Please solve and explain exercise f
An investor has initial wealth Wo = $ 1,200 and faces an uncertain that she partitions into two states, s = 1 and s = 2. She can invest in two securities, j and k, with initial prices of p; = $ 10 and Pk = $ 12, and the following payoff table: Security Payoff s=1 s=2 $10 $12 $20 $8 k a.) If she buys only security j, how many shares can she buy? If she buys only security k, how many can she buy? What would her final wealth, Ws, be in both cases each state? b.) Suppose the investor can issue as well as buy securities; however, she must be able to meet all claims under the occurrence of either state. What is the maximum number of shares of security j she could sell to buy security k and vice versa? What would her final wealth be in both cases in each state? c.) What are the prices of the pure securities implicit in the payoff table? d.) What is the initial price of a third security i for which Qi,1 = $ 5 and Qi,2 $ 12? e.) Summarize the results of (a) through (d) on a graph axes Wand W2. f.) Assume that the investor has a utility function of the following form U = WW%. Find the optimal portfolio assuming the issuance of security is possible, if she restricts herself to a portfolio consisting only of j and k. How do you interpret your results? = = An investor has initial wealth Wo = $ 1,200 and faces an uncertain that she partitions into two states, s = 1 and s = 2. She can invest in two securities, j and k, with initial prices of p; = $ 10 and Pk = $ 12, and the following payoff table: Security Payoff s=1 s=2 $10 $12 $20 $8 k a.) If she buys only security j, how many shares can she buy? If she buys only security k, how many can she buy? What would her final wealth, Ws, be in both cases each state? b.) Suppose the investor can issue as well as buy securities; however, she must be able to meet all claims under the occurrence of either state. What is the maximum number of shares of security j she could sell to buy security k and vice versa? What would her final wealth be in both cases in each state? c.) What are the prices of the pure securities implicit in the payoff table? d.) What is the initial price of a third security i for which Qi,1 = $ 5 and Qi,2 $ 12? e.) Summarize the results of (a) through (d) on a graph axes Wand W2. f.) Assume that the investor has a utility function of the following form U = WW%. Find the optimal portfolio assuming the issuance of security is possible, if she restricts herself to a portfolio consisting only of j and k. How do you interpret your results? = =
