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

the theoretical and empirical research in decision theory on how to measure
risk. Based on this analysis, we will discuss some general properties a risk
measure should have. In section 3, risk-value efficient portfolios are derived.
Equilibrium is analysed in sections 4 and 5. In section 4, we first investigate
individual sharing rules for a rather general class of risk functions and then for
HARA functions. In section 5, results about the pricing kernel are derived.
Its convexity will be shown to increase with the heterogeneity of investors.
Section 6 summarizes the main results.

2 Risk Measurement

2.1 Background²

The separation of value and risk is quite popular in finance. Investors usu-
ally talk about the risk of an investment which then is evaluated against its
expected return. Thus, decisions are made by evaluating risk and return sep-
arately and trading off both components. Taking risk and value separately
allows different investors to have different tradeoffs even though their risk
measures may be the same, in contrast to EU. The explicit consideration of
the investment risk has become even more important in the light of recent
regulations which require broker houses to inform their clients about the risk-
iness of their investments. Risk judgments have also become quite important
in bank regulation and management.

Still the most important measure of risk is variance with value being the
endogenous benchmark. Variance is easy to use, and risk-value models based
on variance as a risk measure are compatible with expected utility. The
problem is, however, that variance does not capture peoples risk perception
as can be easily demonstrated by the following example:

²See Sarin and Weber (1993) and E. Weber (1997) for reviews on risk measurement.

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