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

7~ιΛ^{a +} ∣^e) ¹[i+^v(е)]’ ^vε
7 ^{- 1} ∖    ^{1 -} 7/

with V(ε) being defined in equation (20). The latter follows from f (e⅛)/-

V ⁼ fι(ɛie)/ — Vi — ^sι + ^sii ^i∙ This proves the first part of equation (21).

Now we we prove the second part of equation (21). Substitute f ^z(⅛) / f (⅛)
in equation (31) from (33) and multiply the equation by — (Λ_i + e_iε/(1 - 7))∙

This yields

The factor of d²e_i/de² equals the inverse first term in equation (36). Hence
it follows from equation (36) and (15) that this factor equals

^fi ^(eis'⁾

^-V

Insert (40) in (39) and obtain after aggregation across investors since
∑_i d²e_i/de² = 0,

⁷—^{2 +} Σ -4τ^d2e√^dε2 = c^(ε) f^{A +} γ-^e^^ ( ∀ ^{ε (41)}

7^{- 1 t} ^)               V    ^{1 -} 7 J

44

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