In a market consisting of the three securities in Exercise 5.12, consider the portfolio on the efficient frontier with expected return μV = 21%. Compute the values of γ and μ such that the weights w in this portfolio satisfy γwC = m − μu.

Question

In a market consisting of the three securities in Exercise 5.12, consider the portfolio on the efficient frontier with expected return [latex]μ_V = 21\%[/latex]. Compute the values of [latex]γ[/latex] and [latex]μ[/latex] such that the weights w in this portfolio satisfy [latex]γwC = m− μu.[/latex]

Accepted Answer

Let m be the one-row matrix formed by the expected returns of the three
securities. By multiplying the [latex]γwC = m − μu[/latex] equality by [latex]C^{−1}u^{T}[/latex] and, respectively,[latex]C ^{−1}m^{T}[/latex], we get

[latex]μV (m − μu)C^{−1}u^{T} = (m − μu)C^{−1}m^{T} ,[/latex]

since [latex]wu^{T} = 1[/latex] and [latex]wm^{T }= μ_V[/latex] . This can be solved for μ to get

[latex]\mu =\frac{mC^{-1}(m^{T} − μ_V u^T )}{uC^{-1}(m^T− μ_V u^T)} \cong 0.142.[/latex]

Then, [latex]γ[/latex] can be computed as follows:

[latex]γ = (m − μu)C^{-1}u^T \cong 1.367.[/latex]

Question 5.15: In a market consisting of the three securities in Exercise 5...

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