Consider a market containing three assets whose returns are mutually uncorrelated.
Consider a market containing three assets whose returns are mutually uncorrelated. The expected returns of the three assets are μ1 = 10%, μ2 = 20%, and μ3 = 30%, and the variances of their returns are σ12 = σ2= σ32 = 0.2.
(a) Suppose you wish to find the weights of the portfolio P with the minimum variance for a target portfolio return μP = 25%. Formulate and solve the Markowitz problem using the method of Lagrange multipliers. What are the weights of P and what is σP ?
(b) Now calculate the scalars A, B, C and ∆ and verify your answers for x∗ andσP 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?
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