchange rates related to interest rates? What, at least theoretically, is the “proper”

exchange rate?

To answer these questions we need to first understand the economic fundamentals of international finance, known as parity conditions.

3

Parity Conditions

Parity Conditions provide an intuitive explanation of the movement of prices and interest rates in different markets in relation to exchange rates.

The derivation of these conditions requires the assumption of Perfect Capital Markets (PCM).

no transaction costs no taxes complete certainty

NOTE – Parity Conditions are expected to hold in the long-run, but not always in the short term.

4

Purchasing Power Parity (PPP)

PPP is based on the notion of arbitrage across goods markets and the basic building block of PPP is the Law of One Price (LOP).

LOP states that the price of an identical good should be the same in all markets (assuming no transactions costs). Otherwise, one could make profits by buying the

good in the cheap market and reselling it in the expensive market.

5

The Law of One Price

LOP states that a product’s price may be stated in different currency terms, but the price of the product should remain the same.

Comparison of prices would only require conversion from one currency to the other:

Conversely, the exchange rate could be deduced from the relative local product prices:

£

$£/$ P

PS

££$$ PSP

6

LOP Example

Pwheat, Aust = $4/bushel and Pwheat, UK = £2.5/bushel

Spot rate (A$/£) = 1.70

A$ equivalent price of wheat in UK is A$1.70/£ *£2.5

= $4.25/bushel

Implication: The demand for Australian wheat will increase forcing up its price. The price of UK wheat will drop.

wheatUK

wheatAust PSP £/$

7

The Big Mac Index

The most famous test is The Economist magazine’s Big Mac Hamburger standard.

First launched in 1986, updated ever since. For example, see:

http://www.oanda.com/products/bigmac/bigmac.shtml

8

9

Research on the Big Mac Index

Pakko and Pollard (1996) conclude that Big Mac PPP holds in the long-run, but currencies can deviate from it for lengthy periods. They note several reasons why the Big Mac index may be flawed: It assumes that there are NO barriers to trade. Prices are distorted by taxes. Profit margins may vary according to competition. Prices of non-traded goods (real estate, utilities, labor)

are also inputs that affect production costs.

10

Working for a Big Mac

Big Mac Price (US $)

Net Hourly Wage (US $)

Minutes of work to buy a Big Mac

Big Mac Price (US $)

Net Hourly Wage (US $)

Minutes of work to buy a Big Mac

Argentina 1.42 1.70 50 Mexico 2.18 2.00 65

Australia 1.86 7.80 14 New Zealand 2.22 6.80 20

Brazil 1.48 2.05 43 Peru 2.28 2.20 62

Britain 3.14 12.30 15 Philippines 2.24 1.20 112

Canada 2.21 9.35 14 Poland 1.62 2.20 44

Chile 1.96 2.80 42 Russia 1.32 2.60 30

China 1.20 2.40 30 Singapore 1.85 5.40 21

Colombia 2.13 1.90 67 South Africa 1.85 3.90 28

Czech Republic 1.96 2.40 49 South Korea 2.70 5.90 27

Denmark 4.09 14.40 17 Sweden 3.60 10.90 20

Euro area 2.98 9.59 19 Switzerland 4.60 17.80 16

Hong Kong 1.47 7.00 13 Taiwan 2.01 6.90 17

Hungary 2.19 3.00 44 Thailand 1.38 1.70 49

Indonesia 1.84 1.50 74 Turkey 2.34 3.20 44

Japan 2.18 13.60 10 United States 2.71 14.30 11

Malaysia 1.33 3.10 26 Venezuela 2.32 2.10 66

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A New Index – Starbucks Index

12

Absolute PPP

A less extreme form of the Law of One Price is ABSOLUTE PPP which says that the price of a basket of goods should be the same in each market.

The PPP exchange rate between the two countries should then be:

Absolute PPP:tF

tDFDt PI

PIS

,

,/

PID,t (PIF,t) is the domestic (foreign) price index (e.g., consumer price index) at time t.

13

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

14

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 (appreciate).

FDs

15

Relative PPP Example

Given inflation rates of 5% and 10% in Australia and the UK respectively, what is the prediction of PPP with regards to $A/GBP exchange rate?

= (0.05 – 0.10)/(1 + 0.10) = - 0.045 = - 4.5%

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

1

Relative PPP

16

How well does PPP work?

We have seen that the strictest version of PPP – that all goods and financial assets obey the law of one price – is demonstrably false.

However, there is clearly a relationship between relative inflation rates and changes in exchange rates. Currencies that have had the largest relative decline

(gain) in purchasing power see the sharpest erosion (appreciation) in their foreign exchange values.

17

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).

18

Forecasting Future Spot Rates

Suppose the spot exchange rate and expected inflation

rates are:

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

2% 5%;$;/¥90S ..t0¥/$, JapanSU

$/¥43.8705.1

02.1$/¥90

1

1

$

¥0,/¥1$,/¥

tSPPP

t SS

19

Real Exchange Rate

By definition, the real exchange rate measures deviations from PPP. That is, changes in the spot exchange rate that do not

reflect differences in inflation rates between the two currencies in question.

Real Exchange Rate: PPP1t

1t

S

SE

20

Real Exchange Rate

Appreciation/depreciation in the real exchange rate measures deviations from PPP. When E = 1, the denominator currency is valued correctly.

The competitiveness of this country is unaltered.

When E < 1, the denominator currency is undervalued. Products from the other country seem expensive relative to the base year. That is, the competitiveness of the denominator country improves.

When E > 1, the denominator currency is overvalued. Products from the other country seem cheap relative to the base year. That is, the competitiveness of the denominator country deteriorates.

21

The Fisher Effect

The international Fisher relation is inspired by the domestic relation postulated by Irving Fisher (1930).

The Fisher effect (also called Fisher-closed) states:

This relation is often presented as a linear approximation stating that the nominal interest rate is equal to a real interest rate plus expected inflation:

rriri 111

ri

22

The Fisher Effect

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

It should be noted that this requires a forecast of the future rate of inflation, not what inflation has been in the past.

$ $ $i r ¥¥¥ ri

23

The International Fisher Effect

The International Fisher Effect (also called Fisher-open) states that the spot exchange rate should change to adjust for differences in interest rates between two countries:

F

DFD

t

FDt

i

i

S

S

1

1/

/1

24

The International Fisher Effect

The Fisher effect applied to two different countries like Australia and Japan would be:

(1) (1+i$) = (1+r$)(1+$)

(2) (1+i¥) = (1+r¥)(1+¥)

Dividing (1) by (2), we get:

(3)

¥

$

¥

$

¥

$

1

1

r1

r1

i1

i1

= 1

25

The International Fisher Effect

If real interest rates are equalized across countries, then for equation (3) we get r$ = r¥:

(4)¥

$

¥

$

1

1

i1

i1

(5)¥

¥$

¥

¥$

11

i

ii

Remember this?

F

FD

t

tt

S

SS

11

F

FD

t

tt

i

ii

S

SS

11

International Fisher:

E(St+1)

26

Tests of the International Fisher Effect

Empirical tests lend some support to the relationship postulated by the international Fisher effect (currencies with high interest rates tend to depreciate and currencies with low interest rates tend to appreciate), although considerable short-run deviations occur.

27

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)

28

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,

29

Interest Rate Parity – An Example

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

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/$.

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

30

The Example Continued

90 daysS = SF 1.4800/$

SF 1,480,000

Dollar money market

$1,000,000 $1,020,000 1.02Start End

i $ = 8.00 % per annum(2.00 % per 90 days)

Swiss franc money market

SF 1,494,800 1.01

i SF = 4.00 % per annum(1.00 % per 90 days)

F90 = SF 1.4655/$

$1,019,993*

* Rounding error.

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Interest Rate Parity: Why It Holds

This must hold by arbitrage. Otherwise riskless profits could be made. This is known as covered interest arbitrage (CIA) and occurs whenever IRP does not hold. CIA can involve the following steps:

• 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.