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

the exponential function, an important function to describe people’s risk
judgments. The negative HARA- class is defined as

where 7 ∈ IR∖ { 0, 1 }; A > 0. In the case 7 = 0 we obtain F(ê) =
-ln(A + ê) and in the case 7 = -∞ we get F(ê) = êxp(-Bê) with B > 0.
For 7 > -∞ the domain of F is constrained by (A + ê/(1 — 7)) > 0. A has
to be sufficiently high. For 7 < 1, we need inf ê > —A(1 — 7); for 7 > 1,
we need sup ê < — A(1 — 7) . Since it makes little sense to constrain ê from
above, we shall mostly assume 7 < 1. We have F^z < 0, F" > 0 and

As we require F^zzz(ê) < 0, 7 < 1 or 7 > 2 is implied. Therefore, we will
only consider functions with 7 < 1 or 7 > 2, mostly 7 < 1.

2.3 Risk-value Models and EU Models

So far we have concentrated on modelling risk. We will now briefly dis-
cuss the relationship between risk-value models and EU models. Risk-value
models combine the primitives risk and value into a preference measure with-
out constraining the tradeoff between value and risk. In the expected util-
ity model the utility function determines both, risk measurement and the
tradeoff between risk and value. Thus, the decision maker cannot determine
measurement and tradeoff independently.

Jia and Dyer (1996) consider risk-value models as defined in equation
(1). They show that preference orders which can be derived from a risk-value

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