$($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