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You would like to create a portfolio that is equally invested in a risk-free asset and two stocks. One stock has a beta of 1.14. What does the beta of the second stock have to be if you want the portfolio to be equally as risky as the overall market

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Answer:

Beta of the other stock should be 1.89.

Explanation:

The overall market always has a beta of 1. So if you want the portfolio to be equally risky as market, the overall beta of the portfolio should also be equal to one.  

The beta of a portfolio is the weighted average of the beta of all the stocks in it. This portfolio is comprised of a bond and two stocks. The bond is risk-free so its beta will be 0.    

The portfolio beta will be  

= [tex](weight\ asset\ 1\ \times Beta\ 1)\ +\ (weight\ asset\ 2\ \times Beta\ 2)\ +\ (weight\ risk\ free\ asset\ \times Beta\ risk\ free\ asset)[/tex]

[tex]1 = (0.33\ \times\ B1)\ +\ (0.33\ \times\ 1.14)\ +\ 0.33\ \times\ 0[/tex]

[tex]1 = 0.33B1\ +\ 0.3762\ +\ 0[/tex]

[tex]1\ -\ 0.3762\ =\ 0.33B1[/tex]

[tex]B1\ =\ \frac{0.6238}{0.33}[/tex]

B1 = 1.89    

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