Exchange Rate Economics: Theories and Evidence

384 Spot and forward exchange rates
of the portfolio-balance model is that these terms are restricted and in the
following way:
and
α t =−0.5 · Var t (s t+1 ),
δ t = (1 − φ) · Var t (s t+1 ),
γ t = φVar t (s t+1 ).
The majority of the papers in the mean-variance portfolio-balance approach
involve estimating variants of equation (15.45) and testing the restrictions that
(15.46) imposes on (15.45). It is worth noting that one of the big empirical advantages
of this approach is that it only requires information on the value of total bonds
held in the world denominated in each country,and the share of wealth in each
country,rather than the value of bonds denominated in each country and held in
each country (the latter data are much less readily available than the former).
Frankel (1982a,b,1983),Lewis (1988) and Rogoff (1984) present estimates of
variants of (15.38) (i.e the standard unconstrained portfolio-balance equation) for
a variety of currencies and time periods and essentially find no evidence of a
statistically significant link between excess returns and bond holdings.
Engel and Rodriguez (1989) estimate a version of (15.45) for the demand for
government bonds for six countries. Since they assume all investors evaluate returns
in the same terms,the equation they estimate is equivalent to (15.42) and the
variance is modelled using an ARCH model and also models which relate the
variance to economic data. The estimates of φ turn out to be either insignificantly
different from zero or negative and therefore do not offer support to the meanvariance
approach. Giovannini and Jorion also offer GARCH-based estimates
of (15.42) which are also unsupportive of the mean-variance approach since the
estimates of the coefficient of risk aversion are insignificant. Other unsupportive
estimates of this approach have been produced by Lyons (1988),Thomas and
Wickens (1993),Engel and Rodriguez (1993) and Tesar and Werner (1994).
By incorporating a home country bias effect,as in equation (15.45),and using a
GARCH process to model volatility,Engel (1994) produces a reasonably plausible
estimate of the coefficient of risk aversion which is marginally significant; however,
the risk premiums implied by estimates of equation (15.45) ‘are more than an order
of magnitude greater than those from the estimated CAPM’ (Engel 1996). Black
and Salemi (1988) do not assume the first-order maximisation condition from the
consumers’ maximisation problem holds exactly and add an error term to (15.45)
and this produces a statistically significant value of φ of 4.08,but they do not
provide estimates of the size of the implied risk premiums and how they relate to
estimates derived from equation (15.45). Lewis,however,reports estimates of a
version of the model which is subject to an error term,but in contrast to Black and
Salemi she finds no evidence in support of the model.