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3.9. We have three assets with uncorrelated returns Ri, i = 1, 2, 3. They all have variance 1, and the mean values are 1, 2, and 3, respectively. We consider nonnegative portfolio allocations x1, x2, x3 totaling one, and the portfolio return R(x) = xR1 + x2 R2 + x2 R3 as a function of x. Let r(x) denote its mean, and V (x) its variance. We considered this example in the Introduction (see (1.4)). (a) Find the minimum variance portfolio as the solution of the problem minimize V (x) subject to X e Xo, where Xo is the set of possible allocations. Denote by mo its expected return. (b) The mean-variance efficient portfolios are computed by solving the problem minimize V(x) subject to r(x) = m, X e Xo, for all m > mo for which this problem has a solution. Find the set of all mean-variance efficient portfolios (so-called efficient frontier). (c) Assume that in addition we have a risk-free asset with a guaranteed return of 0.5. Describe the efficient frontier in this case. 3.9. We have three assets with uncorrelated returns Ri, i = 1, 2, 3. They all have variance 1, and the mean values are 1, 2, and 3, respectively. We consider nonnegative portfolio allocations x1, x2, x3 totaling one, and the portfolio return R(x) = xR1 + x2 R2 + x2 R3 as a function of x. Let r(x) denote its mean, and V (x) its variance. We considered this example in the Introduction (see (1.4)). (a) Find the minimum variance portfolio as the solution of the problem minimize V (x) subject to X e Xo, where Xo is the set of possible allocations. Denote by mo its expected return. (b) The mean-variance efficient portfolios are computed by solving the problem minimize V(x) subject to r(x) = m, X e Xo, for all m > mo for which this problem has a solution. Find the set of all mean-variance efficient portfolios (so-called efficient frontier). (c) Assume that in addition we have a risk-free asset with a guaranteed return of 0.5. Describe the efficient frontier in this case