Consider the De Long et al. [549] model described in Sect. 9.3 with a proportion \(\mu \in(0,1)\) of noise traders. Prove Proposition 9.11.

Data From Proposition 9.11

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Proposition 9.11 In the context of the above model (see De Long et al. [549]), consider a steady-state equilibrium, where the unconditional distribution of the equilibrium price p does not depend on the date t = N. Then in a steady state equilibrium the following hold: (i) the price process (p)en of the risky asset satisfies P = 1 + ( - 2) 1+rf 2 + - for all t N; (9.51) rf rj (1+r)' (ii) the expectation of the difference AR between noise traders' and rational investors' total returns (given equal initial wealth) is given by (1+r) + (1+r) E[AR+1] = 2, for all t N. (9.52)