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

Consider a risk-averse investor 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
environment offers two alternatives to the investors including: (i) a safe asset with a fixed
risk-free rate RF=1+rF per invested unit between dates 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 Consider an alternative scenario where is not pre-determined therefore the valu-
ation depends upon the optimal value of the allocation to each asset. Assume the
no-arbitrage condition and discuss the steps the investors undertakes to compute the
optimal value **. The answer is expected to identify main considerations through-
out the pricing procedure and provide methodological approaches used to address
the considerations. Structure the answers under separate bullet points.
Q.2 What is optimal allocation of funds to the risky investment? Your answer should
only provide the fraction or overall fund allocated.
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