Question

A stock with "Beta" of 1.2 has an actual return of 12%. If the risk free rate is 3% and expected return of the market is 9%, what is the "Alpha" of the stock.

Answer 1

To solve for the alpha of a stock with a beta of 1.2, the calculations are based on the CAPM formula. After determining the expected return to be 10.2%, the alpha is found to be 1.8% by subtracting this expected return from the stock's actual return of 12%.

Step-by-step explanation:

To solve completely for the alpha of a stock, we leverage the Capital Asset Pricing Model (CAPM), which expresses a stock's expected return as a function of the risk-free rate, the stock's beta, and the expected market return. The formula is given by:

Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)

However, 'Alpha' represents the stock's return in excess of its CAPM expected return. So, we calculate alpha by subtracting the expected return from the stock's actual return:

Alpha = Actual Return - Expected Return

Let's plug in the values:

• Risk-Free Rate = 3%
• Beta = 1.2
• Market Return = 9%
• Actual Return = 12%

First, calculate the expected return based on the CAPM:

Expected Return = 3% + 1.2 * (9% - 3%)

Expected Return = 3% + 1.2 * 6%

Expected Return = 3% + 7.2%

Expected Return = 10.2%

Now, to find alpha:

Alpha = 12% - 10.2%

Alpha = 1.8%

The alpha of the stock is 1.8%.