MAN 441: Internatıonal Finance Parity Conditions and Currency Forecasting

MAN 441: Internatıonal FinanceMAN 441: Internatıonal Finance

Parity Conditions and Currency ForecastingParity Conditions and Currency Forecasting

22

Chapter Objective

Understand

Parity conditions, and

1. Purchasing Power Parity (PPP)2. The Fisher Effect (FE)3. The International Fisher Effect

(IFE)4. Interest Rate Parity (IRP)5. Unbiased Forward Rate (UFR)

Alternative methods of currency forecasting

33

Arbitrage

So many relationships in international finance, including the parity conditions, depends on arbitrage activities.

Arbitrage is defined as simultaneous purchase and sale of the same assets or commodities on different markets to profit from price discrepancies.

44

Parity Conditions

Exp % change ofspot rate of foreign

currency-3%

Forward discountor premium on

foreign currency-3%

Interest ratedifferential

+3%

Expected inflationrate differential

+3%

UFR IFE

PPP

IRP

FE

UFR=Forward rates as unbiased predictors of future spot rates

PPP=Purchasing power parity

IFE=International Fisher effect

FE=Fisher effect

IRP=Interest rate parity

55

Arbitrage and Law of One Price

So many relationships in international finance, including the parity conditions, depends on arbitrage activities.

Arbitrage is defined as simultaneous purchase and sale of the same assets or commodities on different markets to profit from price discrepancies.

Law of one price (LOP) stems from arbitrage and states that:

In competitive markets free of transportation costs and official barriers to trade, identical goods sold in different countries must sell for the same price when their prices are expressed in terms of the same currency.

Mathematically, for good iiGBR

iUS

BPiGBRBP

iUS

P

PEPEP )()( $$

66

Arbitrage and Law of One Price

Example:

If a DVD sells for $30 in New York, and if the $/BP=1.50 (BP=British Pound), based on the law of one price, same DVD must sell for 20 BP in London.

Suppose the price in US is $28 for the same DVD. In that case, US exporters and British importers will have an incentive to buy the DVD in New York and ship it to London for a profit (of course, in the absence of any transportation costs and barriers to trade). This will

push the prices up in New York, and

push the prices down in London

until the price of same DVD equalized in both locations.

Hence, international arbitrage enforces the law of one price.

77

Purchasing Power Parity

In its absolute version, PPP states that price levels should be equal worldwide when expressed in a common currency – a unit of home currency should have the same purchasing power around the world. In other words, exchange rate between two currencies should be equal to the ratio of the countries’ price levels.

GBR

USBP

P

PE )( $

where PUS and PGBR are the prices of the reference currency baskets.

Hence, PPP theory predicts that a fall in a currency's domestic purchasing power (increase in the domestic price level) will be associated with a proportional currency depreciation in the foreign exchange market.

If, for example, the reference basket costs $200 in US and 120 British pounds in UK, PPP predicts price of BP as 1.67 (200/120).

88


If law of one price holds (for all commodities), then absolute PPP must hold. Could we say that law of one price must hold if absolute PPP holds?

Note that absolute PPP ignores

Transportation costs Tariffs, quotas and other restrictions Product differentiation

Law of one price and absolute PPP (to a degree) are best illustrated by the Big Mac index (initially put together by The Economist).

99


Actual Exchange

Ratein Local Currency

in US dollars 1 USD = United

States $2.65 2.65 1 - -

Argentina Peso 3.85 12,989 2,964 -51,080 1.45

Australia A$3.20 24,228 13,208 -13,689 1.14

Brazil Real4.50 15,963 2,819 -39,695 1.7

Britain £1.99 36,689 1.8437‡ 38,274 0.75

Canada C$3.20 26,494 12,078 0 1.21

China Yuan9.95 12,007 82,865 -54,746 3.75

Euro area 2.75 35,393 0.777 32,561 1.03

Hong Kong HK$11.25 14,465 77,772 -45,482 4.24

Hungary Forint 492 25,728 191.23 -2,735 186

Indonesia Rupiah16,155 17,788 9082.1 -3,288 6,096

Japan ¥263 24,802 106.04 -6,262 99.4

Malaysia M$5.10 13,431 37,971 -49,435 1.92

Mexico Peso22.0 19,224 11,444 -27,473 8.3New Zealand NZ$3.95 27,275 14,482 2,886 1.49

Poland Zloty6.30 18,893 33,346 -28,627 2.38

Russia Rouble40.00 13,903 28.77 -47,550 15.09

Singapore s$3.30 19,931 16,557 -25,107 1.24South Africa Rand14.05 22,985 61,127 -13,295 5.3South Korea Won3,211 2,791 1150.5 5,259 1,211

Sweden Skr30.0 42,456 70,661 60,202 11.32Switzerland SFr6.35 5,346 11,878 102,054 2.4

Taiwan NT$70.55 21,167 33.33 -2,013 26.62

Thailand Baht55.0 13,412 41,007 -49,399 20.75

‡ Dollars per poundSource: http://www.oanda.com/products/bigmac/bigmac.shtml

Country

BigMac Price

Over(+) / Under(-) Valuation

against the dollar, %

Purchasing Power Price

1010


For example, a Big Mac cost 1.99 BP in London, while its price is $2.71 in US. Implied PPP exchange rate for $/BP can be calculated by (2.71/1.99)=1.36 Implied PPP exchange rate for BP/$ can be calculated by (1.99/2.71)=0.73

Actual price of dollar was 0.63 BP on that date, implying US dollar was undervalued and BP was overvalued.

0.73 - 0.630.73 - 0.63 =+16% ( =+16% (note we used Price of dollarnote we used Price of dollar))

0.630.63

What are the problems with the Big Mac approach?

Ignores what is included in the price of a Big Mac:

- cost of real estate; local taxes ;local services

In other words, it includes both traded and non-traded goods and services.

So, absolute PPP doesn’t make sense if the baskets are different.

1111


Relative PPP, which is mostly used, states that the percentage change in the exchange rate over any period equals the difference between the percentage changes in national price levels. In other words, exchange rates should change to offset differences in inflation rates.

For example, if inflation is 5% in US and 1% in Japan, then the dollar value of Japanese Yen must rise by about 4% to equalize the dollar price of goods in the two countries (dollar depreciates).

In mathematical terms,

t

f

th

i

i

e

e

)1(

)1(

0

1

where e1 = future spot rate e0 = spot rate ih= home inflation if = foreign inflation t = time period

and e is the price of foreign currency ($/BP)

1212


If purchasing power parity is expected to hold, then the best prediction for the one-period spot rate should be

tf

th

i

iee

)1(

)1(01

A more simplified but less precise relationship is

fh iie

ee

0

01 PPP says the currency with the higher inflation rate is expected to depreciate relative to the currency with the lower rate of inflation.

1313


Example: Projected inflation rates for the U.S. and Germany for the next Projected inflation rates for the U.S. and Germany for the next twelve months are 10% and 4%, respectively. If the current exchange rate is twelve months are 10% and 4%, respectively. If the current exchange rate is $.50/dm, what should the future spot rate be at the end of next twelve $.50/dm, what should the future spot rate be at the end of next twelve months?months?

0

1

1

t

ht t

f

ie e

i

1

1 1

1.10.50

1.04e

1 .50(1.0577)e

1 $.529e

$0.529 is the best prediction for the future $/DM exchange rate.

1414


As it is clear now, exchange rate changes may indicate nothing more than the reality that countries have different inflation rates (outcome of PPP). Hence, changes in nominal exchange rates may not be significant to evaluate the true effects of currency changes on a firm.

Real exchange rate is the nominal exchange rate adjusted for changes in relative purchasing power of each currency since some base period (so home price of the foreign basket relative to home basket).

h

ftt

r

i

iee

1

1

h

ftt

r

P

Pee

Where Pf is the foreign price level and Ph is the home price level at time 1, both indexed to 100 at time 0.

Note that increases in the foreign price level and foreign currency depreciation have offsetting effects on real exchange rates.

An alternative way is using the inflation rates.

Note if PPP holds than er=e0.

1515


Example1: Assume Canadian reference commodity basket costs Can100, and US basket costs $50 and the nominal exchange rate is E$/Can=0.5 per Canadian dollar.

Er$/Can =0.5*(100/50)=($50 per Canadian basket)/($50 per US basket)

=1 US basket per Canadian basket

Assume the Canadian baskets cost increases to Can110. Real exchange rate becomes 1.1 so we need to give 1.1 US basket for one Canadian basket – real depreciation of dollar against Canadian dollar (Fall in the purchasing power of a US dollar within Canadian borders relative to its purchasing power within US).

1616


Example2: Assume Yen/$ exchange rate moved from Yen226.63/$ to Yen93.96/$ between 1980 and 1995. CPI in Japan rose from 91.0 to 119.2, and US CPI rose from 82.4 to 152.4.

(a) If PPP hold, what would be the exchange rate in 1995 (according to PPP real rates do not change)?

Inflation in Japan was 31%, and in US was 85% over that time period

Yen/$ PPP rate=226.63*(1.31/1.85)=Yen160.51/$ > Yen93.96/$ , so Yen appreciated more than PPP would suggest.

(b) What happened to real value of Yen?

Real rate=93.96*(1.85/1.31)=Yen132.69/$ ın 1995

Real rate ın 1980 is just equal to nominal rate, Yen226.63/$. Yen appreciated in real terms by 71%.

1717


The distinction between nominal and real exchange rate has important implications for foreign exchange risk management. If real exchange rate remains constant, changes in nominal exchange rate will be less important.

Empirical Evidence:

Law of one price doesn’t hold (no surprise here)

There is a clear relationship between relative inflation rates and changes in exchange rates. In general, it appears that PPP holds well in the long-run, but doesn’t perform well in the short-run

– we observe substantial deviations from PPP predicted rates in the short-run, but there is a tendency to move back to PPP predicted rates in the long-run. This is called mean reversion and it is important for currency risk management.

1818


Why do we see deviations in the short-run?

sticky prices in the short-run transportation costs and restrictions departures from free competition differently constructed price indices relative price changesNon-traded goods and services

1919

Fisher Effect

Investors care about real interest rates and not about the nominal interest rates. However, almost all financial contracts are stated in nominal terms.

The Fisher effect states that nominal interest rate, r, is a function of

Real required rate of return, a, and An inflation premium equal to the expected amount of inflation, i

Formally,

1+Nominal rate=(1+Real rate)*(1+Expected inflation rate)

1+r=(1+a)*(1+i)

r=a+i+a*i

This equation can be approximated by

r=a+i (under what conditions?)

2020

Fisher Effect

Example: if a=3% and i=10%, Fisher equation tells us that nominal interest rate, r, should be 13%.

Generalized version of Fisher effect:

Real returns tend towards equality across countries (ah=af)– If ah>af then capital will flow from foreign to home currency.

In the absence of government intervention, nominal interest rate differential should be equal to expected inflation differential between two currencies.

rh-rf= ih-if How did we obtain this condition (remember ah=af)?

Currencies with high rates of inflation should bear higher nominal interest rates than currencies with lower inflation rates.

2121

Fisher Effect

Example: if inflation rates are 4% and 7% in US and UK, respectively, nominal interest rates should be higher by about 3% in UK.

Parity Line

Interest Differential(rh-rf)

Inflation differential

D

C -2

-3

-2

Is D an equilibrium point?

Do we expect capital to flow from home country to foreign country to take advantage of the real difference?

2222

Fisher Effect

Empirical Evidence:

- Evidence is consistent with the hypothesis that most of the variation in nominal interest rates across countries can be attributed to differences in inflationary expectations.-It is much harder to test the hypothesis that real returns are equal between countries. However, arbitrage will force pre-tax real interest rates to converge across all the major nations, if arbitrage is permitted to operate unhindered and capital markets are integrated worldwide.

- Capital market integration means that real interest rates are determined by the global supply and demand for funds.

- Capital market segmentation means that real interest rates are determined by local credit conditions.

2323

Fisher Effect

Empirical evidence shows that capital markets are becoming increasingly integrated worldwide.

However, we still observe real interest rate differential across countries (not arbitraged away).

- Political risk and currency risk (higher inflation risk – Canada example)

- Different tax policies

- Regulatory barriers to free flow of capital

Hence, real interest rates tend to be higher in developing countries.

Furthermore, integration of capital markets (and resulting flow of funds) impose some discipline on mismanagement of economies in developing nations.

2424

International Fisher Effect

Combine PPP and FE to find IFE.

Remember PPP is denoted as:

fh iie

ee

0

01 And FE as rh-rf= ih-if.

rate expected is where 10

01 , erre

eefh

Is this familiar?

Currencies with low interest rates are expected to appreciate relative to currencies with high interest rates. Is this consistent with our earlier discussions?

0

1

1

t

ht t

f

re e

r

2525


Fisher postulated:

1. The nominal interest rate differential should reflect the inflation rate differential.

2. Expected rates of return are equal in the absence of government intervention.

Remember, changes in the nominal interest differential can have two sources:

1. Changes in real interest differential

2. Changes in inflationary expectations

These two have opposite effects on currency values.

If the change is due to a higher real interest rate in the home country, value of home country’s currency will rise.

If the change is because of an increase in inflationary expectations in home country, value of home country’s currency will fall.

2626


If the ¥/$ spot rate is ¥108/$ and the interest rates in Tokyo and New York are 6% and 12%, respectively, what is the future spot rate two years from now?

0

1

1

t

ht t

f

re e

r

2

1.1236108

1.2544e

2 ¥96.74 / $e

2

2 2

1.06108

1.12e

2727

Interest Rate Parity Theory

The Theory states:

The forward rate (F) differs from the spot rate (S) at equilibrium by an amount equal to the interest differential (rh - rf) between two countries.

The forward premium or discount equals the interest rate differential.

F - S/S = (rh - rf)

where rh = the home rate

rf = the foreign rate

THE UNBIASED FORWARD RATE

States that if the forward rate is unbiased, then it should reflect the expected future spot rate.

ft = et

2828

Currency Forecasting

Important for financial executives of multinational corporations

Currency forecasting can lead to consistent profits only if the forecaster

Has superior forecasting model Has access to private information consistently, or has access to public

information with a time lead Can exploit small, temporary deviations from equilibrium Can predict the nature of government intervention in the foreign

exchange market (more applicable for countries who manage their currencies to some extent)

2929


Market-Based Forecasts

Extract the predictions already included in interest and forward rates Forward rate is an unbiased estimate of the future spot rate – limited

to forecast horizon of one year Interest rate differential can be used to predict future – interest rates

exist for longer time periods

Model-Based Forecasts Fundamental analysis involves the examination of macroeconomic

variables and policies. Simplest is to use PPP. Technical analysis focuses on the past price and volume movements

– try to discover price patterns.

3030


The possibility of consistent profit-making through currency forecasting is inconsistent with the efficient market hypothesis. According to efficient market hypothesis current exchange rates reflect all publicly available information.

Note the forecast doesn’t have to be accurate. It needs to be profitable.

Example: Yen/$ spot rate is Yen110 per $. A 90-day forward rate is Yen109/$. If our forecast for 90-day is Yen102/$, we should buy the Yen forward.

Buy $1million worth of Yen forward = 109,000,000 Yen. If the spot exchange rate 90-day from now turns out to be Yen108/$, sell Yen spot for a profit of $9259. Our forecast was off by 6%, but we made a profit.

Assume our forecast was Yen111/$. We would sell Yen forward and we would lose $9259. Our forecast was more accurate, it was off by 3% only.

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MAN 441: Internatıonal Finance Parity Conditions and Currency Forecasting