Lecture 4 (b)

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Lecture 4 (b)
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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

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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)

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Now Were Going to Try and More Carefully
Describe How These Fundamentals Shape Price
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But before going there, lets 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 arent nearly
  that volatile

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Brazilian Real to USD daily change
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But before going there, lets 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 arent nearly
  that volatile
• The volume of FX trading is far in excess of the
  amount demanded for transactions purposes.

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The Magnitude of the Global Foreign Exchange
Market
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• 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 doesnt 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.

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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?

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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

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The law of one price

• A identical good should cost the same in all
  markets

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Absolute Purchasing Power Parity

• Suppose that
• gold is selling in the US for P/oz300
• gold is selling in Europe for P/oz240.
• 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 well
  talk about later). Thus
• S/ P/oz P/oz

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Relative Purchasing Power Parity, Inflation and
Exchange Rates

• Suppose that in December, 2000 gold was selling
  for 300 and 240
• Formally P0/oz300 and P0/oz 300.
• Suppose that the US inflation rate in 2001 was 5
  and the European inflation rate was 10.
• Formally Ius5 and Ieurope10
• This means we expect that in 2001 gold should
  sell for 315300x(1.05)
• 262240x(1.1)
• Formally, P1/oz P0/oz (1IUS) and P1/oz
  P0/oz (1Ieurope)
• A bit of algebra shows that
• S1d/f/S0d/f (1Id)/(1If)
• Or very nearly
• change in Spot rate Id - If

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Relative Purchasing Power Parity
Stated another way
Rate of change in S Domestic inflation
Foreign Inflation

• 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.

e ?U.S. - ?For
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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)

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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!

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Does PPP hold?

• Lets 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
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Burgernomics The Big Mac Index

• The Economists Big Mac index was first launched
  in 1986 as a gastronomes guide to whether
  currencies were at their correct exchange rate.
• Examines the price of a common good (the Big Mac)
  worldwide.

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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

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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
S3.06/2.921.05
However, actual exchange rate is 1.22, so Euro is
overvalued 17
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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
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For a short video on the Big Mac index

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

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Thats just one good Can you think of another
item that is available just about anywhere?
The Tall-Latte Index
Available in 32 countries. Average price in US
(2004) was 2.80 (about the same as a big mac)
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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.

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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.

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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

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The Big Mac Index of Cigarette Affordability
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Burgernomics (cont.)

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

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Burgernomics (cont.)

• Pakko and Pollard (1996) conclude that
• Big 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
• The absolute version of PPP assumes there are no
  barriers to trade.
• High prices in Europe, Japan and South Korea
  partly reflect high tariffs on beef. Differences
  in transport costs also matter shipping lettuce
  and beef is expensive

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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

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Testing PPP
Currencies with the largest relative decline
(gain) in purchasing power saw the sharpest
erosion (appreciation) in their foreign exchange
rate
As measured by relative inflation rates
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The Final Word on PPP
Despite often lengthy departures from PPP, there
is a clear correspondence between relative
inflation rates and changes in nominal exchange
rates
1

• Next , we look at other parity relationships that
  provide insights into what determines FX rates

2
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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(1If)/(1Id)

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Real Exchange Rates (an Example)
Mexico Mexico US US Spot Rate 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 11,50011,500x.091,035). 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.)

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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 (1r)
• If there were inflation, that amount should grow
  by the inflation rate (1r)(1r)(1I) (note if
  r and I are fractions, this is very close to
  saying r rI)
• for example if the inflation rate is 10 and the
  real time value is 2, a dollar today should grow
  to 1.02x1.11.122

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• Irving Fisher (1867-1947)

This Yale economist was an eccentric and colorful
figure.  When Irving Fisher wrote his 1892
dissertation, he constructed a remarkable machine
equipped 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
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International Fisher Equation

• Rearranging terms from the Fisher Equation we get
• (1rd)/(1Id)(1r)
• 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
• (1rd)/(1Id)(1r) (1rf)/(1If)
• or
• (1rd)/((1rf )(1Id)/(1If)
• But then the relative purchasing power relation
  would imply that
• S1/S0(1Id)/(1If) (1rd)/((1rf )
• 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.

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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
  MBAs. If the Law of One Price didnt 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.

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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
  dont 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 Cs on the forward
  market.
• Suppose S/c.80
• F/C1.80.
• rus 5
• rcan10
• This is a no-brainer. Why?

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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 100,000100,000/.80
  C125,000 )
• Investing that amount in the foreign country,
  will yield (1/Sd/f)x(1rf) in one year
• If Canadian rates are 10, you will have
  C137,500125,000x1.1 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(1rf) units of the domestic
  currency.
• If F/C.7636, you will have 105,000.7636x137,5
  00
• All things equal, the two amounts must be the
  same. That is
• (Fd/f/Sd/f)(1rd)/(1rf)
• if F/C.80, investing in Canada would have
  yielded 110,000.8x137,500.

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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

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Interest Rate Parityin a Perfect Capital Market

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

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Why Do We Think IRP Might Be True?

• Think about what happens in the first example
  given above (rus5, rcan10, S/C F/C
  .80).
• As weve 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 Cs 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 isnt exactly an arbitrage condition
  since we havent 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

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Covered Interest Arbitrage. (Example)

• Suppose you got an e-mail from your broker
  advising that you could borrow or lend in US
  dollars at rus5 or borrow or lend in euros
  reuro8.
• You are further advised that you can you can buy
  or sell currency at a spot rate of S1.25 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

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The Forward Rate Unbiased Condition
Forward Rate Unbiased
Todays forward premium (for delivery in n
days) equals the expected percentage change in
the spot rate (over the next n days).
Driving force Market players monitor the
difference between todays forward rate (for
delivery in n days) and their expectation of the
future spot rate (n days from today).
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Foreign Rate as Unbiased Predictor of Future Spot
Rate
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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

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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.
3. 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.