Exchange Rate Economics: Theories and Evidence

372 Spot and forward exchange rates
There are a very large number of estimates of α 1 for different currencies and time
periods (see, inter alia,MacDonald and Taylor 1989) and these studies produce a
preponderance of estimates of α 1 which are closer to −1 than +1. For example,
Froot and Thaler (1990) demonstrate that averaging α 1 over 75 published produces
a value of −0.88. We present an example of an estimated version of expression
(15.4) here,from Fama (1984),for the Swiss franc–US dollar:
s t+k = 0.81
(0.42) − 1.15
(0.50) (f t − s t ) + u t . (15.5)
How may this stylised result be explained? There are essentially two potential
explanations: it is either caused by some form of expectational failure,which can
range from simple irrationality through to a ‘peso’ effect,or learning,or simply
a time-varying risk premium. These alternative explanations may be illustrated
using the so-called Fama (1984) decomposition,but before considering this we
outline some other ways of testing the informational efficiency of the forward
exchange rate.
Forward market efficiency has also been tested using the rational forecast error
(alternatively labelled in the literature,later,as the excess return premium or the
rational risk premium – s t+1 −f t ). By regressing this error onto lagged information
we may obtain alternative,and potentially stronger,tests of efficiency. A so-called
weak-form test of efficiency 1 would simply involve regressing the current forecast
error onto past forecast errors:
s t+1 − f t = δ 0 +
p∑
λ i (s t−i − f t−i−1 ) + ω t ,(15.6)
i=0
where the null hypothesis would be δ 0 = 0 and ∑ p
i=0 λ i= 0. A stronger test would
involve running the following regression:
s t+1 − f t = δ 0 +
p∑
λ i X t−i + ω t ,(15.7)
i=1
where X is an n × 1 vector containing any publicly available information,such
as money supplies,forecast errors from other foreign exchange markets,and so
on. The joint null hypothesis in this case would be δ 0 = 0 and ∑ p
i=1 λ i = 0
and this would be interpreted as a semi-strong-form test of efficiency. Using the
terminology of Fama (1970) a strong-form test of efficiency would involve including
non-publicly available,or inside,information in the information set,X t (the issue
of inside information is not addressed further in this chapter but is considered in
Chapter 14).