Solve these out.

Question 1 (i) Using mean-variance portfolio theory, prove that the efficient frontier becomes a straight line in the presence of a risk-free asset. [3] Consider two independent assets, Asset A and Asset B, with expected returns of 6% pa and 11% pa and standard deviations of returns of 5% pa and 10% pa respectively. (ii) If only Assets A and B are available, calculate the equation of the efficient frontier in expected return-standard deviation space. [3] (iii) A third Asset, Asset C. is risk-free and has an expected return of 4% pa. A Lagrangian function is to be used to calculate the equation of the new efficient frontier. Write down, but do not solve, the five simultaneous equations that result from this procedure. [3] (iv) Use your simultaneous equations to derive the relationship between x, and xg, the holdings of Assets A and B, on the new efficient frontier. [2] (v) Hence derive the equation of the new efficient frontier in expected return- standard deviation space. [4] [Total 15]Question 2 Two assets, A and B with independent returns Ry and Ry, are available to investors. The return on Asset A is assumed to be normally distributed: RA - N (8%, 36%%) The return on Asset B can be described by the following probability distribution: -15% with probability 0.04 1% with probability 0.2 RR = 10% with probability 0.6 20% with probability 0.16 (i) Calculate the expected return, E, and the standard deviation, o , of the return on Asset B. [2] (ii) For both assets, find the value at risk (VaR) at the 5% confidence level on a Elm portfolio invested entirely in that asset. [3] (iii) Compare assets A and B in the light of your answers to parts (i) and (ii) and comment on the use of VaR as a measure of investment risk. [3] (iv) Specify the equation of the efficient frontier in G-E space for portfolios invested in Assets A and B. [4] (v) An investor's risk preferences can be adequately described by indifference curves, in E -V space, of the form: E = 0.017+# -1 for some a > 0. Find the expected return of this investor's optimal portfolio. [5] [Total 17]