Exchange Rate Economics: Theories and Evidence

Introduction 23
considered in Chapter 15. An alternative,and diametrically opposite view to this
is that agents are simply irrational and the excessive volatility of exchange rates
relative to the expected exchange rate is a reflection of this. A final interpretation
is that there is a time-varying risk premium which moves in an opposite way to the
exchange rate change thereby cancelling the effect of the exchange rate volatility
when the two are aggregated together in the overall forward premium. The role
of the risk premium in the forward premium is also considered in Chapter 15.
The kind of exchange rate volatility that we have been discussing is evident in
monthly or even quarterly data. However,when higher frequency data – such as
daily or intra-daily data – are considered exchange rates exhibit volatility features
which are similar to other asset prices. In particular,one of the key features of financial
markets,including the foreign exchange market,is that when high frequency
exchange rate data is used to analyse the volatility,or variance,of the exchange
rate the price is time-varying and such volatility exhibits clustering or bunching;
that is,the phenomenon that large (small) price changes are followed by other
large (small) price changes,although of unpredictable sign. The dependency of the
second moment of the exchange rate distribution on past values is usually modelled
using the autoregressive conditional heteroscedasticity (ARCH) models of Engle
(1982) and the generalised autoregressive conditional heteroscedasticty (GARCH)
model of Bollerlsev (1986). (See Bollerslev et al. 1992 for a literature overview.) For
example,using daily data for five bilateral US dollar spot exchange rates Hseih
(1988) shows that squared nominal exchange rate returns are highly serially correlated,thereby
confirming that conditional volatility is changing over time,and that
and ARCH(12) model with linearly declining lag structure captures most of the
non-linear stochastic dependence (see also Milhoj 1987; Diebold 1988; Diebold
and Nerlove 1989). A number of other papers have gone on to show that GARCH
(1,1) models do at least as well as the ARCH class of model in capturing the dependence
(see McCurdy and Morgan 1988; Hsieh 1989; Kugler and Lenz 1990).
These kinds of results confirm the volatility clustering idea. 12 It is worth noting that
the significance of ARCH and GARCH effects for exchange rate returns weakens
considerably when the data sampling moves from a daily frequency to a monthly
frequency and is usually insignificant at lower frequencies,such as quarterly.
Although the ARCH and GARCH models are able to give a good description
of the behaviour of the conditional variance of the exchange rate the estimates
referred to earlier do not capture all of the excess kurtosis in the data (see,for
example,McCurdy and Morgan 1987; Baillie and Bolerslev 1989; Bollerslev et al.
1992). One way of addressing this issue has involved using alternative conditional
error distributions,such as the Student-t (see,for example,Baillie and Bollerslev
1989) and a normal-Poisson (Hsieh 1989). Lastrapes (1989) and McCurdy and
Morgan (1987) suggest that the remaining leptokurtosis is a reflection of outliers
associated with policy events and when dummy variables are used to capture such
events the leptokurtosis decreases markedly.
Under the maintained assumption of market efficiency,one interpretation of the
volatility clustering phenomenon captured in ARCH and GARCH estimates of
foreign exchange returns could be that the information reaches the market in