$($Computing the standard deviation for a portfolio of two risky investments$)$ Mary Guilott recently graduated from Nichols State University and is anxious to begin investing her meager savings as a way of applying what she has learned in business school. Specifically, she is evaluating an investment in a portfolio comprised of two firms' common stock.

She has collected the following information about the common stock of Firm A and Firm B:

a$.$ If Mary invests half her money in each of the two common stocks, what is the portfolio's expected rate of return and standard deviation in portfolio return?

b$.$ Answer part a where the correlation between the two common stock investments is equal to zero.

c$.$ Answer part a where the correlation between the two common stock investments is equal to $+1.$

d$.$ Answer part a where the correlation between the two common stock investments is equal to $-1.$

e$.$ Using your responses to questions a$-$d$,$ describe the relationship between the correlation and the risk and return of the portfolio.

a$.$ If Mary decides to invest $50\%$ of her money in Firm A$\text{'}$s common stock and $50\%$ in Firm B$\text{'}$s common stock and the correlation between the two stocks is $0\mathrm{.}70,$ then the expected rate of return in the portfolio is $\%.($Round to two decimal places.$)$

Data table

$\backslash$table$[[$Firm A$\text{'}$s common stock,$\backslash$table$[[$Expected$],[$Return$]],\backslash$table$[[$Standard$],[$Deviation$]]],[$Firm B$\text{'}$s common stock,$0\mathrm{.}17,0\mathrm{.}15],[$Correlation coefficient,$0\mathrm{.}19,0\mathrm{.}24]]$