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Consider two stocks, Stock D, with an expected return of 19 percent and a standard deviation of 35 percent, and Stock I, an international company, with an expected return of 10 percent and a standard deviation of 15 percent. The correlation between the two stocks is –0.04. What is the weight of each stock in the minimum variance portfolio?

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Answer:

[tex]W_D=0.0843\\W_I=0.9157[/tex]

Explanation:

A minimum variance portfolio is a portfolio that consists of individually assets which are risky, hedged when traded together, thereby producing the lowest possible risk for the rate of expected return. It reduces the risk of assets by hedging and trading them together.

Given that for stock D:

expected return([tex]E_d[/tex]) = 19% = 0.19 and a standard deviation ([tex]S_d[/tex])=  35% = 0.35

For stock I

expected return ([tex]E_i[/tex]) = 10% = 0.10 and a standard deviation ([tex]S_i[/tex]) =  15% = 0.15

Correlation = -0.04

The weight of stock D ([tex]W_D[/tex]) is given as:

[tex]W_D=\frac{S_i^2-(S_d*S_i*c)}{S_d^2+S_i^2-(2*S_d*S_i*c)} =\frac{0.1^2-(0.35*0.1*-0.04)}{0.35^2+0,1^2-(2*0.35*0.1*-0.04)}=0.0843[/tex]

[tex]W_I=1-W_D=1-0.0843=0.9157[/tex]

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