$26$ 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$]=8\mathrm{.}45\%$ and Var$[$x$)=25.$ The expected return and variance for stock $2$ are E$[$Y$]=3\mathrm{.}2\%$ and Var$($y$)=1.$ The covariance between the returns is $\backslash$sigma XY $=-3.($Hint: in this problem all numbers must be altered. Change from percentages to real numbers. So$,8\mathrm{.}45$ would be $0\mathrm{.}0845$ and Var$($x$)=25$ would be Var$($x$)=0\mathrm{.}25,$ etc.$)$

a What is the standard deviation for the investment in stock $1$ and for the investment in stock $2?$ Using the standard deviation as a measure of risk, which of these stocks is the riskier investment?

Based on the SD an investment in stock $1$ would be risker than stock $2,$ with the SD

for stock $1$ being $0\mathrm{.}5$ while the SD for stock $2$ is only $0\mathrm{.}1.$

b What is the expected return and standard deviation, in dollars, for a person who invests $$500$ in stock $1?$

The expected return in dollars for a person who invests $$500$ in stock $1$

is $42\mathrm{.}25.$ The SD is $250.$

c$.$ What is the expected percent return and standard deviation for a person who constructs a portfolio by investing $50\%$ in each stock.

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 $2?$

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