Question

1a. Your investment club has only two stocks in its portfolio. $50,000 is invested in a stock with a beta of 0.9, and $75,000 is invested in a stock with a beta of 1.3. What is the portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.

1b. AA Corporation's stock has a beta of 0.4. The risk-free rate is 2%, and the expected return on the market is 12%. What is the required rate of return on AA's stock? Do not round intermediate calculations. Round your answer to one decimal place.

Answer 1

Question 1a:

Investment in First stock = $50,000

Investment in Second Stock = $75,000

Total Investment = $50,000 + $75,000 = $125,000

Weight of First Stock = W1= Investment in First Stock / Total Investment = $50,000 / $125,000 = 0.4

Weight of Second Stock =W2 = Investment in Second Stock / Total Investment = $75,000 / $125,000 = 0.6

Beta of first Stock = β1 = 0.9

Beta of Second Stock = β2 = 1.3

Portfolio Beta = [W1* β1] + [W2 * β2]

= [0.4 * 0.9] + [0.6 * 1.3]

= 0.36 + 0.78

= 1.14

Therefore, Portfolio beta is 1.14

Question 1b:

Beta of stock = β = 0.4

Risk free rate = Rf = 2%

Expected Return on Market = Rm = 12%

Required Rate of Return = Rf + β (Rm - Rf)

= 2% + 0.4 *(12%-2%)

= 2% + 4%

= 6%

Therefore, Expected Return on AA's Stock is 6%