Lecture 4 (b)

Foreign Exchange Rates and International Parity (outline)

• What We Mean and Why It Matters

• Purchasing Power Parity

• International Fisher Effects

• Interest Rate Parity

• Parity and Forecasting

What Determines the Exchange Rate? A Review

• We have already seen how, in the end, money is just a commodity and so the FX rate will be determined by supply and demand.

• Supply and demand will depend on

– Relative inflation rates (note the importance of monetary policy)

– Relative interest rates (same note)

– Other factors that influence trade (e.g., productivity)

Now We’re Going to Try and More Carefully Describe How These Fundamentals Shape Price

But before going there, let’s note a couple of things

• Exchange rates are often much more volatile than the underlying fundamentals

– FX rates sometimes change by 10% a day. Inflation rates and interest rates aren’t nearly that volatile

-15

-10

-5

0

5

10

15

1/1/9

9

1/8/9

9

1/15

/99

1/22

/99

1/29

/99

2/5/9

9

2/12

/99

2/19

/99

2/26

/99

3/5/9

9

3/12

/99

3/19

/99

3/26

/99

4/2/9

9

4/9/9

9

4/16

/99

4/23

/99

4/30

/99

Brazilian Real to USD daily % change

But before going there, let’s note a couple of things

• Exchange rates are often much more volatile than the underlying fundamentals

– FX rates sometimes change by 10% a day. Inflation rates and interest rates aren’t nearly that volatile

• The volume of FX trading is far in excess of the amount demanded for transactions purposes.

Average Daily Turnover in billions of US dollarsNotional Amounts for Derivatives

520 590

670900

810

1260688

959

853

1292

390 620

0

500

1000

1500

2000

2500

3000

3500

April 1995 April 1998 April 2001 April 2004

Spot TransactionsOutright Forwards & SwapsOTC Derivative Instruments

590820

Source: Bank for International Settlements Central Bank Survey 2004

The Magnitude of the Global Foreign Exchange Market

• This must mean that the hour-to-hour/day-to-day prices for FX are being shaped by speculators and arbitragers who are trying to anticipate changes and take profits.

• But this certainly doesn’t mean the market is being manipulted

• Nor is it to say that the market is being “set” (in the long term) by forces other than these fundamentals.

The parity conditions give us a starting point to answer some important questions:

– Are changes in exchange rates predictable?– How are exchange rates related to interest rates?– What, at least theoretically, is the “proper”

exchange rate?

What is, at least theoretically, the “proper” exchange rate?

• This is given by our first “parity” relationship

PURCHASING POWER PARITY (PPP) • Provides a benchmark to suggest the levels that

exchange rates should achieve. • Starts with the “Law of One Price”

The law of one price

• A identical good should cost the same in all markets

Absolute Purchasing Power Parity

• Suppose that– gold is selling in the US for P$/oz=$300– gold is selling in Europe for P€/oz=€240. – the spot exchange rate is S$/€ =1.25– This means the dollar price of gold purchased in Europe is

S$/€ P€/oz = $300• The law of one price says that the dollar price of a good like

gold should be same no matter where you buy it (except maybe for some differences due to transactions costs that we’ll talk about later). Thus

S$/€ P€/oz = P$/oz

Relative Purchasing Power Parity, Inflation and Exchange Rates

• Suppose that in December, 2000 gold was selling for $300 and €240– Formally P0

$/oz=$300 and P0€/oz = € 300.

• Suppose that the US inflation rate in 2001 was 5% and the European inflation rate was 10%.– Formally Ius=5% and Ieurope=10%

• This means we expect that in 2001 gold should sell for $315=300x(1+.05)• €262=240x(1+.1)

– Formally, P1$/oz =P0

$/oz (1+IUS) and P1€/oz= P0

€/oz (1+Ieurope)• A bit of algebra shows that

S1d/f/S0

d/f = (1+Id)/(1+If)Or very nearly

$ change in Spot rate = Id - If

Relative Purchasing Power Parity

• Key insight: Relative PPP focus on changes in the exchange rate, not levels

• Key Prediction: Relative PPP says domestic and foreign inflation determine the dynamics of the spot exchange rate.

Rate of change in S = Domestic inflation – Foreign Inflation

Stated another way

e = ΠU.S. - ΠFor

Who came up with PPP and why?

• Our First Famous Dead Guy: Gustav Cassel

• He popularized PPP in the 1920s to explain

what was going on in the world at that time

• In those years, many countries (Germany,

Hungary, and the Soviet Union) had experienced

Hyperinflation.

• As the purchasing power of these countries sharply declined, the same currencies also depreciated sharply against stable currencies like the U.S. dollar

• PPP became popular then, how about now (think Latin America)

Purchasing Power Parity: Caveats

• PPP conditions do not imply anything about causal linkages between prices and exchange rates or vice versa.

• Both prices and exchange rates are jointly determined by other variables in the economy.

• PPP is an equilibrium condition that must be satisfied when the economy is at its long-term equilibrium.

• It does, however, give us a powerful tool if it holds!

Does PPP hold?

• Let’s test absolute PPP first.• How would devise a test of absolute PPP?• The most famous test of absolute PPP is The

Economist magazine's

Big Mac Index

Burgernomics: The Big Mac Index

• The Economist’s Big Mac index was first launched in 1986 as a gastronome’s guide to whether currencies were at their correct exchange rate.

• Examines the price of a common good (the Big Mac) worldwide.

Burgernomics: The Big Mac Index

• Before we get serious, some little known Big Mac Triva– By 1996, you could get one in 80 countries– In China, it is know as Juwuba, “big with no

equal”– In Moscow and Beijing, the McDonalds has over

700 seats and 30 registers

$3.06: Average of NY, Chicago, SF

2.92 Euros: Price of Big Mac in Euro member countries, which at current FX rate of 1.22 is 3.58

S=3.06/2.92=1.05

However, actual exchange rate is 1.22, so Euro is overvalued 17%

Overall, we can get a Big Mac for really cheap in countries like China, Malaysia, Thailand, Philippines

However, it costs 5.05 USD for one in Switzerland

So, it implies that Switzerland has the most overvalued currency and the others the most undervalued

For a short video on the Big Mac index

• http://www.economist.com/media/audio/burgernomics.ram

That’s just one good: Can you think of another item that is available just about anywhere?

Available in 32 countries.

Average price in US (2004) was $2.80 (about the same as a big mac)

The Tall-Latte IndexThe Tall-Latte Index

Burgers or Beans?• Do we see the same story?

• The tall-latte index tells broadly the same story as the Big Mac index for most main currencies

• Where the two measures differ is in Asia: In China, it is 56% undervalued according to the Big Mac, but spot on its dollar PPP according to our Starbucks index. If so, American manufacturers have no grounds to complain about the yuan. The pricing differences probably reflect different competition in the markets for the two products.

Even more fun with Burgernomics

• Working time needed to buy a Big Mac

• It aims to measure well-being by estimating how many minutes workers in various countries must toil to buy a Big Mac.

• In Kenya, UBS says that it takes just over three hours of labor for a typical worker to afford one of McDonald's hefty burgers.

• Americans, lucky for them, need to work for only ten minutes. Such differences reflect variations in productivity as well as disparities in local costs of ingredients.

Another application: The Big Mac Index of Cigarette Affordability

• In calling for increases in tobacco tax, tobacco control advocates often find it useful to compare cigarette prices internationally with those in their own country.

• To do this, they must somehow convert prices in other countries using a standard measure, most commonly the price in $US. Exchange rates, however, may be influenced by many factors including inflation differentials, monetary policy, balance of payments, and market expectations

• The Big Mac index of cigarette affordability provides a reasonable estimation of relative affordability of cigarettes

The Big Mac Index of Cigarette Affordability

Burgernomics (cont.)

• While originally introduced as a bit of fun, it has inspired several serious studies

Burgernomics (cont.)

Pakko and Pollard (1996) conclude thatBig Mac PPP holds in the long run, but currencies can deviate from it for lengthy period. They note several reasons why the Big Mac index may be flawed

1. The absolute version of PPP assumes there are no barriers to trade. • High prices in Europe, Japan and South

Korea partly reflect high tariff’s on beef. Differences in transport costs also matter: shipping lettuce and beef is expensive

Burgernomics (cont.)

2. Prices are distorted by taxes

High rates of VAT in countries such as Denmark and Sweden exaggerate the degree to which their currencies are overvalued

3. Profit margins vary amount countries according to competition

In the US, we have the Whopper, other countries do not have a close substitute

Testing PPP

As measured by relative inflation rates

Currencies with the largest relative decline (gain) in purchasing power saw the sharpest erosion (appreciation) in their foreign exchange rate

Despite often lengthy departures from PPP, there is a clear correspondence between relative inflation rates and changes in nominal exchange rates

Despite often lengthy departures from PPP, there is a clear correspondence between relative inflation rates and changes in nominal exchange rates

Next , we look at other parity relationships that provide insights into what determines FX ratesNext , we look at other parity relationships that provide insights into what determines FX rates2

1

The Final Word on PPP

Real Exchange Rates

• The “real” value of any price is just the actual value (nominal value) adjusted for inflation. That is, you can tell whether the relative value of the price has gone up or down

• The “real” exchange rate accounts for the relative inflation in each country

Sreal = Snominalx(1+If)/(1+Id)

Real Exchange Rates (an Example)

Mexico US Spot Rate

Year Price Index Inflation Rate

Price Index Inflation Rate

Nominal Real

1999 100 100 0.1 0.1

2000 115 15% 105 5% 0.09 0.0986

2001 124.2 8% 109.2 4% 0.09 0.1024

•Suppose that in 1999, a week in Aqcupulco cost MXP 10,000 and week in Miami cost $1000. The two trips cost the same (MXP 10,000 = $1000)•Suppose in 2000, the cost of the two trips rose by the inflation rates within each country. The Mexican vacation costs MXP 11,500 and the US vacation cost $1,050. •In fact the Mexican trip has actually gone down in price (MXP 11,500=11,500x.09=$1,035). This is consistent with the decline in the real exchange rate (from .10 to .0986).•See if you can show why the trip has gone up in price in 2001.)

Fisher Equation:

• Nominal interest rate ( r ) compensates for “real” time value of money (r*) plus Inflation (I)

• Thus, if there were no inflation a unit of currency invested today should grow by the r* to become (1+r*)

• If there were inflation, that amount should grow by the inflation rate (1+r)=(1+r*)(1+I) (note: if r and I are fractions, this is very close to saying r = r*+I)

• for example if the inflation rate is 10% and the real time value is 2%, a dollar today should grow to 1.02x1.1=$1.122

Irving Fisher (1867-1947)

This Yale economist was an eccentric and colorful figure.  When Irving Fisher wrote his 1892 dissertation, he constructed a remarkable machineequipped with pumps, wheels, levers and pipes in order to illustrate his price theory. Socially, he was an avid advocate of eugenics and health food diets.   He  made a fortune with his visible index card system - known today as the rolodex - and advocated the establishment of an 100% reserve requirement banking system   His fortune was lost and his reputation was severely marred by the 1929 Wall Street Crash, when just days before the crash, he was reassuring investors that stock prices were not overinflated but, rather, had achieved a new, permanent plateau

International Fisher Equation

• Rearranging terms from the Fisher Equation we get (1+rd)/(1+Id)=(1+r*)

• The Law of One Price suggests that the real value of money should be the same anywhere– (no matter what the nominal rate, the real rate should be r*).

• Thus, Law of One Price implies (1+rd)/(1+Id)=(1+r*)= (1+rf)/(1+If)

or(1+rd)/((1+rf )=(1+Id)/(1+If)

• But then the relative purchasing power relation would imply thatS1/S0=(1+Id)/(1+If)= (1+rd)/((1+rf )

• That is, the ratio between the expected future spot rate and the current spot rate is determined by the ratio of the relative returns between the two countries.

Question: Do We Believe in the International Fisher Relation?

• This is really like asking real returns tend to be the same across countries

• Yes: The world is full of greedy, grasping MBA’s. If the Law of One Price didn’t hold, then there is a profit opportunity that these people would spot and quickly eliminate.

• No: The world is full of blockheads and bureaucrats. Ignorance and red tape erect all sorts of barriers that prevent the Law of One Price from holding.

Interest Rate Parity: Simple Example• Suppose you want to invest $100,000 for one year.

• Option I: Buy a $100,000 certificate of deposit from a US bank that pays rus

• Option II. Convert your $100,000 into Canadian $’s and buy a CD from a Canadian bank that pays rc.

– The two options are hard to compare since you don’t know what the exchange rate will be in one year, when you cash in the Canadian CD. But

• To eliminate the uncertainty about the future exchange rate, sell the C$’s on the forward market.

• Suppose S$/c$=.80

– F$/C$1=.80.

– rus = 5%

– rcan=10%

• This is a no-brainer. Why?

Interest Rate Parity: Conclusion– If US rates are 5%, $100,000 will yield $105,000 in one year

• Option 2 (Invest abroad):

– Convert at the spot rate to obtain 1/Sd/f units of the foreign currency

– ( if S$/c$ = .80 , then $100,000=100,000/.80= C$125,000 )

– Investing that amount in the foreign country, will yield (1/Sd/f)x(1+rf) in one year

– If Canadian rates are 10%, you will have C$137,500=125,000x1.1 in one year

– Sell the amount of the currency you expect to receive in the forward market, thereby guaranteeing that you will end up with Fd/f(1/Sd/f)x(1+rf) units of the domestic currency.

– If F$/C$=.7636, you will have $105,000=.7636x137,500

• All things equal, the two amounts must be the same. That is

• (Fd/f/Sd/f)=(1+rd)/(1+rf)

• if F$/C$=.80, investing in Canada would have yielded

$110,000=.8x137,500.

Interest Rate Parityin a Perfect Capital Market

• IRP draws on the principle that in equilibrium, two investments exposed to the same risks must have the same returns.

• Suppose an investor puts $1 in a US$ security. At the end of one period, wealth = $1 (1 + i$)

• Alternatively, the investor can put the $1 in a UK£ security and cover his or her exposure to UK£ exchange rate changes. At the end of one period, wealth =

1,£10.1

1$ tt

FiS

Interest Rate Parityin a Perfect Capital Market

• In a perfect world, the two investments would yield the same return and so

$1,£ 11$10.1

1$ iFiS t

t

£

£$1,

1

i

ii

S

SF

t

tt

forward premium = % interest differential

Why Do We Think IRP Might Be True?

• Think about what happens in the first example given above (rus=5%, rcan=10%, S$/C$ = F$/C$ =.80).

• As we’ve already seen, investors will start to favor investments in Canada. As this happens:– Canadian interest rates fall and US rates go up (the ratio of the relative

discount factors gets bigger)– The spot rate goes up as investors sell US dollars and buy Canadian dollars.– The Forward rate goes down (remember the investors would be selling C$’s in

the forward market)• Notice how all of these market forces would drive the various factors back into the

alignment described by the interest rate parity condition. • But this isn’t exactly an “arbitrage” condition since we haven’t seen how someone

could make an instant profit by taking advantage of the imbalance. If there were such an arbitrage condition, it would be true that the IRP condition would almost continually hold. (If not, the arbitrageur would take a profit..) In fact, there is an arbitrage condition

•

Covered Interest Arbitrage. (Example)

• Suppose you got an e-mail from your broker advising that you could borrow or lend in US dollars at rus=5% or borrow or lend in euros reuro=8%.

• You are further advised that you can you can buy or sell currency at a spot rate of S=1.25 and a one-period forward rate of F =1.2125.

• Good News!!! • Borrow 1 euro at 8%, noting that this obligates you to pay 1.08 euro in one

year.• Since you know you will owe the euro, buy this amount in the forward

market (obligating you to pay 1.08x1.2125 = $1.3095) • Convert that 1 euro into $1.25• Lend at 5% (claiming $1.3125)• In one year you will have $1.3125-1.3095 = .0030• Repeat several billion times

The Forward Rate Unbiased Condition

Forward Rate Unbiased

Today’s forward premium (for delivery in n days)equals the expected percentage change in the spot rate

(over the next n days).

ttntttt SSSESSF ~

Driving force: Market players monitor the difference between today’s forward rate (for delivery in n days) and their expectation of the future spot rate

(n days from today).

Foreign Rate as Unbiased Predictor of Future Spot Rate

The Forward Rate Unbiased Condition

If UIP does not holds:

• Positions in different currencies can lead to profit opportunities– Could imply market inefficiency

Empirical Evidence:

•Early studies were supportive

•Recent studies are not

•People are willing to pay for FX advisors

•More when we get to Market Efficiency

OK, ENOUGH ALREADY: What are the takeaways from the Parity Conditions?

1. When IRP holds, the covered cost of funds is identical across all currencies and the covered return on funds is identical across all currencies; there are neither bargains or nor bad deals on a covered basis.

2. When the International Fisher Effect Holds, the expected cost of borrowed funds is identical across currencies and the expected return on invested funds is identical across currencies on an uncovered basis. 1. Some currencies may have high nominal interest rates

and others may have low nominal interest rates, but when the expected exchange rate change is taken into account, all currencies return the same nominal interest rate.