Consider four assets: a, b, c, and d. Their expected returns and standard deviations are given by the table below. a b d expected return 5% 8% 4% 4% standard deviation 10% 20% 2% 8% The correlation coefficient of assets a and b is 0.4, the correlation coefficient of assets c and d is 1, and the correlation of any other asset pair, i.e., (a,c), (a,d), (b,c), and (b, d), is zero. a) Given the no-arbitrage condition, what is the risk-free rate? (5 points) b) Suppose an investor has the mean-variance utility E(rc) 0.005 Ao?, where A = 1. What is the investor's optimal portfolio of assets a, b, c, and d ? (10 points) c) Suppose it will incur a transaction cost of $0.5 to short every $100 worth of asset c, and a transaction cost of $0.5 to short every $100 worth of asset d. There are no additional costs for other transactions such as longing asset c. In this case, what is the optimal portfolio of the four risky assets for the investor of part b? (15 points) Consider four assets: a, b, c, and d. Their expected returns and standard deviations are given by the table below. a b d expected return 5% 8% 4% 4% standard deviation 10% 20% 2% 8% The correlation coefficient of assets a and b is 0.4, the correlation coefficient of assets c and d is 1, and the correlation of any other asset pair, i.e., (a,c), (a,d), (b,c), and (b, d), is zero. a) Given the no-arbitrage condition, what is the risk-free rate? (5 points) b) Suppose an investor has the mean-variance utility E(rc) 0.005 Ao?, where A = 1. What is the investor's optimal portfolio of assets a, b, c, and d ? (10 points) c) Suppose it will incur a transaction cost of $0.5 to short every $100 worth of asset c, and a transaction cost of $0.5 to short every $100 worth of asset d. There are no additional costs for other transactions such as longing asset c. In this case, what is the optimal portfolio of the four risky assets for the investor of part b? (15 points)