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 Alpha Corp at $10 a share and adding it to your portfolio. Alpha has an expected return of 21.5% and a beta of 1.70. 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 Alpha stock? Do not round your intermediate calculations.

a. 12.29%; 1.48

b. 13.98%; 1.28

c. 12.05%; 1.25

d. 9.40%; 1.34

e. 12.41%; 1.56

Answer 1

We have an old portfolio and then Alpha Corp stocks with a market value of $10,000 are added to the old portfolio to get the new portfolio.

Investment in old portfolio is $90,000

Investment in Alpha Corp. = 1000 * $10 = $10,000

Total investment = $100,000

Expected return of old portfolio = E[R₁] = 11%

beta of old portfolio = β₁ = 1.2

Weight of the old portfolio = W₁ = Investment in old portfolio/Total Investment = 90000/100000 = 9/10

Expected Return on Alpha Corp. = E[R₂] = 21.5%

Beta of Alpha Corp = β₂ = 1.7

weight of Alpha Corp in new portfolio = W₂ =Investment in Alpha Corp/Total Investment = 10000/100000 = 1/10

Expected return on new portfolio = W₁*E[R₁] + W₂*E[R₂] = (9/10)*11% + (1/10)*21.5% = 12.05%

Beta of the new portfolio = W₁*β₁ + W₂*β₂ = (9/10)*1.2 + (1/10)*1.7 = 1.25556 = 1.25

Answer -> c. 12.05%, 1.25