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Consider a risk - averse invest or with the power preferences ( where denotes the risk aver - sion magnitude ) and an initial fund

Consider a risk-averse invest or with the power preferences (where denotes the risk aver-
sion magnitude) and an initial fund value of Wt=250,000 at date t. The investment
envir onment offers two alternatives to the investor including: (i) a safe asset with a fixed
risk-free rate RF=1+rF per invested unit between dat es t and t+1; and (ii) common
equity share of a private company. The equity return (RE) involves risk depending on
the future company's performance. Consider that the company's dividend per share value
summarises the performance and follows a Normal distribution with Dt+iN(,2) for
any future date i1.
Q.1. Assume that the investor intends to invest all of their fund value where the fraction
is allocated to the risky investment and the remaining 1- is allocated to the
risk-free investment such that RW=(1-)*RF+*RE. Derive the pricing expres-
sion for the common equity (price per share Pt) according to the first fundamental
asset pricing equation. Denote all additional terms you used and define the stochastic
discount fact or in this context. (0.5 page)
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