$($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 $0\mathrm{.}40,$ then the expected rate of return in the portfolio is $\%.($Round to two decimal places.$)$

The standard deviation in the portfolio is

$6.($Round to two decimal places.$)$

b$.$ 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 zero, then the expected rate of return in the portfolio is $\%.($Round to two decimal places.$)$

The standard deviation in the portfolio is

$\%.($Round to two decimal places.$)$

c$.$ 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 coefficient between the two stocks is $+1,$ then the expected rate of return in the portfolio is $\%.($Round to two decimal places.$)$

The standard deviation in the portfolio is

$\%.($Round to two decimal places.$)$

d$.$ 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 coefficient between the two stocks is $-1,$ then the expected rate of return in the portfolio is $\%.($Round to two decimal places:$)$

The standard deviation in the portfolio is $\%.($Round to two decimal places.$)$

Data table between the correlation and the risk and return of the portfolio? $($Select the best

ation coefficient is to one, the lower the risk.

$\backslash$table$[[,\backslash$table$[[$Expected$],[$Return$]],\backslash$table$[[$Standard$],[$Deviation$]]],[$Firm A$\text{'}$s common stock,$0\mathrm{.}13,0\mathrm{.}18],[$Firm B$\text{'}$s common stock,$0\mathrm{.}19,0\mathrm{.}24],[$Correlation coefficient,$0\mathrm{.}40,]]$

he correlation coefficient is to negative one, $-1,$ the lower the risk.

lation coefficient is to negative one, $-1,$ the higher the risk.