Question

In: Finance

You have a $9,000 portfolio which is invested in stocks A, B, and a risk-free asset....

You have a $9,000 portfolio which is invested in stocks A, B, and a risk-free asset. $4,000 is invested in stock A. Stock A has a beta of 1.84 and stock B has a beta of 0.68. How much needs to be invested in stock B if you want a portfolio beta of .95?
Select one:
a. $7,279
b. $5,000
c. $0
d. $1,750
e. $3,279

Solutions

Expert Solution

Answer: d

Portfolio Beta = (Weight of security A to the portfolio * Beta of Security A) + (weight of security B to the portfolio * Beta of security B)

Here Portfolio Beta (Beta p = 0.95)

Beta of Security A (Beta a = 1.84)

Beta of security B (Beta b = 0.68)

Weight of Security A (Wa) = 4000/9000 = 4/9

Total Portfolio value = $ 9000

Therefore,

Portfolio Beta = Wa*Ba + Wb*Bb

==> 0.95 = (4/9)*1.84 + Wb* 0.68

==> Wb* 0.68 = 0.95 -(4/9)*1.84

==> Wb*0.68 = 0.1322

==> Wb = 0.1944

Amount of Security B to the portfolio = Wb * Portfolio Value

                                                       = 0.1944 * 9000

                                                       = 1750

Therefore, $ 1750 needs to be invested in portfolio B.

Therefore, the answer is d.

jeff jeffy answered 1 month ago
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