$5.$ Calculating a beta coefficient for a single stock

Suppose that the standard deviation of returns for a single stock A is $\backslash$sigma A

$=40\%,$ and the standard deviation of the market return is $\backslash$sigma M

$=20\%.$ If the correlation between stock A and the market is $\backslash$rho AM

$=0\mathrm{.}7,$ then the stock$$s beta is $.$

Is it reasonable to expect that the beta value estimated via the regression of stock A$$s returns against the market returns will equal the true value of stock A$$s beta?

No

Yes

Next, consider a two$-$asset portfolio consisting of stock A with wA

$=75\%$ and an expected return rA

$=5\%$ and a standard deviation of $\backslash$sigma A

$=4\%,$ and stock B with rB

$=8\%$ and $\backslash$sigma B

$=10\%.$ Assuming that the correlation between stocks A and B is zero, the expected return to the portfolio is $,$ and the portfolio$$s standard deviation is $.$

Suppose that the correlation between stocks A and B is $\backslash$rho AB

$=1,$ instead of zero. Which of the following statements correctly reflects the new data?

The risk associated with the portfolio is higher.

The expected return to the portfolio is higher.

The expected return to the portfolio is lower.

The risk associated with the portfolio is lower.

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