Exercise 2 An investor with mean-variance utility U(P) = p a can invest both in a...

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Exercise 2 An investor with mean-variance utility U(P) = p a can invest both in a risk-less asset, asset 0, and in a risky asset. The risk-less asset has expected return = 2%. The risky asset has expected return = 6% and standard deviation = 10%. Denote with a the fraction of wealth invested in this portfolio and assume that the agent cannot borrow. (a) Find the Sharpe ratio of the risky asset and draw the set of feasible portfolios P in the plane (p, p). (b) Find the maximal value of the risk aversion such that the investor chooses to invest all in the risky asset and name it . (c) Find the optimal portfolio when a = /2 and provide a graphical representation. Exercise 2 An investor with mean-variance utility U(P) = p a can invest both in a risk-less asset, asset 0, and in a risky asset. The risk-less asset has expected return = 2%. The risky asset has expected return = 6% and standard deviation = 10%. Denote with a the fraction of wealth invested in this portfolio and assume that the agent cannot borrow. (a) Find the Sharpe ratio of the risky asset and draw the set of feasible portfolios P in the plane (p, p). (b) Find the maximal value of the risk aversion such that the investor chooses to invest all in the risky asset and name it . (c) Find the optimal portfolio when a = /2 and provide a graphical representation.