Practice Problem – Alpha (CAPM)

Practice Question

Intro to Finance
Capital Asset Pricing Model (CAPM)
Alpha, Stock Valuation
Short Answer

Stock A is valued at \$21.65 per share. The return of the market portfolio is 12% and the return of Stock A is 9%. The risk-free rate is 2% and the company’s beta is 1.00. What is the alpha of Stock A under CAPM?

Answer +
Correct Answer: -3% or -0.030
Explanation +

Let’s calculate the alpha of Stock A using the given data.

Given Data

  • Return of Stock A: \( R_A = 9\% \)
  • Return of market: \( R_M = 12\% \)
  • Risk-free rate: \( R_f = 2\% \)
  • Beta: \( \beta = 1.00 \)

Formula for Alpha

\[ \alpha = R_A - \left[ R_f + \beta \cdot (R_M - R_f) \right] \]

Step-by-Step Calculation

  • Expected return using CAPM: \[ R_{\text{expected}} = R_f + \beta \cdot (R_M - R_f) = 0.02 + 1.00 \cdot (0.12 - 0.02) = 0.12 \]
  • Alpha: \[ \alpha = R_A - R_{\text{expected}} = 0.09 - 0.12 = -0.03 \]

Final Answer

The alpha of Stock A is -3%.

Explanation

We first used the CAPM formula to determine the expected return for Stock A based on its beta. The CAPM-predicted return was 12%, but the actual return was only 9%. Therefore, the alpha is -3%, indicating Stock A is underperforming relative to what its risk level would suggest.