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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?

Respuesta :

jepessoa

Answer:

the beta of stock₂ = 1.69

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