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International Parity International Finance Forward Points

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					International Finance

          Chapter 5
 Part 1: International Parity
       Relationships
         FORWARD RATES
• Involves contracting today for the future
  purchase or sale of foreign exchange.
  – Forward rate is set today!
• Forward rate can be:
  – Equal to spot (flat)
  – Worth more than spot (premium)
  – Worth less than spot (discount)
    EXAMPLES OF FORWARD
           RATES
• Wednesday, June 4, 2004
• American Terms
  – U.K. (Pound)         $1.8343
     • 1 month forward   $1.8289
• European Terms
  – Japan (yen)          110.07
     • 1 month forward   109.95
   FORWARD DISCOUNTS AND
         PREMIUMS
• Is the pound selling at a forward discount
  or forward premium?
  – U.K. (Pound)           $1.8343
     • 1 month forward     $1.8289


• Answer:
  – Discount: 1 month forward is less than the
    spot by $.0054
    FORWARD PREMIUMS AND
         DISCOUNTS
• Is the Japanese yen selling at a forward
  premium or forward discount?
  – Japan (yen)           110.07
     • 1 month forward    109.95

• Answer:
  – Premium: Dollar is selling at a discount; with the 1
    month forward less than the spot by .12 yen.
  – Convert to American terms (110.07 = $.009085;
    109.95 = $.009095). Yen 1 month forward is worth
    $.000010 more than the spot.
     WHAT DETERMINES THE
       FORWARD RATE?
• What does NOT determine forward rate:
  – Market’s expectation about where spot rate
    will be in the future.
• What does determine forward rate:
  – Assuming no capital controls, in equilibrium
    the rate represents the difference in interest
    rates between the two currencies in question.
     INTEREST RATE PARITY
• Interest rate parity theory provides a linkage
  (and explanation) between international money
  markets and (forward) foreign exchange
  markets.

• The theory states that the difference in the
  national interest rates for securities of similar risk
  and maturity should be equal to, but opposite in
  sign to, the forward rate discount or premium for
  the foreign currency (except for transaction
  costs)
                      EXAMPLE
• Assume a US dollar-based investor has $1 million to
  invest for 90 days and can select from two
  investments:
   – Invest in the U.S. and earn 4.0% p.a.
   – Invest in Switzerland and earn 8.0% p.a.
• Problem with Swiss franc investment:
   – Uncertainty about the future spot rate, or what if the franc
     depreciates against the dollar!
• Solution for investor:
   – Cover the Swiss franc investment by selling the Swiss francs
     anticipated from the investment forward 90 days.
   – But what will the forward rate be?
     FORWARD RATE UNDER
     INTEREST RATE PARITY
• In equilibrium, the forward rate must settle
  at a rate to offset the interest rate
  differential between the two currencies in
  question.
• This is to insure that the two investments
  will yield similar returns.
  – To prevent covered interest arbitrage
    opportunities!!!
COVERED INTEREST ARBITRIGE
• Assume:
  – 90 day Interest rate in U.S. is 4%
  – 90 day Interest rate in Switzerland is 8%
• Assume the spot rate and the 90 day forward
  rate are the same
• A U.S. investor could invest in Switzerland, and
  cover (sell francs forward) and obtain a (foreign
  exchange) riskless return of 8% which is 400
  basis points greater than investing in the U.S.
• This is covered interest arbitrage!
              EQUILIBRIUM
• In equilibrium the forward rate will price the
  currency to offset the interest rate differential.
• In the previous example, the “correct” 90 day
  forward Swiss franc rate will be at a discount of
  4% of its spot.
• When the U.S. investor covers, the 8% Swiss
  return is reduced by the 4% discount, resulting in
  a covered return of 4%.
                VIEWING IRP
                   i $ = 4.00 % per annum
                     (1.00 % per 90 days)
    Start                                       End
  $1,000,000                1.01             $1,010,000

                    Dollar money market        $1,010,000



S = SF 1.4800/$            90 days           F90 = SF ?/$


                  Swiss franc money market

 SF 1,480,000               1.02             SF 1,509,600


                   i SF = 8.00 % per annum
                      (2.00 % per 90 days)
                EQUILIBRIUM
                   i $ = 4.00 % per annum
                     (1.00 % per 90 days)
    Start                                        End
  $1,000,000                1.01              $1,010,000

                    Dollar money market        $1,010,000



S = SF 1.4800/$            90 days           F90 = SF 1.49465/$



                  Swiss franc money market

 SF 1,480,000               1.02             SF 1,509,600


                   i SF = 8.00 % per annum
                      (2.00 % per 90 days)
  HOW IS THE FORWARD RATE
        CALCULATED?
• The forward rate is calculated from three
  observable elements:
  – The (current) spot rate
  – The foreign currency deposit rate
  – The home (U.S.) currency deposit rate
 FORWARD RATE FORMULA
                             FC    N 
                        1   i x 360 
                                       
      FC/$
     Fn     SFC/$   x
                              $    N 
                         1   i x 360 
                                      

• Where:
  Fn = forward rate (FC/$), n business days in the future.
  S = spot rate (FC/$)
  N = number of days in forward contract
  iFC = interest rate on foreign currency deposit
  i$ = interest rate on U.S. dollar deposit
                   EXAMPLE
• Assume:
  – Current Yen Spot rate = ¥120.0000
  – 90 day dollar rate = 2.0%
  – 90 day yen rate = .5%
• Calculate the 90-day yen forward rate

                                FC    90 
                           1   i x 360 
                                          
    FFC/$
            S   FC/$
                        x
                                      90 
     90
                                  $
                            1   i x 360 
                                         
                        SOLUTION
                  FC 90                                           90 
                 1   i x 360                       
                                                              
                                                          1   .005x      
                                                                  360 
F90  SFC/$                                           x                     
 FC/$
              x                        F90  S120/$
                                        FC/$

                   $ 90                                           90 
                  1   i x 360                       1   .020 x 360 
                                                                         
                               


                      1 .00125 
FFC/$
 90     S
         120/$
                 x
                        1.005        F FC/$
                                         90       119.5522
   SOLUTION TO SWISS FRANC
          EXAMPLE
• Recall, the following information about the Swiss
  franc example:
  – Swiss franc spot rate of Sfr1.4800/$,
  – a 90-day Swiss franc deposit rate of 8.00%
  – a 90-day dollar deposit rate of 4.00%.
                                               
                         
                            1  0.08 x
                                 
                                 
                                        90 
                         
                         
                                 
                                       360 
                                                       Sfr1.4800 x 1.02  Sfr1.4947/$
                                 
  FSfr/$  Sfr1.4800 x   
                                                 
   90                    
                                              
                                                                   1.01
                         
                         
                             1  0.04 x 90
                                 
                                 
                                 
                                                
                                                
                                                
                         
                         
                                 
                                 
                                        360     
                                                
                                                 
        COVERED INTEREST
           ARBITRAGE
• If the forward rate is not correct, the
  chance of covered interest arbitrage
  exists.
• Generally, these situations will not last
  long
• As the market takes advantage of them,
  equilibrium will be restored.
                           EXAMPLE
                                i $ = 4.00 % per annum
                                  (1.00 % per 90 days)
           Start                                                     End
         $1,000,000                      1.01                     $1,010,000

                                 Dollar money market               $1,020,000*



       S = SF 1.4800/$                  90 days                  F90 = SF 1.4800/$



                              Swiss franc money market

         SF 1,480,000                    1.02                    SF 1,509,600


                               i SF = 8.00 % per annum
                                  (2.00 % per 90 days)

•Assume the forward rate is 1.48. Then, the covered Swiss investment yields $1,020,000,
 $10,000 more than the U.S. investment.
  USING IRP TO FORECAST
• While the forward rate under the
  assumption of the Interest Rate Parity
  model assumes:
  – The forward rate simply represents interest
    rate differentials
  – And NOT the market’s view of the future spot
    rate.
• Some forecasters do use this model to
  forecast future spot rates.
         Forward Rates as an
          Unbiased Predictor
• Some forecasters believe that the forward rate is
  an “unbiased” predictor of the future spot rate.
• This is roughly equivalent to saying that the
  forward rate can act as a prediction of the future
  spot exchange rate, but
   – it will generally “miss” the actual future spot
     rate
   – and it will miss with equal probabilities
     (directions) and magnitudes (distances) which
     offset the errors of the individual forecasts!
Forward Rates: Unbiased Predictor
  Exchange rate


                           S2                    F2


                                     Error                Error
    S1                                                                 F3

                           F1                     S3                            Error



                                                                       S4

                                                                                         Time
         t1                     t2                 t3                   t4
The forward rate available today (Ft,t+1), time t, for delivery at future time t+1, is used as a
“predictor” of the spot rate that will exist at that day in the future. Therefore, the forecast spot
rate for time St2 is F1; the actual spot rate turns out to be S2. The vertical distance between the
prediction and the actual spot rate is the forecast error. When the forward rate is termed an
“unbiased predictor,” it means that the forward rate over or underestimates the future spot rate
with relatively equal frequency and amount, therefore it misses the mark in a regular and orderly
manner. Over time, the sum of the errors equals zero.
           Other Parity Models
• Two other important parity models are:

• Purchasing Power Parity
   – Exchange rate between two countries should be
     equal to the ratio of the two countries price level.
   – The change in the exchange rate will be equal to the
     difference in inflation.
• International Fisher Effect
   – The change in the exchange rate will be equal to the
     difference in the nominal interest rate between two
     countries.
       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
    being equal (i.e., no transaction costs or other
    frictions) a product’s price should be the same
    in all markets (countries).
  – Why? The principle of competitive markets
    assumes that prices will equalize if costs of
    moving such goods does not exist.
        LAW OF ONE PRICE
• When prices for a particular product are
  expressed in different currencies, the law
  of one price states that after adjusting for
  exchange rates, prices will be the same.

• Example (U.S. and Japan):
  – The price of a product in US dollars (P$), multiplied by
    the spot exchange rate (S = yen per dollar), equals
    the price of the product in Japanese yen (P¥), or:

                    P$  S = P¥
               EXAMPLE
• If a Big Mac costs $2.00 in the United
  States and if the current spot rate is ¥110,
  then the Law of One Price would suggest
  a price in Japan of:

• $2.00 x ¥111 = ¥222.00
     PPP EXCHANGE RATE
• Conversely, if the prices for similar goods
  were known in local currencies, the
  appropriate (PPP) spot exchange rate (S)
  could be calculated from relative product
  prices, or

• Spot PPP rate = Foreign Price/Home Price
        PPP Example: Sept 11, 2003
•   Big Mac: Boulder, Colorado: $2.29
•   Big Mac: Osaka, Japan:      ¥250
•   PPP Exchange Rate = Yen Price/Dollar Price
•   PPP Exchange Rate = ¥250/$2.29 = ¥109.17
•   The PPP rate can be compared to the actual rate,
    and if:
    –   Actual > PPP = currency may be undervalued!
    –   Actual < PPP = currency may be overvalued!
    –   Rate on September 11, 2003 = 117.1240
    –   Thus, this model suggested the yen was undervalued at
        that time (or dollar was overvalued).
          ABSOLUTE PPP
• The “absolute” PPP measures the
  “correctness” of the current spot rate on
  the bases of similar goods in different
  countries.
• A popular version of the absolute PPP
  technique is found in the Economist “Big
  Mac” index.
  Big Mac Index: Explanation From
      the Economist Magazine
• “Burgernomics is based on the theory of purchasing-
  power parity, the notion that a dollar should buy the
  same amount in all countries.
• Thus in the long run, the exchange rate between two
  countries should move towards the rate that equalizes
  the prices of an identical basket of goods and services in
  each country.
• The Economist "basket" is a McDonald's Big Mac, which
  is produced in about 120 countries.
• The Big Mac PPP is the exchange rate that would mean
  hamburgers cost the same in America as abroad.
• Comparing actual exchange rates with PPPs indicates
  whether a currency is under- or overvalued.”
      Big Mac Index Web Site
• The Economist Magazine publishes their Big
  Mac Index twice a year.
  – http://www.economist.com/markets/Bigmac/Index.cfm


• Currently the index (May 27, 2004) suggests:
  – Swiss franc: PPP = 2.19; actual = 1.25
     • World’s most overvalued currency!
  – Philippine peso: PPP = 23.8; actual = 55.8
     • World’s most undervalued currency!
        OECD PPP MEASURES
• A more comprehensive measure of a country’s
  PPP is provided by the OECD for 30 member
  countries. It can be found on the following web-
  site:
• http://www.oecd.org/home/

• Or:

• http://www.oecd.org/department/0,2688,en_264
  9_34357_1_1_1_1_1,00.html
           RELATIVE PPP
• The relative Purchasing Power Parity
  model is concerned with the “rate of
  change” in the exchange rate.
• Model suggests that the percent change in
  the exchange rate should be equal to the
  difference in the rates of inflation between
  countries, or
   % change in FX rate = Home inflation rate –
   Foreign inflation rate.
   RELATIVE PPP EXAMPLE
• Assume the following:
  – Annual rate of inflation in U.S. = 2.0%
  – Annual rate of inflation in U.K. = 3.0%
• The British pound should depreciate 1%
  per year against the U.S. dollar.
• If the current rate is $1.80, then
  – 1 year from now the rate should be: $1.7820
  – 2 years from now the rate should be: $1.7642
  – Etc….
       TESTS OF THE PPP
• The existing empirical tests of the PPP
  have proved disappointing.
• Generally the results do not support the
  PPP.
• However, PPP can still provide us with a
  “benchmark” test of whether a currency is
  overvalued or undervalued against other
  currencies.
     INTERNATIONAL FISHER
           EFFECT
• The last major parity model is the
  International Fisher Effect.

• Begins with the Fisher Effect:
  – A change in the expected rate of inflation will
    result in a direct and proportionate change in
    the market rate of interest.
             FISHER EFFECT
• Market rate of interest is comprised of two
  components:
  – Real rate requirement
     • Relates to the real growth rate in the economy
  – Expected rate of inflation


• Real rate requirement is assumed to be
  relatively stable
• Thus, changes in market interest rates occur
  because of changes in expected inflation!
  FISHER EFFECT EXAMPLE
• Assume the following:
  – real rate requirement is 3.0%
  – Expected rate of inflation is 1.0%
• Under these conditions, the market
  interest rate would be 4%
• If the expected rate of inflation increases
  to 2.0%, the market interest rate would
  rise to 5%.
      FISHER EFFECT DATA
                CPI Forecast    2 Year Gov’t
Country         2004 2005       Bond Rate

Australia       +2.2%   +2.5%   5.27%
U.S.            +1.9%   +1.8%   2.45%
Switzerland     +0.7%   +0.4%   1.13%
Japan           -0.1%    nil    0.14%

Forecast: The Economist Poll,
Date: May 29, 2004
FISHER EFFECT ASSUMPTIONS
• Model assumes that the real rate requirement is
  the same across countries.
• Thus market interest rate differences between
  counties is accounted for on the basis of
  differences in inflation expectations.
• If the interest rate is 5% in the U.S. and 7% in
  the U.K. then:
  – The expected rate of inflation is 2% higher in the U.K.
      INTERNATIONAL FISHER
            EFFECT
• Changes in exchange rates will be driven by
  differences in market interest rates between
  countries.
• Because differences in interest rates capture
  differences in expected inflation.
  – High interest rate countries (due to high expected
    rates of inflation) will experience currency
    depreciation.
  – Low interest rate countries (due to low expected rates
    of inflation) will experience currency appreciation.
      INTERNATIONAL FISHER
         EFFECT EXAMPLE
• Using interest rate data from Bloomberg’s
  web site (rates and bonds):
  – http://www.bloomberg.com/markets/index.html


• 2 year U.S. Government rate         2.65%
• 2 year Japanese Government rate: 0.14%
• Higher U.S. rate is accounted for on the basis of
  higher expected U.S. inflation:
• 2.65 – 0.14 = 2.51
  EXCHANGE RATE CHANGE
• Given the expected inflation differences,
  the yen will appreciate 2.51% per year.
• Current spot rate 110.
• Spot rate 1 year from now: 107.239
• Spot rate 2 years from now: 104.547
• Etc…

				
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