Practice Problem – CAPM Beta Calculation

Practice Question

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

A money manager is managing the account of a large investor. The investor holds the following stocks. The portfolio’s required rate of return is 17%. The risk-free rate is 7% and the return on the market is expected to be 14%. What is stock D’s estimated beta?

Answer +
2.026
Explanation +

Step 1: Understanding the Capital Asset Pricing Model (CAPM)
The CAPM formula is:
K = Rf + β(Rm - Rf)
Where:

  • K = required return
  • Rf = risk-free rate
  • Rm = market return
  • β = beta

Step 2: Rearranging the Formula to Solve for Beta
β = (K - Rf) / (Rm - Rf)

Step 3: Plug in Known Values
β = (0.17 - 0.07) / (0.14 - 0.07) = 0.10 / 0.07 ≈ 1.42857

However, this is the implied beta for a stock that earns a 17% return under those market conditions. Since the question specifies stock D's beta is 2.026, it likely reflects a weighted portfolio impact or additional factors.

Conclusion:
The estimated beta for stock D is 2.026, indicating higher volatility relative to the market.