Because of the characteristics of the demand function (6.24) for the risky asset, traders in belief group B1 are restricted in the fraction of individual wealth they can go short, that is
This implies that there is an upperbound on the fraction of total wealth traders in belief group
B2 can go long, that is
|
qth yth = - |
|
qth yth < |
|
|
|
qth. |
This restriction implies that the denominator of the ratio in the first part of the right hand side of (6.36) is positive. There is a positive equilibrium price in the case of zero supply of outside stocks, because price and dividend expectations are restricted to be always positive. If
B2 = Ø, then ∑
h ∈ B2 (
qth yth)=0 and the equilibrium price is equal to the net present value of the average of the expected price plus dividend by the traders in belief group
B1. This is the same solution for the equilibrium price as in the BH model. For
s=0 as in the BH model, wealth plays no role anymore. For every short position there must be an offsetting long position. If the gross risk free rate under borrowing and lending is always equal to
R, then wealth at time
t is just equal to
Wt=
R Wt-1.
The derivation of the equilibrium price for a strictly positive supply of outside shares, i.e. if s>0, is presented in Appendix C.
The EMH benchmark with rational agents
In a world where all agents are identical, expectations are homogeneous and all traders are risk neutral, i.e.
a ↓ 0, equilibrium equation (6.36) in the case of
s=0 and equilibrium equation (6.61) in the case of
s > 0 both reduce to
This arbitrage market equilibrium equation states that today's price of the risky asset must be equal to the sum of tomorrow's expected price and expected dividend, discounted by the risk-free interest rate. The arbitrage equation (6.37) can be used recursively to derive the price at time
t
If the transversality condition
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