You have a $15,000 portfolio which is invested in stocks a and b, and a risk-free asset. $6,000 is invested in stock a. stock a has a beta of 1.63 and stock b has a beta of .95. how much needs to be invested in stock b if you want a portfolio beta of 1.10?

$7073.68

Explanation:

Data provided in the question:

Worth of portfolio = $15,000

Amount invested in stock A = $6,000

Beta of stock A = 1.63

Beta of stock B = 0.95

Beta of portfolio = 1.10

Now,

Beta portfolio = ∑(Weight × Beta)

let the amount invested in Stock B be 'x'

thus,

1.10 = [($6,000 ÷ $15,000 ) × 1.63] +  [( x ÷ $15,000 ) × 0.95 ]

or

1.10 = 0.652 + [( x ÷ $15,000 ) × 0.95 ]

or

0.448 = [( x ÷ $15,000 ) × 0.95 ]

or

x = ( 0.448 × $15,000 ) ÷ 0.95

or

x = $7073.68