Journal of Economic Literature, 27(4), pp. 15831621. (2004),
Rational exuberance, Journal of Economic Literature, 47(3),
pp. 783804. LeRoy, S. F., and R. D. Porter (1981), The
present-value relation: tests based on implicit variance bounds,
, the excess expected return on the market portfolio. The actual
value of KH is not especially interesting (it is derived in
appendix 11.3). But KH is not the same as in the CAPM,
because H need not be the rate of return on any portfolio. It can
i=1 Nt+iEtdt+i, the expectations operator is applied on the
assumption that the discount factors are non-random i.e. the
risk-free interest rates, though not necessarily constant across
time, are known with certainty at date t.
Barberis, N., an
Journal of Economic Perspectives, 17(1), pp. 83104. Shleifer,
A. (2000), Inefficient Markets: An Introduction to Behavioral
Finance, Oxford: Oxford University Press. Shleifer, A., and L.
H. Summers (1990), The noise trader approach to finance,
(10.27) Note that E t 9; has a time subscript: the state
probabilities depend on the date at which they are evaluated.
Equation (10.27) holds for any date, t+s, in the future and hence
can be written pt+s = E t+s9dt+s+1+pt+s+1;
1+rt+s+1 for s 0 (10.28) By
factor, H, is unobserved, it is usually replaced by the rate of
growth of aggregate consumption, though, in principle, it could
be replaced by any variable with which H has a perfect positive
11.6Summary This chapter has shown how the FVR con
consumption and portfolio selection model. In the CCAPM, the
rate of growth of consumption plays a role analogous to the rate
of return on the market portfolio in the static CAPM.
Further reading Important though they are, the topics studied in
, as required. The main limitation of the CCAPM as expressed
by (11.18) is immediately apparent: H, the stochastic discount
factor, is a purely subjective reflection of preferences and can
differ from one investor to another. Without additional
of finance based on the stochastic discount factor, together with
empirical applications. Chapter 21 focuses explicitly on the
equity premium puzzle. At a similarly advanced level,
Campbell, Lo and MacKinlay (1997, chap. 8) present a concise
survey of the
. When the life of the asset is finite so that pt+N is
exogenously determined its value ensures a unique solution.
Otherwise, allowing an unbounded life for the asset, the solution
to equation (10.3) is not unique, unless some other condition is
must be well defined (i.e. conditions must be placed on the
convergence of the present value of the dividend stream), and
(b) the solution for p
t is not unique unless some condition is imposed to rule out the
presence of bubbles. In a further generalizat
c and Kc, as before, is a number that is the same for all assets.
With identical reasoning as for H, a regression model for rj and c
can be constructed: rj =Gjc+jcc+j j=1(2(n (11.21) where Gjc =
jjcE9c; and j is assumed to have the same properties as
saves or borrows between the present, t, and the future, t+1.
Here it is assumed that the endowment takes the form of wealth,
Wt, available at the present, date t. (Presumably, Wt was
accumulated in the past i.e. dates prior to t.) The difference
;1, for s1, so that Nt+s denotes the discount factor for the time
period t to date t+s. Note that, if the individual discount factors
are all equal, then Nt+s=
1+rs that is, the common discount factor expressed in terms
of a constant interest rate. If a b
if r>g (10.26)
If r g, pt is unbounded i.e. formally undefined.
Appendix 10.3: The RNVR with multiple time periods In
chapter 7 it was shown that the absence of arbitrage
opportunities is equivalent to the risk-neutral valuation
relationship. Applying the
H: the beta-coefficient between j and H;
0 = the expected return on an asset with zero beta-coefficient
with H i.e. 0H = 0; and KH = a number, the same for all assets.
Equation (11.18) can be interpreted similarly to that for the
CAPM. It states that