Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2002/iii/paper-32/2/b/solution

Using from part (a), the portfolio variance is
Thus the minimum-variance correspondence for fixed means has the two branches . The lower branch is dominated by the upper one with the same variance, and portfolios with mean below are also dominated by the risk-free position. Consequently the actual mean-variance efficient frontier is the upper capital market line:
Its slope in standard-deviation/mean coordinates is the maximal Sharpe ratio . In variance/mean coordinates it is the upper branch of .

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