Compute the weights in a portfolio consisting of two kinds of stock if the expected return on the portfolio is to be E(KV ) = 20%, given the following information on the returns on stock 1 and 2:

Question

Compute the weights in a portfolio consisting of two kinds of stock if the expected return on the portfolio is to be [latex]E(K_V ) = 20\%[/latex], given the following information on the returns on stock 1 and 2:

Scenario	Probability	Return [latex]K_1[/latex]	Return [latex]K_2[/latex]
[latex]ω_1[/latex](recession)	0.1	−10%	10%
[latex]ω_2[/latex](recession)	0.5	0%	20%
[latex]ω_3[/latex] (boom)	0.4	20%	30%

Accepted Answer

First we find [latex]E(K_1 ) = 7\%[/latex] and [latex]E(K_2 ) = 23\%[/latex] . If the expected return on the portfolio is to be [latex]E(K_V ) = 20\%[/latex], then by (5.4) and (5.1)

[latex]E(K_V ) = w_1E(K_1) + w_2E(K_2).[/latex] (5.4)

[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)

the weights must satisfy the system of equations

[latex]7w_{1 }+ 23w_{2} = 20,[/latex]
[latex]w_{1} + w_{2} = 1.[/latex]

The solution is [latex]w_1 = 18.75\%.[/latex] and [latex]w_2 = 81.25\%.[/latex]

Question 5.7: Compute the weights in a portfolio consisting of two kinds o...

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