Practice Question
An investor is forming a portfolio by investing $50,000 in stock A that has a beta of 1.50, and $25,000 in stock B that has a beta of 0.90. The return on the market is equal to 6 percent and Treasury bonds have a yield of 4 percent. What is the required rate of return on the investor’s portfolio?
Answer +
A
Explanation +
Step 1: Calculate the Portfolio Beta (Bp)
Use the weighted average of the individual stock betas:
- Stock A: $50,000 at β = 1.50
- Stock B: $25,000 at β = 0.90
Total investment: $75,000
WA = 50,000 / 75,000 = 0.67
WB = 25,000 / 75,000 = 0.33
Bp = (0.67 × 1.50) + (0.33 × 0.90)
= 1.005 + 0.297
= 1.302
Step 2: Apply the CAPM Formula
CAPM: K = Rf + Bp × (Rm - Rf)
- Risk-free rate (Rf) = 4%
- Market return (Rm) = 6%
- Bp = 1.302
K = 4% + 1.302 × (6% - 4%)
= 4% + 1.302 × 2%
= 4% + 2.604%
= 6.604%
Final Answer
The required rate of return on the investor’s portfolio is approximately 6.6%.
Answer: A