FREE online courses on Investment Decisions in Exchange Rates - The International Version of the Fisher Equation

 

The Fisher Equation (named after Irving Fisher) expresses the nominal or dollar denominated rate of interest in terms of the expected rate of inflation and the real or purchasing power denominated rate of interest.  Although the Fisher Equation is not a precise theory of the relation between interest rates and the expected rate of inflation, it is a fairly close approximation.  If we denote the real rate of interest by and the expected rate of inflation by I, the Fisher Equation is given by

 

                   1 + R     =     (1 + ) (1 + I)

 

For example, if the real rate of interest is 0.0125 (1.25 percent) and the expected rate of inflation is 4 percent, then the nominal (dollar denominated) rate of interest will be the solution to

 

                   1 + R   =     (1 + .0125) (1 + .04)

 

which implies that

 

                   R        =     1.0125 x 1.04   -   1

 

                             =     5.30 percent (.0530)

 

An international version of the Fisher effect is often used to specify how differences in the respective rates of inflation across countries determine the differences in interest rates across countries.  If we assume that the Fisher Equation holds simultaneously in both the U.S. and in country FR, then we have

 

                             =     .

 

If capital flows freely from one country to another, chasing the highest interest rates, then there will be a tendency for real rates to be equalized across countries.  If this is the case, then the U.S. and contry F should have the same real rate of interest (i.e., US equals F).  Therefore,

 

                             =       .

 

The expression above implies that all we have to do to infer the difference in the expected rates of inflation in two countries is to observer the difference in the nominal interest rates in those two countries.  For example, suppose that the nominal rate of interest in the U.S. is 6 percent and that the nominal rate of interest in Japan is 2.5 percent.  Then assuming that the real rate of interest in the U.S. is equal to the real rate of interest in Japan, the difference between the expected rates of inflation in the U.S. and Japan is

 

                                   =      ,

 

                                      =     1.034  ,

 

indicating that inflation in the U.S. is approximately 3.4 percent greater in the U.S. than in Japan. 

 

In order to forecast future exchange rates using Relative Purchasing Power Parity, we need a good forecast in the difference in the expected rates of inflation in the two countries in question,

 

          E(S)     =     S[ ]N   .

 

Forecasting the inflation rate is always very difficult.  However, if we are satisfied that the real interest rates in two countries are approximately equal, then the Fisher Equation allows us to approximate differences in expected inflation rates using the difference in the nominal interest rates.  Therefore, we can forecast exchange rates using the nominal rates of interest,

 

          E(S)     =     S[ ]N  .

 

For example, suppose that the exchange rate between the dollar and the Swiss franc is $0.6500/SF1.  Further, the U.S. interest rate is 5.3 percent per year and the Swiss interest rate is 2.5 percent per year.  Our forecast of the expected exchange rate in one year would be

 

          E(S)      =     $0.6500/SF1 x [ ]1  ,

 

                   =      $0.6678/SF1.

 

Similarly, the appropriate forecast for the exchange rate between the dollar and the Swiss franc in 2 years would be

 

          E(S)      =      $0.6500/SF1 x [ ]2   ,

 

                   =     $0.6860/SF1.