Using the data in Example 5.6, find the weights in a portfolio with expected return μV = 46% and compute the risk σ^2V of this portfolio.

Question

Using the data in Example 5.6, find the weights in a portfolio with expected return [latex]μ_V = 46\%[/latex] and compute the risk [ latex]σ^{2}_{V} [/latex] of this portfolio.

Accepted Answer

First, we find compute [latex]μ_1 = 4\%[/latex] and [latex]μ_2 = 16\%[/latex] from the data in Example 5.6. Next, (5.7) and (5.1)

[latex]μ_V = w_1μ_1 + w_2μ_2,[/latex] (5.7)

[latex]w_1 + w_2 =\frac{x_1S_1(0)+x_2S_2(0)}{V(0)} =\frac{V(0)}{V(0)}=1 [/latex] (5.1)

give the system of equations

[latex]4w_1 + 14w_2 = 46,[/latex]
[latex]w_1 + w_2 = 1,[/latex]

for the weights [latex] w_1[/latex] and [latex] w_2[/latex]. The solution is [latex] w_1= −3.2[/latex] and [latex]w_2 = 4.2[/latex]. Finally, we use (5.7) with the values [latex] \sigma^{2}_{1} \cong 0.0184, \sigma^{2}_{2} \cong 0.0024 [/latex] and [latex]ρ_{12}\cong −0.96309 [/latex] computed in Example 5.6 to find the risk of the portfolio:

[latex] \sigma^{2}_{V} \cong (−3.2)^2 × 0.0184 + (4.2)^2 × 0.0024+2 × (−3.2) × 4.2 × (−0.96309) ×\sqrt{0.0184} imes \sqrt{0.0024} [/latex]
[latex]\cong 0.40278.[/latex]

Question 5.8: Using the data in Example 5.6, find the weights in a portfol...

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