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Determinants of Exchange Rates

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					Parity Conditions


        Eiteman and Stonehill

        Chapter 4



May 16, 2012        Parity Conditions   1
Big Mac index
 The Big Mac, in real terms, should cost the
  same everywhere
 Prices increase with inflation
     prices of Big Macs in Canada increase by 1.9%
     prices of Big Macs in US increase by 2.3%
 If nothing real changes, exchange rates
  should adjust for the difference
     CD appreciates



May 16, 2012           Parity Conditions              2
The Law of one price
 The Law of One Price does not hold -
  given an exchange rate of 1.1254

 Pcd equiv, BigMac          Pusd , BigMac  ecd ,usd       
                1.005 cd
     3.41 usd                                3.43 cd
                   usd
     3.41             3.88
May 16, 2012           Parity Conditions                3
Example - the Law of One Price
 Price = 3.41 usd          in January 2007
     Expected inflation 2.7% in 2007
     Price = 3.50 usd in January 2008
 Price = 3.80 cd in January 2007
     Inflation 1.7% in 2007
     Price = 3.86 cd in January 2008
 Implied exchange rate
     3.80 cd / 3.41usd = 1.1144 cd / 1 usd   Jan 07
     3.86cd / 3.50 usd = 1.1029 cd / 1 usd   Jan 08



May 16, 2012          Parity Conditions                4
Purchasing Power Parity (PPP)
 Absolute PPP - the law of one price
     the price of any good is the same after
      adjusting for exchange rate changes and
      relative inflation rates
 Relative PPP
     exchange rates adjust to take into
      account relative inflation rates



May 16, 2012        Parity Conditions       5
Purchasing Power Parity
 Absolute parity
                                                            P x , cd
    P x , cd  e cd , usd  P x , usd                                         e cd , usd
                                                            P x , usd



 Relative parity                                                        n


    n                                 n
                                                                        
                                                                        i1
                                                                              w i  Pi , cd
        w i  Pi , cd  e cd , usd   w i  Pi , usd                   n                      e cd , usd
   i1                               i1
                                                                        
                                                                        i1
                                                                              w i  Pi , usd


May 16, 2012                                    Parity Conditions                                             6
Purchasing Power Parity
 The exchange rate changes to
  accommodate differential rates of
  inflation
     If this is so, then relative PPP holds
                  
                 eT     1.1659
                                              0.9895 
                 e0     1.1783
                                T
                1   cd 
                                                       1
                                      1.021
                                           0.9980
                1   usd          1.023 
May 16, 2012                        Parity Conditions       7
Theory behind relative PPP
 international competition in efficient
  goods markets will cause arbitrage of
  real prices of goods
 relative inflation will cause internal
  prices to change
 exchange rates will adjust for relative
  inflation so that real prices remain
  unchanged


May 16, 2012     Parity Conditions      8
PPP for forecasting
 Known: forecasts of
      Expected cd inflation,
      Expected usd inflation
 Known: the current exchange rate
      Calculate the expected future spot
      Compare to the quoted future spot
                    1
 
        1.017    12
eT                    1.0012        1.0004      1.0009
        1.027 
May 16, 2012                 Parity Conditions                 9
Relative Purchasing Power Parity
                         % chg in spot
               x




                                         % chg in relative inflation




May 16, 2012       Parity Conditions                        10
Empirical does PPP hold ?
 international goods mkts not efficient
  short run
     barriers to trade, transactions costs
     measurement problems
          indices measure changes in a market
           basket of goods, not traded goods
     differences exist in tastes, level of
      development, income
 approximately efficient in the long
  run
May 16, 2012           Parity Conditions         11
Exchange Rate pass through
 exchange rate adjusts for relative
  inflation
     relative inflation means
          some prices increase faster than inflation
          some slower
          some prices decrease
 relative real prices of goods may
  change internationally
               
               P   cd    P  ecd , usd
                           usd
May 16, 2012                 Parity Conditions          12
Real exchange rates

  n


i1
       w i  P i , usd
                                                      142.67
  n                         e cd , usd                      11783
                                                                .      
                                                      171.20
 
 i1
       w i  P i , cd


0.9819             real exchange rate index




May 16, 2012                      Parity Conditions                        13
  Real effective exchange rates



100




  May 16, 2012   Parity Conditions   14
Differential Price movements
 Calculate the expected price of
  buying US
               
         P         cd    P  ecd , usd
                           usd

 Expected greater than actual price
     if you are selling this product, you may
      face competitive pressures to lower price
                    
               P  Pcd
                   cd
May 16, 2012                  Parity Conditions   15
Price elasticity of demand
 How do the revenues of the firm react
  to changes in price
                                        d ln Q
                   %Qd
                                       dt
                   %P                  d ln P
                                          dt
 revenues decline if elasticity of own
  demand is less than 1
                                        1
May 16, 2012      Parity Conditions              16
Inelastic own demand
         P

                  Decrease in revenue
                  due to price decrease
         P0

         PT

                                 Increase in revenue
                                 due to increased sales

               Q0 QT                               Q
May 16, 2012           Parity Conditions                  17
Elastic own demand
         P

                    Decrease in revenue
                    due to price decrease
      P0
                                           Increase in revenue
      PT                                   due to increased sales




               Q0     QT                                Q
May 16, 2012           Parity Conditions                            18
The Fisher Effect
 The nominal interest rate

               i  r  
                                   r        


 relative nominal interest rates are proportional
  to relative inflation rates
                          T                        T
    1.0418  1  icd             1    
                                                        1.021
                                    cd
                                                      
                                 1  
                                         
    1.0533 1  iusd                    usd            1.023

               0.9891  0.9980
May 16, 2012         Parity Conditions                      19
Empirical evidence
 capital market integration
     real returns are equal across economies
     efficient capital markets will arbitrage
      differences
 capital market segmentation
     investor preferences may lead to real
      interest rate differentials
     each economy is a separate market


May 16, 2012        Parity Conditions            20
International Fisher Effect
 expected future spot should
  accommodate any interest rate
  differentials
                                        T
               1  icd 
                                                  1
  1.1659 eT                1.0418 
                             
  1.1783 e0   1  iusd   1.0533 

               0.9895  0.9891
May 16, 2012         Parity Conditions       21
Interest Rate parity
 interest rate differentials are covered
  by the forward rate
                                        T
                   1  icd 
                                                 1
      1.1566 fT                 1.0418 
                                  
      1.1783 e0    1  iusd   1.0533

               0.9816  0.9891
May 16, 2012        Parity Conditions       22
Covered Interest Arbitrage
 If US interest rates are higher than
  interest rate parity would forecast
     Buy usd denominated bonds
          100,000 cd*0.8485 =84,846 usd
          receive 84,846 * 1.0533 = 89,369 usd in
           one year
          Forward contract at deliver of 104,195 cd in
           one year @ 1.1659 cd/usd in one year
          Invest in Canada 100,000 cd * 1.0418 =
           104,180
May 16, 2012            Parity Conditions            23
Unbiased forward expectations
 forward rate is the best predictor of
  the expected future spot
     market determined
     it is the best predictor?
     it is not unbiased predictor?


                                 
               fT     eT
May 16, 2012         Parity Conditions    24
Comparative statistics

            usd
             *
                         25 %
                           .                               cd
                                                            *
                                                                     2.2 %

                                  US           Canadian          Canadian
                                 T-bill          T-bill           forward
                                 rates           rates              rates
                One
                                                                  1.1622
               month
               Three
                                 5.13%            4.27%           1.1605
               month
                Six
                                 5.21%            4.30%           1.1575
               month
                   One
                                 5.09%            4.34%           1.1520
                   year
May 16, 2012                       Parity Conditions                          25
Purchasing Power Parity
                            T

eT        1     *
                                                                    1

        
                  cd
                                               .
                                               11622      1022 
                                                            .       12
                                0.9987                                   0.9998
          1                                            1025 
                  *
e0               usd   
                                               .
                                               11637        . 

                                                                    0.25
                                         11605
                                          .       1022 
                                                    .
  Three months                  0.9973                                    0.9993
                                          .
                                         11637    1025 
                                                    . 
                                                                    0.5
     Six months                           .
                                         11575    1022 
                                                    .
                                0.9947                                   0.9985
                                          .
                                         11637    1025 
                                                    . 
                                                                    1
      One year                            .
                                         11520    1022 
                                                    .
                                0.9899                                   0.9970
                                          .
                                         11637    1025 
                                                    . 

May 16, 2012                      Parity Conditions                             26
Fisher Effect
                       T                             T
      1  i cd                    1   cd
                                            *
                                                 
                                             
      1  i usd                    1   usd
                                           *
                  
                                               
                                                 
                           0.25                      0.25
         10427 
           .                           1022 
                                         .
09979  
 .                                                          09993
                                                                .
         10513 
           .                          1025 
                                         .                             Three months

                            0.5                       0.5
         10430 
           .                           1022 
                                         .
09957  
 .                                                          09985
                                                                .
         10521                       1025 
                                                                        Six months
           .                            . 
                               1                         1
           10434 
             .                         1022 
                                         .                               One year
 0.9929                                                   0.9990
           10509 
             .                        1025 
                                         .   

May 16, 2012                               Parity Conditions                         27
Interest rate parity
International Fisher effect
                                        T
  fT           
               eT      1  i cd    
                                 
  e0           e0      1  i usd
                                   
                                    
                                                 0.25
          11605
           .       10427 
                     .
 0.9973                                                0.9979
                   10513 
                                                                    Three months
          11637
           .              

                                             0.5
        11575
         .       10430 
                   .
09947 
 .                                                     09956
                                                           .        Six months
         .
        11637    10521 
                        
                                             1
        11520
         .       10434 
                   .
09899 
 .                                                 09929
                                                       .             One year
         .
        11637    10509 
                        


May 16, 2012                                Parity Conditions                      28

				
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