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?

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

New beta = 1.23

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