Suppose that you have found an optimal portfolio P of risky assets which will have a stochastic return Rp. It has an expected return denoted by E[Rp] and a volatility denoted by p. You form your complete portfolio C by deciding on the portfolio weight y invested into P and the weight 1 y invested into the risk-free asset which has a deterministic return rf (risk free rate).

a. Write down an expression for the return on the complete portfolio, Rc.[4]

b. Suppose you have preferences given by U(y) = E[Rc] 1/2A_c² ; where A is a parameter that determines risk aversion, E[Rc] is the expected return on the complete portfolio and _c² is the variance of the complete portfolio. Solve for the optimal weight in P . [6

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