Question

Assume that you hold a well-diversified portfolio that has an expected return of 11.0% and a beta of 1.20. You are in the process of buying 1,000 shares of Garden Corp at $10 a share and adding it to your portfolio. Garden Corp has an expected return of 13.0% and a beta of 1.50. The total value of your current portfolio is $90,000. What will the expected return and beta on the portfolio be after the purchase of the Garden Corp stock?

Answer 1

Expected return on the portfolio be after the purchase of the Garden Corp stock = $11,200

New beta = 1.23

Step-by-step explanation:

Data provided in the question:

Expected return on portfolio = 11.0% = .011

Beta of portfolio = 1.20

Number of shares to buy = 1,000

Cost of share = $10

Expected return on Golden Corp = 13.0% = 0.13

Beta of Golden Corp = 1.50

The total value of your current portfolio = $90,000

Now,

Total value of Golden corp shares = $10 × 1,000

= $10,000

Expected return on the portfolio be after the purchase of the Garden Corp stock

= ∑ (Expected return × Total value)

= 0.11 × $90,000 + 0.13 × $10,000

= $9,900 + $1,300

= $11,200

New beta = ∑ (Beta × Weight)

Now,

Total value of the new portfolio = $90,000 + $10,000 = $100,000

thus,

New beta = 1.20 × [90,000 ÷ 100,000] + 1.50 × [10,000 ÷ 100,000]

= 1.20 × 0.9 + 1.5 × 0.1

= 1.08 + 0.15

= 1.23