Let an investor have initial wealth mo 2 1 and the following vonNeumannMorgenstern utility of wealth: (a) u('w) : In to. Suppose that she can invest a fraction h of her wealth in a risky asset and the remainder 1 h in a riskfree asset. The only restriction on the weights h and 1 h is that they sum to one. The risky asset has a payoff of 3 in case of success and payoff 0 if it is a failure. The investor believes that success and failure are equally likely. The riskfree asset has a payoff of 1.2, regardless whether the risky investment is a success or a failure. Derive an expression of the expected wealth and expected utility if she invests h in the risky asset and 1 h in the riskfree asset. Use the information above to derive her optimal investment portfolio. What is the expected wealth associated with this portfolio? Assume now that everything is as above, but the risky asset is only paying off 2 if it is a success (instead of 3). What is the optimal investment portfolio in this case? Explain briey what this investment strategy entails. What is her expected wealth resulting from this portfolio