Problem 4: (a) Suppose that there are many stocks in the security market and that the characteristics of Stocks A and B are given as follows Stock Expected Return Standard Deviation A 10% 5% B 15% 10% Correlation = -1 Suppose that it is possible to borrow at the risk-free rate, . What must be the value of the risk-free rate? Explain. HINT!!! The stocks are perfectly negatively correlated. (b) Calculate the expected return and standard deviation of an equally weighted portfolio of Stock A, Stock B and the risk-free asset. (c) What is the optimal portfolio? Assume the investors risk aversion coefficient is given by A=4. Provide all the relevant portfolio weights for all three assets. The utility function is given below. HINT: The formula sheet contains a formula for the optimal risky portfolio for the special case of two risky assets. Ui = E(ri) - 0.5A sigma^2 i Problem 4: (a) Suppose that there are many stocks in the security market and that the characteristics of Stocks A and B are given as follows Stock Expected Return Standard Deviation A 10% 5% B 15% 10% Correlation = -1 Suppose that it is possible to borrow at the risk-free rate, . What must be the value of the risk-free rate? Explain. HINT!!! The stocks are perfectly negatively correlated. (b) Calculate the expected return and standard deviation of an equally weighted portfolio of Stock A, Stock B and the risk-free asset. (c) What is the optimal portfolio? Assume the investors risk aversion coefficient is given by A=4. Provide all the relevant portfolio weights for all three assets. The utility function is given below. HINT: The formula sheet contains a formula for the optimal risky portfolio for the special case of two risky assets. Ui = E(ri) - 0.5A sigma^2