Ch $08$: End$-$of$-$Chapter Problems GRADED $-$ Risk and Rates of Return

a$.$ Calculate the expected rate of return, hat$(r{)}_B,$ for Stock $.)$ Do not round intermediate calculations. Round your answer to two

decimal places.

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b$.$ Calculate the standard deviation of expected returns, ${}_A,$ for Stock A $({}_B=27\mathrm{.}73\%.)$ Do not round intermediate calculations. Round your

answer to two decimal places.

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Now calculate the coefficient of variation for Stock B$.$ 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 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.

II$.$ 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.

III. 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.

IV$.$ 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.

V$.$ 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.

c$.$ Assume the risk$-$free rate is $2\mathrm{.}5\%.$ What are the Sharpe ratios for Stocks A and B$?$ Do not round intermediate calculations. Round your answers

to two decimal places.

Stock A:

Stock B:

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

I. 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.

II$.$ 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.

III. 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.

IV$.$ 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.

V$.$ 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.