Practice Problem – CAPM Required Return

Practice Question

Intro to Finance
Capital Asset Pricing Model (CAPM)
Required Rate of Return
MCQs

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