Exchange Rate Economics: Theories and Evidence

Spot and forward exchange rates 375
case the market’s subjective probability distribution of s is not the same as the true
distribution because E m t ̸= E t where E m t is the market expectation and so
λ ir
t = f t − E m t (s t+1 ),
where λ ir
t denotes the ‘irrational’ risk premium and ˆα 1 = 1 −ˆα 3 −ˆα ss −ˆα ir ,where
ˆα 3 = Cov(Em t s t+1̂−s t+1 ) + Var(λ ̂ir
Var ̂(f t −s t )
t )
,
and
ˆα ss = Cov(f t − ŝ
t , E t s t+1 − E t s t+1 )
,
Var ̂(f t −s t )
ˆα ir = Cov(f t − ŝ
t , E m t s t+1 − E t s t+1 )
.
Var ̂(f t −s t )
The latter will be positive if f − s is correlated with the expected error. When the
consensus estimate of the future exchange rate is above what is rational and this
results in a higher forward premium this will produce a positive α ir . So positive
values of ˆα 3 , ˆα ss and ˆα ir can all contribute to a finding that ˆα 1 is less than unity.
We have a more formal discussion of expectational issues in the following section.
15.3 The forward premium puzzle, the risk premium
and the Lucas general equilibrium model
In this section we focus on explanations for the biasedness result which exploit the
existence of a risk premium and,in particular,emphasise risk premium approaches
based on the general equilibrium model of Lucas and also the portfolio-balance
model.
15.3.1 The Lucas model and the general equilibrium
approach to the risk premium
Consider again a variant of the first-order condition from the Lucas model derived
in Chapter 5:
S t P ∗
t
P t
= u∗ c t
u ct
,(15.12)
where terms have the same interpretation as before. If we now assume an arbitrary
asset i which has a home currency price Vt i and a payoff in period t + 1ofVt+1 i +
,where D has the interpretation of either a coupon payment or dividend. The
D i t+1