17. INTERNATIONAL PARITY CONDITIONS
Supply and demand analysis allows investors and economists to predict directional changes
in a country's exchange rate. Unfortunately, the analysis cannot answer quantitative changes.
Consequently, this chapter builds on the supply and demand analysis and uses several theories to
predict quantitative changes in a country's currency exchange rates. We will study the random
walk, Purchasing Power Parity Theory, the Relative Purchasing Parity Theory, Interest Rate
Parity Theorem, and International Fisher Effect. Furthermore, we study the Big Mac Index from
the Economist because we can easily determine whether a country's currency is over or
undervalued relative to the U.S. dollar. Then we can predict which direction the exchange rate
should move over time.
A Random Walk
Currency market exchange rates could exhibit a random walk in the short run. Statisticians
define a random walk whose current value is the previous period’s value plus a random
disturbance. We show a random walk in Equation 1. Value of the spot exchange rate today is st,
which equals yesterday's exchange rate, st- 1 , plus a random disturbance, et. We assume the
random disturbance is distributed normally with a mean of zero with a fixed standard deviation.
For example, if the U.S. dollar-euro exchange rate equals $1.3 per euro today, then we expect
the exchange rate to be $1.3 per euro tomorrow plus a random fluctuation.
ݏ௧=ݏ௧ିଵ+݁௧ (1)We show the monthly U.S. dollar-euro exchange rate in Figure 1. A random walk has an
unique characteristic – the variable drifts in a particular direction before changing direction. If
we take a first difference of the exchange rate, then the difference equals the random
disturbance, illustrated in Equation 2. A first difference is we take today's spot exchange rate
and subtract the previous period, which is monthly for our case. We show the first difference for
the U.S dollar-euro exchange rate in Figure 2. Line indicates the randomness of the exchange
rate, but it is not completely random. Moreover, statistical tests indicate the U.S. dollar-euro
exchange rate is almost a random walk^1. However, these statistical tests are beyond the scope of
this book.
ݏ௧−ݏ௧ିଵ=݁௧ (2)Although currency exchange rates exhibit a random walk in the short run, economists and
financial analysts use several theories to explain long-run movements.
(^1) The U.S. dollar-euro exchange rate has the structure, ݏ
௧=ଵݏ௧ିଵ+ଶݏ௧ିଶ+݁௧, where p^1 is close to one
while p 2 has a significant second lag. Unfortunately, this is not an anomaly. Many exchange rates exhibit this
structure or exhibit a pure random walk.