bv_cvxbook_extra_exercises

We are interested in determining the values of r r w

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Unformatted text preview: ve about the mean return vector p. For example, l7 = 0.02 and u7 = 0.20 means that we believe the ¯ mean return for asset 7 is between 2% and 20%. Define the worst-case mean return Rwc , as a function of portfolio vector x, as the worst (minimum) value of pT x, over all p consistent with the given bounds l and u. ¯ ¯ (a) Explain how to find a portfolio x that maximizes Rwc , subject to a budget constraint and risk limit, 2 1T x = 1, xT Σx ≤ σmax , where Σ ∈ Sn and σmax ∈ R++ are given. ++ (b) Solve the problem instance given in port_qual_forecasts_data.m. Give the optimal worstcase mean return achieved by the optimal portfolio x⋆ . In addition, construct a portfolio xmid that maximizes cT x subject to the budget constraint and risk limit, where c = (1/2)(l + u). This is the optimal portfolio assuming that the mean return has the midpoint value of the forecasts. Compare the midpoint mean returns cT xmid and cT x⋆ , and the worst-case mean returns of xmid and x⋆ . Briefly comment on the results. 115 14 Mechanical and aerospace engineering 14.1 Optimal design of a tensile str...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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