1. Consider a market containing three assets whose returns are mutually uncorrelated. The expected returns of the three assets are1= 10%,2= 20%, and3= 30%, and the variances of their returns are12=2=32= 0.2.
2. (a)Suppose you wish to find the weights of the portfolioPwith the minimum variance for a target portfolio returnP= 25%. Formulate and solve the Markowitz problem using the method of Lagrange multipliers. What are the weights ofPand what isP?
3. (b)Now calculate the scalarsA,B,Cand and verify your answers forxandPfrom part (a). Remember that a diagonal matrix can be inverted by inverting each element of the diagonal.
4. (c)Calculate the expected return and standard deviation of returns for the global MVP,G. Is the portfolioPefficient?
5. (d)Write down the equations for the asymptotes of the MVS.
6. (e)Sketch the MVS and its asymptotes in mean-standard deviation space. Your diagram should indicate the positions ofP,G, and the three underlying assets. You should also identify the efficient and inefficient components of the MVS.
7. (f)CompareGwith the three global MVP's that result when combining only two of the above assets at a time. Does adding a third asset improve things?