- 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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