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



a more aggressive investor, i.e. an investor, who uses a higher exogenous
benchmark return or, in the case of an endogenous benchmark, demands a
higher expected portfolio return.

Proposition 6 characterizes the sharing rules of investors.

Proposition 6 ; Consider two investors i and j who have HARA-risk func-
tions with the same
7.

a) Suppose that the risk sensitivity, ∣1∩ A* for 7 > -∞ resp. BWq for
7 = -∞, is higher for investor i than for investor j and/or she demands
a higher expected portfolio return. Then investor i,s sharing rule is strictly
convex relative to that of investor j.

bl) Suppose that for both investors the risk sensitivity is the same, but
investor i demands a higher expected portfolio return. Then there exists some
portfolio return R1 such that

Ri[=][>]Rj   for   Rj < [=][>]R1.

b2) Suppose that the risk sensitivity is higher for investor i but both in-
vestors demand the same expected portfolio return. Then there exist R0 and
R°° with R0
R00 such that

Ri > Rj for Rj < R0 and Rj > R00,

Ri < Rj   for R0 Rj < R00.

Proof. See Appendix E.

25



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