Exchange Rate Economics: Theories and Evidence

382 Spot and forward exchange rates
representative agent models of the risk premium,with rational expectations,do
not appear to shed much light on whether it is a risk premium which explains the
forward premium puzzle.
15.3.3 Portfolio-balance approach to measuring risk
The essence of the portfolio-balance model,discussed in Chapter 7,may be
summarised as:
B t S t F −1
t = γ(i t − i ∗ t − s e t+k ),(15.36)
which states that relative home to foreign bond supplies are determined by the
excess return,which on the basis of covered interest parity,may be thought of
as a risk premium. By assuming that agents are rational,an inversion of (15.36)
produces:
i t − i ∗ t − s t+k = γ −1 (B t S t F t ) −1 + υ t+k ,(15.37)
which may be rewritten as:
i t − i ∗ t − s t+k = β 0 + β 1 (B t S t F t ) −1 + u t+k ,(15.38)
which predicts that the risk premium,or excess return,is driven by the relative
supplies of bonds. A number of researchers have exploited a different,although
related,portfolio literature to that used to derive the portfolio-balance model in
Chapter 7 in order to place restrictions on the parameters in (15.38). This related
literature seeks to explain the composition of investors’ portfolios and involves
considering an investor who maximises a function of their mean and variance over
the coming period (the earliest variants of this approach are Stultz 1981 and Adler
and Dumas 1983). Here we consider a version of the two-country model as set out
in Engel (1994) in which agents can invest in two assets: home and foreign country
bonds. More specifically,individuals in the home country at time t are assumed to
maximise a function of the mean and variance of their portfolio:
E t (W t+1 ) −
φ
2W t
Var t (W t+1 ),(15.39)
where φ is related to the coefficient of relative risk aversion and in this set-up
investors like to have a higher return but dislike variance. If ω represents the
fraction of wealth invested in the foreign country bonds,then:
and
E t (W t+1 ) = W t [(1 + i t )(1 − ω t ) + (1 + i ∗ t )ω tE t (S t+1 /S t )],(15.40)
Var t (W t+1 ) = W 2
t (1 + i ∗ t )2 ω 2 t Var t(S t+1 /S t ),