Problem

$8$

$.$

$0$

$6$

$($

Expected Returns

$)$

eBook Problem Walk

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Through

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

Probability A B

$0$

$.$

$1$

$($

$1$

$0$

$\%$

$)$

$($

$3$

$7$

$\%$

$)$

$0$

$.$

$1$

$6$

$0$

$$

$0$

$.$

$5$

$1$

$2$

$2$

$0$

$$

$0$

$.$

$2$

$2$

$2$

$2$

$7$

$$

$0$

$.$

$1$

$3$

$2$

$4$

$3$

$$

Calculate the expected rate of return,

$,$

$$for Stock B

$($

$=$

$1$

$3$

$.$

$2$

$0$

$\%$

$.$

$)$

$$Do not round intermediate calculations. Round your answer to two decimal places.

$8$

$0$

$$

$\%$

Calculate the standard deviation of expected returns,

$\backslash$

sigma A

$,$

$$for Stock A

$($

$\backslash$

sigma B

$=$

$2$

$0$

$.$

$2$

$9$

$\%$

$.$

$)$

$$Do not round intermediate calculations. Round your answer to two decimal places.

$1$

$.$

$2$

$7$

$$

$\%$

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.

$-$

Select

$-$

Assume the risk

$-$

free rate is

$1$

$.$

$5$

$\%$

$.$

$$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

$-$