Lecture 8 parity models and foreign exchange rates
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Lecture 8: Parity Models and Foreign Exchange Rates. Evaluating Current Spot Rates and Forecasting Rates with Parity Models: The Purchasing Power Parity Model. Where is this Financial Center?. Frankfurt: Home of the ECB. New ECB Towers: Completion Date 2014. What are Parity Models?.

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Lecture 8: Parity Models and Foreign Exchange Rates

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Lecture 8 parity models and foreign exchange rates

Lecture 8: Parity Models and Foreign Exchange Rates

Evaluating Current Spot Rates and Forecasting Rates with Parity Models:

The Purchasing Power Parity Model


Where is this financial center

Where is this Financial Center?


Frankfurt home of the ecb

Frankfurt: Home of the ECB


New ecb towers completion date 2014

New ECB Towers: Completion Date 2014


What are parity models

What are Parity Models?

  • Parity is defined as a state of equilibrium.

  • Foreign exchange parity models “estimate” what the equilibrium spot exchange rate should be (under the model’s assumptions):

    • (1) Is today’s spot rate appropriate?

    • (2) What might the spot rate be in the future (forecasting future spot rates).

      • Generally involving a long term forecasting horizon.

  • Parity models have an economic basis (i.e., theory) for their spot rate determination.


Why are parity models important

Why are Parity Models Important?

  • Testing the “correctness” of a spot rate.

    • Could be important for a trading strategy.

    • Is the currency overvalued or undervalued?

      • Overvalued: perhaps a sell short strategy.

      • Undervalued: perhaps a buy long strategy.

  • Establishing a future spot rate

    • Could be important for:

      • International capital budgeting decisions

        • Converting estimated foreign currency cash flows into MNC’s home currency as part of the capital budgeting process (location decision).

      • Investment and Financing decisions

        • Converting estimated investment inflows from investments into home currency equivalents and converting estimated financing outflows into home currency equivalents.


Two major spot fx parity models

Two Major Spot FX Parity Models

  • (1) Purchasing Power Parity (PPP)

    • Model assumes relative rates of inflation (or relative prices) between two countries as the major determinant of future spot exchange rates.

      • The subject of this lecture

  • (2) International Fisher Effect (IFE)

    • Model assumes relative rates of long term interest between two countries as the major determinant of future spot exchange rates.

      • The subject of the next lecture


Purchasing power parity theory

Purchasing Power Parity Theory

  • The Purchasing Power Parity (PPP) explains and quantifies the relationship between inflation and spot exchange rates.

  • The theory of Purchasing Power Parity says that in the long run, differences in inflation rates between countries are transmitted through changes in relative exchange rates. I

  • The theory states that the spot exchange rate between two currencies should be equal to the ratio of the two countries’ price levels.

    • Idea was first proposed by the classical economist, David Ricardo, in the 19th century.

    • The concept was expanded by the Swedish economist, Gustav Cassel, during the years after WW1 (1918 -) when countries in Europe were experiencing hyperinflation.


Anecdotal evidence in support of ppp model

Anecdotal Evidence in Support of PPP Model

  • Historically low inflation rate countries have been associated with strong currencies:

    • Switzerland, Japan, Germany

  • Historically high inflation rate countries have been associated with weak currencies:

    • Countries in South America and Africa

      • Argentina, Brazil, Peru and Chile

      • Zimbabwe


Two forms of ppp

Two Forms of PPP

  • Absolute PPP:

    • At a point in time, the equilibrium spot exchange rate is that rate which results in the prices of similar goods in two different countries being equal.

      • This form of the PPP can be used to test how “appropriate” a current spot exchange rate is and to indicate a future move in the exchange rate.

  • Relative PPP:

    • Over time, the change in the exchange rate between two currencies should be equal to the rate of change in the prices of similar goods between the two countries.

      • This form of the PPP is used to forecast the equilibrium spot exchange rate in the future and generally over a long time horizon.


Rationale behind the ppp the law of one price

Rationale Behind the PPP: The Law of One Price

  • The Purchasing Power Parity model is based on the Law of One Price:

    • The Law of One Price states that all else equal (i.e., no transaction costs or other frictions, like tariffs or cultural differences) a product’s price (adjusted by the exchange rate) should be the same in all markets.

    • Why will the product’s price be the same?

      • The principle of competitive markets assumes that prices will equalize as consumers shift their purchases to those markets (or countries) where prices are the lowest.

      • Also arbitrage activities will (might) result in similar prices.


Law of one price formulas

Law of One Price Formulas

  • The Law of One Price assumes that prices for similar products between two countries should be the same after adjusting for exchange rates, or

    • The price of product A in the United States in U.S. dollars (PUSD), adjusted by the spot exchange rate, should equal the foreign currency price (PFC) of product A in a foreign country.

  • Law of One Price formulas:

    • PUSD Spot FX rateET = PFC

      • Where ET = European Terms quote

    • PUSD/Spot FX rateAT = PFC

      • Where AT = American Terms quote


Example 1 law of one price

Example 1: Law of One Price

  • Assume:

    • A Big Mac hamburger costs $4.00 in the United States and

    • The current yen spot exchange rate (USD/JPY) is ¥76.75

  • According to the Law of One Price, the “equilibrium” Big Mac hamburger price in Japan should be:

  • PUSD Spot FX RateET = P¥

  • $4.00 x ¥76.75 = ¥307

    • At these two local currency prices ($4.00 and ¥307) and given the spot exchange rate (76.75) there is no difference in exchange rate adjusted prices for a Big Mac in the United States and Japan.


Example 2 law of one price

Example 2: Law of One Price

  • Assume:

    • A Big Mac hamburger costs $4.00 in the United States and

    • The current British pound spot exchange rate (GBP/USD) is $1.5380

  • According to the Law of One Price, the “equilibrium” Big Mac hamburger price in the UK should be:

  • PUSD/Spot FX RateAT = P£

  • $4.00/$1.5380 = £2.60

    • At these two local currency prices ($4.00 and £2.60) and given the spot exchange rate (1.5380) there is no difference in exchange rate adjusted prices for a Big Mac in the United States and the United Kingdom.


The absolute ppp exchange rate

The Absolute PPP Exchange Rate

  • The absolute PPP spot exchange rate is the exchange rate which results in the prices of similar goods between two countries being the same.

  • For European Terms quoted currencies the absolute PPP formula is:

    • Absolute PPP FX RateET = PFC/PUSD

    • Where PFC is the price in the foreign market

    • And PUSDis the price in the U.S. market


Example the absolute ppp exchange rate for european terms quotes

Example: The Absolute PPP Exchange Rate For European Terms Quotes

  • Example: Assume the price of a Starbuck’s grande vanilla latte in the United States is $3.75 and 7.40CHF in Switzerland. Given this information, calculate the absolute PPP USD-CHF spot exchange rate.

  • Absolute PPP FX RateET = PFC/PUSD

  • USD-CHF ______________


Answer

Answer

  • Example: Assume the price of a Starbuck’s grande vanilla latte in the United States is $3.75 and 7.40CHF in Switzerland. Given this information, calculate the absolute PPP spot exchange rate.

  • Absolute PPP FX RateET = PFC/PUSD

  • Spot USD-CHF FX RateET = 7.40/3.75 = 1.9733

  • At 1.9733 the price of this Starbucks is the same in the U.S. and Switzerland:

    • 7.40/1.9733 = $3.75


The absolute ppp exchange rate american terms quotes

The Absolute PPP Exchange Rate: American Terms Quotes

  • For American Terms quoted currencies the absolute PPP formula is:

    • Absolute PPP FX RateAT = PUSD/PFC

    • Where PFC is the price in the foreign market

    • And PUSDis the price in the U.S. market

  • Example: Assume the price of an official NBA basketball in the U.S. is $180 and in the U.K the price is 105 pounds.

  • Calculate the Absolute PPP Exchange Rate.


Answer1

Answer

  • Example: Assume the price of an official NBA basketball in the U.S. is $180 and in the U.K the price is 105 pounds. Given this information, calculate the Absolute PPP Exchange Rate

    • Absolute PPP FX RateAT = PUSD/PFC

  • Spot GBP-USD = 180/105 = 1.7143

  • At 1.7143 the price of this basketball is the same in the U.S. and the U.K.:

  • 105 x 1.7143 = $180.00


Evaluating spot rates

Evaluating Spot Rates

  • Once we have calculated the absolute PPP exchange rate, we can compare that rate to the actual spot rate as one test of the “correctness” of the actual spot rate as well as the future move in the exchange rate.

  • Using the Absolute PPPs on the previous slides and actual spot rates (Oct 26, 2012), comment on the data (is the foreign currency overvalued or undervalued? What about the U.S. dollar?):

    • (1) USD-CHF PPPET = 1.9733 (actual spot = 0.9346)

    • (2) GBP/USD PPPAT = 1.7143 (actual spot = 1.6106)


Answers

Answers

  • Using the Absolute PPPs on the previous slides and actual spot rates (Oct 26, 2012), comment on the data.

  • Is the foreign currency overvalued or undervalued? What about the U.S. dollar?:

    • (1) USD-CHF PPPET = 1.9733 (actual spot = 0.9346)

      • CHF is overvalued (USD is undervalued)

    • (2) GBP/USD PPPAT = 1.7143 (actual spot = 1.6106)

      • GBP is undervalued (USD is overvalued)


Rules for the absolute ppp

Rules for the Absolute PPP

  • The Absolute PPP can be used to “estimate” whether a foreign currency’s spot rate is overvalued or undervalued and possible future move by using the following rules:

  • Absolute PPP European Terms:

    • If PPP Spot < Current Spot, then the currency is undervalued (thus currency may appreciate).

      • E.g.: PPP = 100; Current Spot = 110

    • If PPP Spot > Current Spot, then the currency is overvalued (thus currency may depreciate).

      • E.g.: PPP = 100; Current Spot = 90

  • Absolute PPP American Terms:

    • If PPP Spot > Current Spot, then the currency is undervalued (thus currency may appreciate).

      • E.g.: PPP = $1.20; Current Spot = $1.00

    • If PPP Spot < Current Spot, then the currency is overvalued (thus currency may depreciate).

      • E.g.: PPP = $1.20 Current Spot = $1.40


Using the absolute ppp

Using the Absolute PPP

  • In theory, the “absolute” PPP Spot exchange rate can be used to assess the “correctness” of a current spot rate on the basis of similar goods in different countries.

    • It suggests the possibility that a currency is overvalued or undervalued, and by how much?

    • Perhaps we can use this model for forecast the future move of a currency.

  • Where can we get data for the Absolute PPP model?

    • One source is the Economist "Big Mac” index.

    • http://www.economist.com/markets/Bigmac/Index.cfm


Big mac index

Big Mac Index

October 14, 2010

Interpreting the Data

In the United States, a Big Mac costs $3.71.

While in China, a Big Mac costs 14.5 yuan.

Given the Oct 2010 exchange rate (USD/CNY) of 6.6514 a Big Mac in China worked out to $2.18 (14.5/6.6514). Note this is the Big Mac price on the chart.

The Absolute PPP for the yuan is the ratio of the yuan cost to the dollar cost, or: 14.5/3.71 = 3.9084.

Comparing spot (6.6514) to PPP (3.9084) suggested that the yuan was undervalued by 41%

(6.6514-3.9084/6.6514 = .41%)


Big mac index january 2012

Big Mac Index, January 2012


Changes in currencies 2007 2012

Changes in Currencies, 2007 - 2012


A test of the big mac 1999 the introduction of the euro

A Test of the Big-Mac: 1999, The Introduction of the Euro

  • The Euro was introduced on January 1, 1999. The first day ending trading price was $1.1874.

    • According to the Big-Mac data, at the time of the euro’s introduction the Absolute PPP Spot rate could be calculated as follows:

      • Average price of a Big-Mac in the euro zone = €2.53

      • Average price of a Big-Mac in the U.S. = $2.63

      • Absolute PPP Spot RateAT = $2.63/€2.53 = $1.04

    • What does the Absolute PPP spot rate suggest about the euro on the day it was introduced?

    • Comparing the actual spot ($1.1874) to the Absolute PPP Spot ($1.04) suggested the euro was overvalued by about 12.5% on the day it began trading.


What happened to the euro january 1 1999 december 31 1999

What Happened to the Euro? January 1, 1999 – December 31, 1999


Absolute ppp in practice

Absolute PPP in Practice

  • In practice, use of the absolute PPP to test the “correctness” of a spot exchange rate depends on a number of factors:

    • Goods that are tradable; necessary for the assumption of competitive markets.

    • Goods that are comparable. Are the goods really similar in quality and quantity?

    • Are there government policies (tariffs and quotas) which render such goods not useful for absolute PPP calculations?

    • Are there cultural differences which render such goods not useful for absolute PPP calculations?


Impacts of cultural differences and government policy on absolute ppp

Impacts of Cultural Differences and Government Policy on Absolute PPP

Cultural Differences (Melons)

Tariffs and Quotas (Rice)

$37 USD

$32 USD


Examining discrepancies between absolute ppp and actual fx rates

Examining Discrepancies Between Absolute PPP and Actual FX Rates

  • When the actual FX rate differs from the Absolute PPP rate, one needs to examine reasons for the discrepancy to determine if the spot rate will, or will not, move towards the Absolute PPP.

  • (1) Examine the exchange rate regime and the commitment of the government for that regime.

    • Does this account for the discrepancy between the Absolute PPP and the spot rate?

    • Chinese yuan and Hong Kong dollar.

  • (2) Are there economic or financial conditions which could account for the observed discrepancy and how long might they dominate the spot rate?

    • Relative economic performance, interest rates, trade balances, capital flows, safe haven effects, etc.

    • Swiss franc


Other sources of absolute ppp

Other Sources of Absolute PPP

  • To this point, we have focused on single goods when explaining and using the absolute PPP model.

  • However, a better use of the Absolute PPP model would probably involve a market basket of goods, not just one.

    • Market basket PPP exchange rates are published by both the OECD and the World Bank.

      • http://stats.oecd.org/Index.aspx?datasetcode=SNA_TABLE4


Oecd ppp exchange rates and actual rates

OECD PPP Exchange Rates and Actual Rates


Comparing actual to ppp

Comparing Actual to PPP


Comparing actual to ppp1

Comparing Actual to PPP


Comparing actual to ppp2

Comparing Actual to PPP


Relative purchasing power parity

Relative Purchasing Power Parity

  • The second PPP model, the Relative Purchasing Power Parity model, is concerned with the “change” in the exchange rate over time.

    • The Relative Purchasing Power is not assessing the “correctness” of the current spot rate.

  • The relative PPP model suggests that spot exchange rates move in a manner opposite to the inflation differential between the two countries.

    • Specifically, the Relative PPP model suggests that the percent change in a spot exchange rate should be equal to, but opposite in direction to, the difference in the rates of inflation between countries.

    • This is a model which may be used to forecast an actual future spot rate.


Hyperinflation and exchange rates zimbabwe in 2008 july 2008 annual inflation 231 150 888

Hyperinflation and Exchange Rates: Zimbabwe in 2008 (July 2008, Annual Inflation 231,150,888%)


Zimbabwe with stable prices since 2009 july 2012 3 24 annual rate of inflation

Zimbabwe With Stable Prices Since 2009 (July 2012: 3.24% Annual Rate of Inflation)


Ppp over the long term 1980 2000

PPP Over the Long Term, 1980 - 2000

Lower Rates of Inflation

High Inflation

Countries


Relative ppp formula american terms

Relative PPP Formula: American Terms

  • For an American Term quoted currency:

    • PPP Spot RateAT = Current Spot RateAT x ((1 + INFUS)n/(1 + INFFC)n)

  • Where:

    • PPP Spot RateAT is the expected American Terms quoted spot rate some date in the future.

    • Current spot rate expressed in American terms.

    • INFUS is the expected annual rate of inflation in the United States (in decimal form).

    • INFFC is the expected annual rate of inflation in the foreign country (in decimal form).

    • N is the number of years in the future (which corresponds to the forecasted time period).


Relative ppp formula american terms1

Relative PPP Formula: American Terms

  • Assume:

    • Current spot rate for British pounds (GBP/USD = $1.80

    • Expected annual rate of inflation in the U.S. = 2.0%

    • Expected annual rate of inflation in the U.K. = 3.0%

  • Given this data, calculate the Relative PPP spot pound FX rate 2 years from now using:

    • PPP Spot RateAT = Current Spot RateAT x ((1 + INFUS)n/(1 + INFFC)n)


Answer2

Answer

  • Given:

    • Current spot rate for British pounds = $1.80

    • Expected annual rate of inflation in the U.S. = 2.0%

    • Expected annual rate of inflation in the U.K. = 3.0%

  • Then, the spot pound 2 years from now is equal to:

    • PPP Spot RateAT = Current Spot RateAT x ((1 + INFUS)n/(1 + INFFC)n)

    • Spot rate in 2 years = 1.80 (1+.02)2/(1+.03)2

    • Spot rate in 2 years = 1.80 (1.0404/1.0609)

    • Spot rate in 2 years = 1.80 (.9807)

    • Spot rate in 2 years = $1.7653


Relative ppp formula european terms

Relative PPP Formula: European Terms

  • For European Term quoted currency:

    • PPP Spot RateET = Current Spot RateET x ((1 + INFFC)n/(1 + INFUS)n)

  • Where:

    • PPPET spot rate is the expected European Terms quote spot rate at some date in the future.

    • Current spot rate expressed in European terms.

    • INFFC is the expected annual rate of inflation in the foreign country (in decimal form).

    • INFUS is the expected annual rate of inflation in the United States (in decimal form).

    • N is the number of years in the future (which corresponds to the forecasted time period).


Relative ppp formula european terms1

Relative PPP Formula: European Terms

  • Assume:

    • Current spot rate for Japanese yen = 111.00

    • Expected annual rate of inflation in the U.S. = 2.0%

    • Expected annual rate of inflation in Japan = 1.0%

  • Given this data, calculate the Relative PPP spot yen FX rate 2 years from now using:

    • PPP Spot RateET = Current Spot RateET x ((1 + INFFC)n/(1 + INFUS)n)


Answer3

Answer

  • Given:

    • Current spot rate for Japanese yen = 111.00

    • Expected annual rate of inflation in the U.S. = 2.0%

    • Expected annual rate of inflation in Japan = 1.0%

  • Given this data, calculate the Relative PPP spot yen FX rate 2 years from now:

    • PPP Spot RateET = Current Spot RateET x ((1 + INFFC)n/(1 + INFUS)n)

    • Spot rate in 2 years = 111 (1+.01)2/(1+.02)2

    • Spot rate in 2 years = 111 (1.0201/1.0404)

    • Spot rate in 2 years = 111 (.9805)

    • Spot rate in 2 years = 108.84


Testing the ppp model

Testing the PPP Model

  • The PPP model has been the subject of many empirical tests.

  • The tests involving the absolute PPP have generally concluded that commodity price arbitrage does not exist.

    • Thus, prices of similar goods do not seem to equalize between countries.

    • Perhaps this is explained on the basis of barriers to commodity price arbitrage across borders (e.g., transportation, tariffs, ,culture).

  • Tests of the relative PPP, over long periods of time, are more encouraging (recall the slide of the Relative PPP from 1980 – 2000)


Ppp over the long term 1980 20001

PPP Over the Long Term, 1980 - 2000

Lower Rates of Inflation

High Inflation

Countries


Is the relative ppp useful for short time periods

Is the Relative PPP Useful for Short Time Periods?

  • While some studies have validated the reliability of the relative PPP model for “explaining” the long term relationship between inflation and exchange rate, studies which have examined the short term relationship have shown that actual FX rates can often move against the PPP rate.

    • See 2 slides which follow.

  • Perhaps this can be explained on the basis of short term potential factors which can move the exchange rate away from PPP.

    • Safe haven effects, government intervention, carry trade transactions, dirty floats, etc.


Tests of the ppp over the short run the euro and cad

Tests of the PPP over the Short Run: The Euro and CAD

The Euro

The Canadian Dollar


Ppp over the short term g 9 countries quarterly data 1974 1998

PPP Over the Short Term: G-9 Countries Quarterly Data; 1974 - 1998

  • Quarterly inflation differentials to the U.S. against the exchange rate change.

  • Source: Catherine Ho, “Time to Equilibrium in Exchange Rates, Global Financial Journal, 2012


The relative ppp in practice

The Relative PPP in Practice

  • While some historical data tends to validate the relative PPP over long periods of time, the practical issue for users is estimating future rates of inflation.

  • How can we do this?

    • Use recent historical data to estimate the future, or for a benchmark starting point.

    • Combine historical data with likely outcomes which might affect inflation (e.g., government deficits, economic growth, monetary policy)

    • Use independent forecasts of inflation date


Historical inflation data

Historical Inflation Data

  • Historical and Current Data:

    • Visit Central Bank Web sites at:

      • http://www.bis.org/cbanks.htm

    • Or visit the Economist

      • http://www.economist.com/index.html

        • Link to Economic and Financial Indicators (go to output, prices and jobs data).


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