Question 6 (15 marks)

Consider a risk averse investor. He has a risk-free asset with a certain return rf = 0.05. He also considers a stock with random return rm with mean E[rm] = 0.1, variance 2 m = 1. The investor has mean-variance utility E[rp] k 2 p where k > 0 is a parameter, and that E[rp], 2 p are the expected return and variance of the portfolio formed by mixing the risk-free asset and the stock. He chooses E[rp] and 2 p to maximize this utility. All parts below share the same setting.

Question 6 (15 marks) Consider a risk averse investor. He has a risk-free asset with a certain return r;= 0.05. He also considers a stock with random return rm with mean E[ym] 0.1, variance om = 1. The investor has mean-variance utility E[ro] - ko where k > 0 is a parameter, and that E['p],0are the expected return and variance of the portfolio formed by mixing the risk-free asset and the stock. He chooses E[rp] and o to maximize this utility. All parts below share the same setting. Part a. (10 marks) Find the optimal standard deviation of the portfolio op in terms of k. Part a. (10 marks) Find the optimal standard deviation of the portfolio o, in terms of k. Part b. (5 marks) Mathematically show how the the optimal standard deviation of the portfolio changes with k (increase/decrease). Question 6 (15 marks) Consider a risk averse investor. He has a risk-free asset with a certain return r;= 0.05. He also considers a stock with random return rm with mean E[ym] 0.1, variance om = 1. The investor has mean-variance utility E[ro] - ko where k > 0 is a parameter, and that E['p],0are the expected return and variance of the portfolio formed by mixing the risk-free asset and the stock. He chooses E[rp] and o to maximize this utility. All parts below share the same setting. Part a. (10 marks) Find the optimal standard deviation of the portfolio op in terms of k. Part a. (10 marks) Find the optimal standard deviation of the portfolio o, in terms of k. Part b. (5 marks) Mathematically show how the the optimal standard deviation of the portfolio changes with k (increase/decrease)