6.3 Proof of Proposition 2
We know that for constant aggregate RRA
Var
Vτ Vτ
ln —
к Vt
Dt
D D D-
= Var I ln —
к Dt
t<τ.
By Proposition 1, for declining aggregate RRA ηtΦ,D, the elasticity ηtS,D > 1
so that the conditional variance of asset returns is higher than the (condi-
tional) variance of the dividend process, i.e.
Var
(l,∙ V
Dt
Dτ
> Var I ln —
Dt
t<τ.
(11)
Consider now the unconditional variance (i.e. θ =0):
Var
(I- S)
Var(E(lnVτ |Dt) -lnVt)+E(Var(lnVτ |Dt))(12)
with
E(lnVτ |Dt)-lnVt
- 1∑V (Ss)2)
ds
We need to show that Var
is greater than
Var
(∣-3
Var(lnDτ |Dt) .
(14)
From (11) it follows that the second term on the right hand side of equa-
tion (12) exceeds Var ɑn D-^. As the first term on the right hand side of
equation (12) is also positive, we are done. The proof is the same for the
variance conditional on Dθ ; 0 < θ < t.
6.4 Proof of Proposition 3
Since by definition CERt- ≡ f- (dSs/ Ss) + f- ( Ds/ Ss — rf ) ds, and the
riskless rate rf is assumed constant, the covariance is given by
Cov ( CERt-,μv (S- ) — rf ∣ Dt) = Cov
---
ddSs DDs D
J Ss- + J S-ds, J dμv(Ss)
22
More intriguing information
1. Hemmnisse für die Vernetzungen von Wissenschaft und Wirtschaft abbauen2. The name is absent
3. Modelling Transport in an Interregional General Equilibrium Model with Externalities
4. The name is absent
5. The magnitude and Cyclical Behavior of Financial Market Frictions
6. Business Networks and Performance: A Spatial Approach
7. The name is absent
8. The name is absent
9. Secondary stress in Brazilian Portuguese: the interplay between production and perception studies
10. Konjunkturprognostiker unter Panik: Kommentar