Problem $8\mathrm{.}06($Expected Returns$)$

eBook Problem Walk$-$Through

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

Probability A B

$0\mathrm{.}1(10\%)(37\%)$

$0\mathrm{.}160$

$0\mathrm{.}51220$

$0\mathrm{.}22227$

$0\mathrm{.}13243$

Calculate the expected rate of return, $,$ for Stock B $(=13\mathrm{.}20\%.)$ Do not round intermediate calculations. Round your answer to two decimal places.

$80$

$\%$

Calculate the standard deviation of expected returns, $\backslash$sigma A$,$ for Stock A $(\backslash$sigma B $=20\mathrm{.}29\%.)$ Do not round intermediate calculations. Round your answer to two decimal places.

$1\mathrm{.}27$

$\%$

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 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.

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.

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Assume the risk$-$free rate is $1\mathrm{.}5\%.$ 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 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.

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.

$-$Select$-$