A person is interested in constructing a portfolio. Two stocks are being considered. Let $x=$ percent

return for an investment in stock $1,$ and $y=$ percent return for an investment in stock $2.$ The expected

return and variance for stock $1$ are $E(x)=7\mathrm{.}63\%$ and Var$(x)=36.$ The expected return and variance

for stock $2$ are $E(y)=4\mathrm{.}20\%$ and Var$(y)=9.$ The covariance between the returns is ${}_{xy}=-2.$

a$.$ What is the standard deviation for an investment in stock $1$ and for an investment in stock $2?$

Stock $1$

Stock $2$

$\%$

$\%$

Using the standard deviation as a measure of risk, which of these stocks is the riskier investment?

Investments in

would be considered riskier than investments in

ecause the standard deviation is

b$.$ What is the expected return and standard deviation, in dollars, for a person who invests $$500$ in stock

$1($to $2$ decimals$)?$

Expected Return

Standard Deviation

c$.$ What is the expected percent return and standard deviation for a person who constructs a portfolio by

investing $50\%$ in each stock $($to $3$ decimals$)?$

Expected Return

$\%$

Standard Deviation

$\%$

d$.$ What is the expected percent return and standard deviation for a person who constructs a portfolio by

investing $70\%$ in stock $1$ and $30\%$ in stock $2($to $3$ decimals$)?$

Expected Return

$\%$

Standard Deviation

$\%$

e$.$ Compute the correlation coefficient for $x$ and $y$ and comment on the relationship between the returns

for the two stocks. Enter negative value as negative number.

The correlation coefficient is

$($to $2$ decimals$).$

There is a fairly $-$ Select your answer $-$ relationship between the variables.