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Lecture 4 _b_ ppp and parity


									Lecture 4 (b)
    Foreign Exchange Rates and International Parity

•   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

                                               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.
              The Magnitude of the Global Foreign Exchange Market
                   Average Daily Turnover in billions of US dollars
                         Notional Amounts for Derivatives

         3500           Spot Transactions
         3000           Outright Forwards & Swaps
         2500           OTC Derivative Instruments                              1292

         2000                                  959
         1500             688
         1000             670
                          520                  590          820       390
              0                      590
                      April 1995           April 1998           April 2001   April 2004

Source: Bank for International Settlements Central Bank Survey 2004
• 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

•    This is given by our first “parity” relationship
•    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

• 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/S0d/f = (1+Id)/(1+If)
                                 Or very nearly
                        $ change in Spot rate = Id - If
            Relative Purchasing Power Parity

               Stated another way
Rate of change in S = Domestic inflation – Foreign Inflation

               e=       ΠU.S. - ΠFor

      • 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.
          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
• 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
       Purchasing Power Parity: Caveats
• PPP conditions do not imply anything about causal
  linkages between prices and exchange rates or vice
• 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
• 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)
       Burgernomics: The Big Mac Index

• Before we get serious, some little known Big Mac
   – By 1996, you could get one in 80 countries
   – In China, it is know as Juwuba, “big with no
   – In Moscow and Beijing, the McDonalds has over
     700 seats and 30 registers
$3.06: Average
of NY, Chicago,

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


 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,
However, it costs 5.05
USD for one in
So, it implies that
Switzerland has the most
overvalued currency and
the others the most
       For a short video on the Big Mac index

 That’s 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)
                     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

• 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
• 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

• 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 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
      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
        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
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
            The Final Word on PPP

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

    Next , we look at other parity relationships that
2   provide insights into what determines FX rates
                   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   Price Index    Inflation   Nominal           Real
                              Rate                       Rate
 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
•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 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
                 International Fisher Equation

• Rearranging terms from the Fisher Equation we get
• 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)
                          (1+rd)/((1+rf )=(1+Id)/(1+If)
• But then the relative purchasing power relation would imply that
                       S1/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
    Question: Do We Believe in the International Fisher

• 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
• Option II. Convert your $100,000 into Canadian $’s and buy a CD from a
  Canadian bank that pays rc.
   – The two options are hard to compare since you don’t know what the
      exchange rate will be in one year, when you cash in the Canadian CD.
• To eliminate the uncertainty about the future exchange rate, sell the C$’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/S d/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
                Interest Rate Parity
            in 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  i£   Ft ,1
                Interest Rate Parity
            in a Perfect Capital Market

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

                   1  i£   Ft ,1  $1 1  i$ 

                     Ft ,1  S t     i$  i£
                                  
                         St          1  i£

         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
     – 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
• 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
• 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).

          Ft  St           
                       St  E St n  St St
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
  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.

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