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A $36,000 portfolio is invested in a risk-free security and two stocks. The beta of stock A is 1.29 while the beta of stock B is 0.90. One-half of the portfolio is invested in the risk-free security. How much is invested in stock A if the beta of the portfolio is 0.58

Respuesta :

federicoceverino

Answer:

12,000 dollars are invested in A.

Explanation:

This portfolio Beta is calculated

[tex]Stock.A.Beta * invested.A + Stock.B.Beta * invested.B + Risk.free beta * invested.Rf[/tex]

Replacing the text with data (Beta of Riskfree = 0)

[tex]1.29 * A + 0.9 * B + 0 * Rf = 0.58[/tex]

Where, as Rf = 0.5, then A + B = 0.5, then A = 0.5 - B

  • [tex]1.29 * (0.5-B) + 0.9 * B = 0.58[/tex]
  • [tex]0.645 - 1.29 * B + 0.9 * B = 0.58[/tex]
  • [tex] - 0.39 * B = - 0.065[/tex]
  • [tex] B = - 0.065/-0.39 = 16.67%[/tex]
  • Then A = 33.33%
  • So, the investment in A = 36,000 * 33.33% = $12,000