Question

You own a portfolio equally invested in a risk-free asset and two stocks. One of the stocks has a beta of 1.31 and the total portfolio is equally as risky as the market. What must the beta be for the other stock in your portfolio?

Answer 1

the beta of stock₂ = 1.69

Step-by-step explanation:

the weight of each security is ¹/₃ of the portfolio:

• the risk free asset has a beta of 0
• stock₁ has a beta of 1.31
• stock₂ has a beta of ?

the portfolio's beta is 1

1 = (¹/₃ x 0) + (¹/₃ x 1.31) + (¹/₃ x ?)

1 = 0.437 + (¹/₃ x ?)

1 - 0.437 = (¹/₃ x ?)

0.563 = (¹/₃ x ?)

? = 0.563 / ¹/₃ = 1.689 = 1.69

the beta of stock₂ = 1.69