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? 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? 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 (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 The Purchasing Power Parity (PPP) explains and

quantifies the relationship between inflation and spot exchange rates.

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.

Two Forms of PPP Absolute PPP:

At a point in time, the equilibrium 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 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 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.

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 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 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 spot exchange rate is the

exchange rate which will result in the prices of similar goods between two countries being the same. 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.

USD/CHF ______________

The Absolute PPP Exchange Rate The absolute PPP spot exchange rate is the

exchange rate which will result in the prices of similar goods between two countries being the same. 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.

USD/CHF = $3.75 x Spot FX RateET = 7.40 Spot FX RateET = 7.40/3.75 = 1.9733

The Absolute PPP Exchange Rate The absolute PPP spot exchange rate is the

exchange rate which will result in the prices of similar goods between two countries being the same. 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.

USD/CHF = $3.75 x Spot FX RateET = 7.40 Spot FX RateET = 7.40/3.75 = 1.9733

Formulas for Absolute PPP Exchange Rate with Examples

For European Terms quoted currencies: Absolute PPP FX RateET = PFC/PUSD

Assume: Grande Vanilla Latte, Prague = 99 Czech Koruna (Crown) Grande Vanilla Latte, U.S. = $3.75 Absolute PPP FX RateET = USD/CZK = __________

For American Terms quoted currencies: Absolute PPP FX RateAT = PUSD/PFC

Assume: Grande Vanilla Latte, London = 2.50 Pounds Grande Vanilla Latte, U.S. = $3.75 Absolute PPP FX RateAT = GBP/USD = ___________

Using the Calculated Absolute PPP FX Exchange Rate 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 4, 2011), comment on the data (is the foreign currency overvalued or undervalued? What about the U.S. dollar?): (1) USD/CZK PPPET = 26.4 (actual spot = 18.13) (2) GBP/USD PPPAT = 1.50 (actual spot = 1.5380) (3) USD/CHF PPPET = 1.9733 (actual spot = 0.9038)

Using the Calculated Absolute PPP FX Exchange Rate Using the Absolute PPPs on the previous

slides and actual spot rates (Oct 4, 2011), comment on the data (is the foreign currency overvalued or undervalued? What about the U.S. dollar?): (1) USD/CZK PPPET = 26.4 (actual spot = 18.13)

CZH is overvalued; USD is undervalued (2) GBP/USD PPPAT = 1.50 (actual spot = 1.5380)

GBP is slightly overvalued; USD is slightly undervalued (3) USD/CHF PPPET = 1.9733 (actual spot = 0.9038)

CHF is overvalued; USD is undervalued

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 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? Where can we get data for the Absolute PPP

model? The "Big Mac” index. http://www.economist.com/markets/Bigmac/Index.

cfm

Big Mac IndexOctober 14, 2010

Interpreting the Data In the United States, a Big Mac

costs $3.71. In China, a Big Mac costs 14.5

yuan. Given the exchange rate

(USD/CNY) of 6.6514 a Big Mac in China works 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%)

One Test of the Big-Mac: The Introduction of the Euro The Euro was introduced on January 1, 1999. The

first day 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

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?

Cultural Differences and Government Policy Impacts on Absolute PPP ModelCultural Differences (Melons) Tariffs and Quotas (Rice)

Examining Discrepancies Between Absolute PPP and Actual FX Rates When the actual FX rate differs from the Absolute PPP

rate, one should also 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 exchange rate regime. Does this account for the discrepancy between the Absolute PPP

and the spot rate? Chinese yuan undervalued by 41% (Big Mac, 2010)

(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. Brazilian real overvalued by 40% (Big Mac, 2010)

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 RatesFX 2005 2006 2007 2008 2009 2010

USD/JPY 110.22 116.30 117.75 103.36 93.57 87.78

PPP: 129.55 124.61 120.16 116.84 115.35 111.38

USD/CHF 1.2452 1.2538 1.2004 1.0831 1.0881 1.0429

PPP: 1.7427 1.6593 1.5997 1.5505 1.5313 1.5104

USD/CNY 8.1943 7.9734 7.6075 6.9487 6.8314 6.7703

PPP: 3.448 3.465 3.622 3.821 3.764 3.946

EUR/USD 1.2436 1.2545 1.3687 1.4648 1.3892 1.3244

PPP: 1.1670 1.2035 1.2157 1.2383 1.2505 1.2357

GBP/USD 1.8182 1.8400 2.0001 1.8384 1.5578 1.5452

PPP: 1.5719 1.5949 1.5506 1.5638 1.5570 1.5349

AUD/USD 0.7637 0.7530 0.8368 0.8388 0.7799 0.9173

PPP: 0.7203 0.7095 0.7008 0.6761 0.6887 0.6611

Comparing Actual to PPP

Comparing Actual to PPP

Comparing Actual to PPP

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.

PPP Over the Long Term, 1980 - 2000

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. INFFC is the expected annual rate of inflation in the

foreign country. N is the number of years in the future (which corresponds

to the forecasted time period).

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)

Relative PPP Formula: American Terms Answer: 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 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. INFUS is the expected annual rate of inflation in the United

States. N is the number of years in the future (which corresponds

to the forecasted time period).

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)

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: 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 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 - 2000

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 CADThe Euro The Canadian Dollar

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 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).