Stocks A and B have the following probability distributions of expected future returns:

Probability A B

$0\mathrm{.}1(12\%)(30\%)$

$0\mathrm{.}150$

$0\mathrm{.}61322$

$0\mathrm{.}12230$

$0\mathrm{.}13639$

Calculate the expected rate of return, $,$ for Stock B $(=12\mathrm{.}90\%.)$ Do not round intermediate calculations. Round your answer to two decimal places.

$\%$

Calculate the standard deviation of expected returns, $\backslash$sigma A$,$ for Stock A $(\backslash$sigma B $=18\mathrm{.}17\%.)$ Do not round intermediate calculations. Round your answer to two decimal places.

$\%$

Now calculate the coefficient of variation for Stock B$.$ Do not round intermediate calculations. Round your answer to two decimal places.

Is it possible that most investors might regard Stock B as being less risky than Stock A$?$

If Stock B is more highly correlated with the market than A$,$ then it might have the same beta as Stock A$,$ and hence be just as risky in a portfolio sense.

If Stock B is less highly correlated with the market than A$,$ then it might have a lower beta than Stock A$,$ and hence be less risky in a portfolio sense.

If Stock B is less highly correlated with the market than A$,$ then it might have a higher beta than Stock A$,$ and hence be more risky in a portfolio sense.

If Stock B is more highly correlated with the market than A$,$ then it might have a higher beta than Stock A$,$ and hence be less risky in a portfolio sense.

If Stock B is more highly correlated with the market than A$,$ then it might have a lower beta than Stock A$,$ and hence be less risky in a portfolio sense.

$-$Select$-$

Assume the risk$-$free rate is $4\mathrm{.}5\%.$ What are the Sharpe ratios for Stocks A and B$?$ Do not round intermediate calculations. Round your answers to four decimal places.

Stock A:

Stock B:

Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b$?$

In a stand$-$alone risk sense A is more risky than B$.$ If Stock B is less highly correlated with the market than A$,$ then it might have a lower beta than Stock A$,$ and hence be less risky in a portfolio sense.

In a stand$-$alone risk sense A is more risky than B$.$ If Stock B is less highly correlated with the market than A$,$ then it might have a higher beta than Stock A$,$ and hence be more risky in a portfolio sense.

In a stand$-$alone risk sense A is less risky than B$.$ If Stock B is more highly correlated with the market than A$,$ then it might have the same beta as Stock A$,$ and hence be just as risky in a portfolio sense.

In a stand$-$alone risk sense A is less risky than B$.$ If Stock B is less highly correlated with the market than A$,$ then it might have a lower beta than Stock A$,$ and hence be less risky in a portfolio sense.

In a stand$-$alone risk sense A is less risky than B$.$ If Stock B is less highly correlated with the market than A$,$ then it might have a higher beta than Stock A$,$ and hence be more risky in a portfolio sense.

$-$Select$-$Stocks A and $B$ have the following probability distributions of expected future returns:

a$.$ Calculate the expected rate of return, hat$(r{)}_B,$ for Stock B $($ hat$(r{)}_A=12\mathrm{.}90\%.)$ Do not round intermediate calculations. Round your answer to two decimal places.

$\%$

b$.$ Calculate the standard deviation of expected returns, ${}_A$ for Stock $.)$ Do not round intermediate calculations. Round your answer to two decimal places.

$\%$

Now calculate the coefficient of variation for Stock B$.$ Do not round intermediate calculations. Round your answer to two decimal places.

Is it possible that most investors might regard Stock B as being less risky than Stock A$?$

I. If Stock B is more highly correlated with the market than $A,$ then it might have the same beta as Stock $A,$ and hence be just as risky in a portfolio sense.

II$.$ If Stock B is less highly correlated with the market than $A,$ then it might have a lower beta than Stock $A,$ and hence be less risky in a portfolio sense.

III. If Stock B is less highly correlated with the market than $A,$ then it might have a higher beta than Stock $A,$ and hence be more risky in a portfolio sense.

IV$.$ If Stock $B$ is more highly correlated with the market than $A,$ then it might have a higher beta than Stock $A,$ and hence be less risky in a portfolio sense.

V$.$ If Stock B is more highly correlated with the market than A$,$ then it might have a lower beta than Stock A$,$ and hence be less risky in a portfolio sense.

c$.$ Assume the risk$-$free rate is $4\mathrm{.}5\%.$ What are the Sharpe ratios for Stocks A and B$?$ Do not round intermediate