Question

A single stock, A has a variance of 0.006 and a covariance with the market portfolio given by 0.013.

The market portfolio has an expected return of 10.50%, a market risk premium 4.30% and a variance of 0.013.
What is the stock's fair expected return under the CAPM?

Answer 1

The stock's fair expected return under the CAPM is approximately 11.18%.

Step-by-step explanation:

The Capital Asset Pricing Model (CAPM) formula is given by:

`\[ \text{Expected Return} = \text{Risk-Free Rate} + \beta * (\text{Market Risk Premium}) \]`

Here,
`\(\beta\)` represents the stock's beta, which is the covariance of the stock with the market portfolio divided by the variance of the market portfolio. Mathematically,
`\(\beta = \frac{\text{Covariance(A, Market)}}{\text{Variance(Market)}}\)`.

Given that the market portfolio has an expected return of 10.50%, a market risk premium of 4.30%, and a variance of 0.013, we can calculate the market risk premium as
`\(0.043 * 100\% = 4.30%\)`. The beta for stock A is
`\((0.013)/(0.006) = 2.1667\)`. Substituting these values into the CAPM formula:

`\[ \text{Expected Return} = 0 + 2.1667 * 4.30\% = 9.32\% + 4.30\% = 13.62\% \]`

However, the question asks for the stock's fair expected return, so we need to adjust for the risk-free rate. Assuming the risk-free rate is 2%, the fair expected return is
`\(13.62\% - 2\% = 11.18%\)`. Therefore, the stock's fair expected return under the CAPM is approximately 11.18%.