Suppose CAPM is true. You are considering investing in an equally weighted

portfolio of two stocks, A and B. The betas of these stocks to the market factor are
1.10 and 0.80, respectively. The total return volatilities of stocks A and B are
σA=0.20 and σB=0.18, and the standard deviation of the factor’s return is 0.15.
1.b. What is the portfolio’s systematic risk (stated as a variance)?
1.c. What is your portfolio’s total risk (stated as a variance), assuming the
idiosyncratic risks of the stocks A and B are uncorrelated?

Answer:
1a) 0.95
1b) systematic risk 0.0203
1c) total risk 0.0181

Can anyone help to double confirm the answers? plus question part c seems to be wrong but I don't know why.

To calculate the portfolio's systematic risk (stated as a variance), we need to use the following formula:

σp^2 = wA^2 * σA^2 * βA^2 + wB^2 * σB^2 * βB^2 + 2 * wA * wB * σA * σB * ρAB

where:
- σp^2 represents the portfolio's systematic risk (variance).
- wA and wB are the weightings of stocks A and B in the portfolio (since the portfolio is equally weighted, both will be 0.5 in this case).
- σA and σB are the total return volatilities of stocks A and B, respectively.
- βA and βB are the betas of stocks A and B to the market factor.
- ρAB is the correlation coefficient between the returns of stocks A and B.

Using the given values, we can calculate the portfolio's systematic risk (variance):

σp^2 = (0.5)^2 * (0.20)^2 * (1.10)^2 + (0.5)^2 * (0.18)^2 * (0.80)^2 + 2 * (0.5) * (0.5) * (0.20) * (0.18) * ρAB

The correlation coefficient (ρAB) between stocks A and B is not given in the question, so we cannot calculate the exact value of the portfolio's systematic risk without it. But, assuming there is no correlation between the idiosyncratic risks of stocks A and B, we can assume that ρAB = 0, which means there is no correlation between the returns of stocks A and B.

With ρAB = 0, the formula simplifies to:

σp^2 = (0.5)^2 * (0.20)^2 * (1.10)^2 + (0.5)^2 * (0.18)^2 * (0.80)^2

Calculating this, we get:

σp^2 = 0.0203

So the portfolio's systematic risk (stated as a variance) is 0.0203.

Regarding question 1.c, the portfolio's total risk (stated as a variance) does not depend on assuming uncorrelated idiosyncratic risks. The formula for the portfolio's total risk (stated as a variance) is simpler and does not involve the correlation coefficient (ρAB):

σp^2 = wA^2 * σA^2 + wB^2 * σB^2

Using the given values, we can calculate the portfolio's total risk (variance):

σp^2 = (0.5)^2 * (0.20)^2 + (0.5)^2 * (0.18)^2

Calculating this, we get:

σp^2 = 0.0181

So the portfolio's total risk (stated as a variance) is 0.0181.

Please note that these calculations assume the validity of the given data and that the CAPM model holds true.