4. An investor has to decide how to allocate her wealth of W = 200000 into...

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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 U(WT) = W-1 1-p with p=2. The final amount at the end of the investment period T is WT. 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 pis 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? 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 U(WT) = W-1 1-p with p=2. The final amount at the end of the investment period T is WT. 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 pis 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?

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a The optimal investment allocation problem is set up by maximizing the expect... View the full answer