Question

You have $140,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 17.6 percent. Stock X has an expected return of 14 percent and a beta of 1.42, and Stock Y has an expected return of 10.0 percent and a beta of 1.18.
How much money will you invest in stock Y?


What is the beta of your portfolio?

Answer 1

Answer:

Amount investment in Sock Y = - $126,000

Beta of portfolio = 1.636

Explanation:

Data provided in the question:

Total amount to be invested = $140,000

Stock                          X       Y

Expected return       14%     10%

Beta                          1.42     1.18

Expected return of portfolio = 17.6%

Now,

let the weight invested n stock X be W

therefore,

Weight of Stock Y = 1 - W

thus,

( W × 14% ) + (1 - w) × 10% = 17.6 %

or

14W + 10% - 10W = 17.6%

or

4W = 7.6

or

W = 1.9

Therefore,

weight of Y = 1 - 1.9 = -0.9

Thus,

Amount investment in Sock Y = Total amount to be invested × Weight

= 140,000 × ( - 0.9 )

= - $126,000 i.e short Y

Beta of portfolio = ∑ (Beta × Weight)

= [ 1.42 × 1.9 ] + [ 1.18 × (-0.9) ]

= 2.698 - 1.062

= 1.636