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Suppose there is no riskless asset and we have three stocks: A, B and C. Their expected returns are given by r = 2 64

Suppose there is no riskless asset and we have three stocks: A, B and C. Their expected returns are given by r = 2 64 10% 20% 30% 3 75 : The covariance matrix is V = 2 64 1 0 0 0 1 0 0 0 1 3 75 : (a) Let p be a portfolio on the minimum-variance frontier (MVF). Write the return stan- dard deviation of p, p, as a function of its expected return rp. (b) Using the result you obtained from part (a), plot the MVF. (c) Find the global minimum-variance portfolio xGMV . (d) Label the minimum-variance portfolio p0 with E[rp0 ] = 25% on the MVF you draw in part (b). (e) Find a portfolio p00 on the MVF which is uncorrelated with p0 and label it on the plot you draw in part (b). p00 is called the zero-beta portfolio for p0. (f) Now draw a straight line that passes through (0; rp00) and (p0 ; rp0 ). What do you nd? Hint: you should conclude that you have found a geometric method to determine the expected return of the zero-beta portfolio for almost any portfolio on the MVF.

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