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Mr. John has initial wealth W0=$600 and faces an uncertain future that he partitions into two states, S=1 and S=2. He can invest in two
Mr. John has initial wealth W0=$600 and faces an uncertain future that he partitions into two states, S=1 and S=2. He can invest in two securities, J and K, with initial prices of PJ=$5 and PK=$6, and the following payoff table:
Payoff
Security
S=1 S=2
J $5 $6
K $10 $4
- If he buys only security J, how many shares can he buy. If he buys only security K, how many shares can he buy.
- What would his final wealth, WS, be in both above cases and each state.
- Suppose Mr. John can issue as well as buy securities; however he must be able to meet all claims under the occurrence of either state. What is the maximum number of shares of security J he could sell to buy security K. what would his final wealth be in this case and in each state.
- What are the prices of pure securities implicit in the payoff table.
- What is the initial price of a third security L with payoffs $2.5 and $6 at state 1 and 2 respectively.
- Suppose hat Mr. John's utility function can be written as, whereW2andW1are the final wealth in state 2 and 1 respectively. Find the optimal portfolio assuming the issuing of securities is possible, and his portfolio is restricted to securities J and K.
- If Mr. John wanted to buy a completely risk-free portfolio, how many shares J and K would he buys.
- Summarize the results of (1) through (7) on a graph with axesW1andW2.
- Form pure security 1 including traded securities J and L.
- Compute the one period interest rate.
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