1. Consider a portfolio containing two risky assets (1 and 2). Suppose that the investor chooses the value weights wi and w2 to maximise the expression Log(R Ri) V Logo where Log(.) denotes the natural logarithm, R, is the portfolio expected return, o is the portfolio variance, and Rf is the return on the riskless asset. a. Write down the Lagrangian for this problem. [5 marks] b. Demonstrate that a = Rf/(Rp Rf), where a is the Lagrange multiplier. [15 marks] c. Using your answer in (b), show that the portfolio lies on the security market line. [5 marks] 1. Consider a portfolio containing two risky assets (1 and 2). Suppose that the investor chooses the value weights wi and w2 to maximise the expression Log(R Ri) V Logo where Log(.) denotes the natural logarithm, R, is the portfolio expected return, o is the portfolio variance, and Rf is the return on the riskless asset. a. Write down the Lagrangian for this problem. [5 marks] b. Demonstrate that a = Rf/(Rp Rf), where a is the Lagrange multiplier. [15 marks] c. Using your answer in (b), show that the portfolio lies on the security market line. [5 marks]