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4. An investor has to decide how to allocate her wealth of W = (200000 into a risky asset and a risk-less asset. The risky asset can pay a return of 30% or loose 10% with probabilities p and 1 - p, respectively. The risk-less asset offers a return of 5% with no risk. The investor risk preferences are described by following function WI - 1 U(WT) = 1 - p with p = 2. The final amount at the end of the investment period T is Wr. a) Explain how you set up this optimal investment allocation problem. b) How does the optimal allocation depend on the probability p? c) Find the optimal investment allocation when the probability p is 45%. d) What is the lowest value of the probability p for the investor to allocate a positive share to the risky asset? Is this lower bound of probability dependent on the level of risk aversion? (Hint: How would your answer change if the level of risk aversion p is not fixed at 27) e) What is the lowest probability p above which the investor wants to borrow money at the risk-less interest rate in order to invest in the risky asset an amount of wealth larger than W