Consider a market containing three assets whose returns are mutually uncorrelated. The expected retu
Consider a market containing three assets whose returns are mutually uncorrelated. The expected returns of the three assets are ?1 = 10%, ?2 = 20%, and ?3 = 30%, and the variances of their returns are ?12 = ?2= ?32 = 0.2.(a) Suppose you wish to find the weights of the portfolio P with the minimum variance for a target portfolio return ?P = 25%. Formulate and solve the Markowitz problem using the method of Lagrange multipliers. What are the weights of P and what is ?P ?(b) Now calculate the scalars A, B, C and ? and verify your answers for x? and?P from part (a). Remember that a diagonal matrix can be inverted by inverting each element of the diagonal.(c) Calculate the expected return and standard deviation of returns for the global MVP, G. Is the portfolio P efficient?(d) Write down the equations for the asymptotes of the MVS.(e) Sketch the MVS and its asymptotes in mean-standard deviation space. Your diagram should indicate the positions of P, G, and the three underlying assets. You should also identify the efficient and inefficient components of the MVS.(f) Compare G with 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?
