You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a$$ $$1,000$ investment in each stock under four different economic conditions has the probability distribution shown to the right. Complete parts$($a$)$ through$($g below.

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Returns

Probability

Economic Condition

Stock X

Stock Y

$0\mathrm{.}1$

Recession

negative $130$

negative $90$

$0\mathrm{.}3$

Slow growth

$40$

$30$

$0\mathrm{.}4$

Moderate growth

$140$

$100$

$0\mathrm{.}2$

Fast growth

$210$

$160$

Question content area bottom

Part $1$

a$.$ Compute the expected return for stock X and for stock Y$.$

The expected return for stock X is $$$

$$

enter your response here.

$($Type an integer or a decimal. Do not$$ round.$)$

The expected return for stock Y is $$$

$$

enter your response here.

$($Type an integer or a decimal. Do not$$ round.$)$

b$.$ Compute the standard deviation for stock X and for stock Y$.$

The standard deviation for stock X is $$$

$$

enter your response here.

$($Round to two decimal places as$$ needed.$)$

The standard deviation for stock Y is $$$

$$

enter your response here.

$($Round to two decimal places as$$ needed.$)$

c$.$ Would you invest in stock X or stock$$ Y$?$ Explain. Choose the correct answer below.

A$.$

Since the expected values are approximately the$$ same, either stock can be invested in$.$ However, stock Upper Y has a larger standard$$ deviation, which results in a higher risk. Due to the higher risk of stock Upper Y$,$ stock Upper X should be invested in$.$

B$.$

Based on the expected $$value$,$ stock Upper X should be chosen. $$However$,$ stock Upper X has a larger standard $$deviation$,$ resulting in a higher $$risk$,$ which should be taken into consideration.

C$.$

Since the expected values are approximately the$$ same, either stock can be invested in$.$ However, stock Upper X has a larger standard$$ deviation, which results in a higher risk. Due to the higher risk of stock Upper X$,$ stock Upper Y should be invested in$.$

D$.$

Based on the expected $$value$,$ stock Upper Y should be chosen. $$However$,$ stock Upper Y has a larger standard $$deviation$,$ resulting in a higher $$risk$,$ which should be taken into consideration.

d$.$ The covariance of stock X and Y is

$$

enter your response here.

$($Round to an integer as$$ needed.$)$

e$.$ What does the covariance indicate about the relationship between stock X and$$ Y$?$

A$.$

As stock X decreases in$$ value, stock Y increases in value.

B$.$

As stock X increases in$$ value, stock Y increases in value.

C$.$

There is not enough information to determine an answer.

D$.$

As stock X increases in$$ value, stock Y decreases in value.

f$.$ Suppose $15\%$ is invested in stock X and the rest in stock Y$.$ Then the expected portfolio return is $$$

$$

enter your response here with a portfolio risk of $$$

$$

enter your response here.

$($Round to two decimal places as$$ needed.$)$

g$.$ Suppose $81\%$ is invested in stock X and the rest in stock Y$.$ Then the expected portfolio return is $$$

$$

enter your response here with a portfolio risk of $$$

$$

enter your response here.

$($Round to two decimal places as$$ needed.$)$