Real Exchange Rate Changes and Exchange Risk
The exchange rate changes that give rise to operating exposure are real exchange rate changes. As presented in Chapter 4, the real exchange rate is defined as the nominal exchange rate (e.g., the number of dollars per franc) adjusted for changes in the relative purchasing power of each currency since some base period. Specifically,
where
e’t = the real exchange rate (home currency per one unit of foreign currency) at time t
et = the nominal exchange rate (home currency per one unit of foreign currency) at time t
if,t = the amount of foreign inflation between times 0 and t
ih t = the amount of domestic inflation between times 0 and t
Given that the base period nominal rate, e0, is also the real base period exchange rate, the change in the real exchange rate can be computed as follows:
For example, suppose the Danish krone has devalued by 5% during the year. At the same time, Danish and U.S. inflation rates were 3% and 2%, respectively. Then, according to Equation 11.1, if e0 is the exchange rate (dollar value of the krone) at the beginning of the year, the real exchange rate for the krone at year’s end is
Applying Equation 11.2, we can see that the real value of the krone has declined by 4% during the year:
In effect, the krone’s 5% nominal devaluation more than offset the 1% inflation differential between Denmark and the United States, leading to a 4% decline in the real value of the krone.