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$6.$ Calculating a beta coefficient for a single stock

Suppose that the standard deviation of returns for a single stock $A$ is ${}_A=40\%,$ and the standard deviation of the market return is ${}_M=20\%.$ If the correlation between stock A and the market is ${}_{AM}=0\mathrm{.}7,$ then the stock's beta is $q,.$

Is it reasonable to expect that the volatility of the market portfolio's future expected returns will be greater than the volatility of stock A$\text{'}$s returns?

No

Yes

Next, consider a two$-$asset portfolio consisting of stock A with $w_A=10\%$ and an expected return $r_A=8\%$ and a standard deviation of ${}_A=10\%,$ and stock $B$ with $r_B=11\%$ and ${}_B=4\%.$ Assuming that the correlation between stocks A and $B$ is ${}_{AB}=0\mathrm{.}75,$ the expected return to the portfolio is $,$ and the portfolio's standard deviation is $.$

Suppose that the correlation between stocks A and $B$ is ${}_{AB}=-1,$ instead of ${}_{AB}=0\mathrm{.}75.$ Which of the following statements correctly reflects the new data?

The risk associated with the portfolio is lower.

The expected return to the portfolio is lower.

The expected return to the portfolio is higher.

The risk associated with the portfolio is higher.