Heterogeneity of Investors and Asset Pricing in a Risk-Value World

market value of these claims.

R* : = expected gross portfolio return on the forward endowment required
by the investor.

The pricing kernel is assumed to be twice continuously differentiable. To
simplify notation, the state index will be dropped unless necessary for clarity
of exposition.

In risk-value models the investor, first, derives the set of risk-value efficient
portfolios and, second, chooses one of these portfolios according to his tradeoff
between risk and value. The advantage of our analysis is that asset pricing
in a risk-value equilibrium can be analyzed as in the CAPM-world without
making assumptions about this tradeoff.

A risk-value efficient portfolio minimizes the risk subject to the constraint
that the expected portfolio payoff E(e) does not fall below some exogenously
given value WqR* (payoff constraint). Hence, the expected gross portfolio
return has to be equal or higher than R*. In this section, the prices for state-
contingent claims are assumed to be exogenously given. Then an efficient
portfolio is the solution to the following problem.

Minimize

e If (ê)l                                (4)

subject to the budget constraint:

E [eπl = W₀                          (5)

and the payoff constraint:

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