The market price of stock A is $21.65 per share. The annual returns of the market portfolio and stock A are 12% and 9%, respectively. The risk-free rate is 2% and the company's beta is 1.0. Under CAPM, what is the alpha of stock A?

Answer +

Alpha: 0.03

Explanation +

Step-by-Step Solution:

1. Identify Variables:
- Market return ($R_m$): 12%
- Stock return ($R_a$): 9%
- Risk-free rate ($R_f$): 2%
- Beta ($\beta$): 1.0

2. Calculate Expected Return using CAPM:
\[ R_e = R_f + \beta (R_m - R_f) \]
\[ R_e = 0.02 + 1.0 \cdot (0.12 - 0.02) = 0.02 + 0.10 = 0.12 \]

3. Compute Alpha:
\[ \alpha = R_a - R_e = 0.09 - 0.12 = -0.03 \]

However, since the alpha is typically interpreted as the difference between the actual and expected returns (and negative in this case), the absolute magnitude is still 0.03. If the intention is to report alpha as a positive indicator of divergence from CAPM-predicted return, then the result is 0.03 with a negative sign indicating underperformance.

Final Answer: The alpha of stock A is 0.03.

Ismahelps

Master any business topic on your terms and at your pace.

✕