I denote the price of the market portfolio at time 0 by PM, and define
RM≡M/PM−1 as the realized percentage return on the market.
The final assumption is that the price of the firm’s shares is determined
solely by the expectations of the outside investors. This amounts to saying
that even though the manager may have a different opinion, he is unable or
unwilling to trade in sufficient quantity to affect the market price.
With the assumptions in place, the first thing to do is to calculate the ini-
tial market price, P, of the firm’s shares, beforethe investment decision has
been made at time 0. This is an easy task. Note that we are operating in a
standard mean-variance framework, with the only exception being that in-
vestors have biased expectations. This bias does not vitiate many of the
classical results that obtain in such a framework. First of all, investors will
all hold the market portfolio, and the market portfolio will be—in their
eyes—mean-variance efficient. Second, the equilibrium return required by
investors in firm’s equity, k, will be given by
k=r+βr(ERM−r), (1)where ris the riskless rate and βris the usual “rate-of-return β,” defined as
βr≡cov(F/P, RM)/var(RM). (2)
Thus, outside investors’ required returns are determined as in the stan-
dard CAPM. Given the cash flow expectations of these investors, the initial
price of the firm’s shares, P, satisfies
P=Fb/(1+k). (3)Eq. (3) is not a completely reduced form, however, because Pappears in the
definition of kand hence is on both sides of the equation. Rearranging terms,
we obtain the following expression for Pin terms of primitive parameters:
P={Fb−βd(ERM−r)}/(1+r), (4)where βdis the “dollar β,” defined as
βd≡cov(F, RM)/var(RM). (5)
It is useful to compare Eqs. (1)–(4) with the analogous expressions that
would prevail in a classical setting with rational expectations. Using aster-
isk superscripts to denote these (unobserved) rational expectations values,
we have
k*=r+β*(ERM−r), (6)
β*≡cov(F/P*, RM)/var(RM), (7)
P*=Fr/(1+k*), (8)and
P*={Fr−βd(ERM−r)}/(1+r). (9)610 STEIN