$($Computing the standard deviation for a portfolio of two risky investments$)$ Mary Guilott recently graduated from college and is evaluating an investment in two companies' common stock. She has collected the following information about the common stock of Firm A and Firm B:

a$.$ If Mary decides to invest $10$ percent of her money in Firm A$\text{'}$s common stock and $90$ percent in Firm B$\text{'}$s common stock, what is the expected rate of return and the standard deviation of the portfolio return?

b$.$ If Mary decides to invest $90$ percent of her money in Firm A$\text{'}$s common stock and $10$ percent in Firm B$\text{'}$s common stock, what is the expected rate of return and the standard deviation of the portfolio return?

c$.$ Recompute your responses to both questions a and $b,$ where the correlation between the two firms' stock returns is $-0\mathrm{.}50.$

d$.$ Summarize what your analysis tells you about portfolio risk when combining risky assets in a portfolio.

a$.$ If Mary decides to inv the portfolio is $\%.($R

The standard deviation i

b$.$ If Mary decides to iny the portfolio is $\%.($R

The standard deviation i

c$.$ If Mary decides to inv the portfolio is $\%.($R

Data table

petween the two stocks is $0\mathrm{.}50,$ then the expected rate of return in

$\backslash$table$[[,\backslash$table$[[$Expected$],[$Retu:ns$]],\backslash$table$[[$Standard$],[$Deviation$]]],[$Firm A$\text{'}$s common stock,$0\mathrm{.}15,0\mathrm{.}12],[$Firm B$\text{'}$s common stock,$0\mathrm{.}08,0\mathrm{.}07],[$Correlation coefficient,$0\mathrm{.}50,],[($Click on the icon in order to copy its contents into a spreadsheet.$),,]]$

petween the two stocks is $0\mathrm{.}50,$ then the expected rate of return in

The standard deviation i

If Mary decides to invest portfolio is $q,\%($Roun $$

$$ veen the two stocks is $-0\mathrm{.}50,$ then the expected rate of return in the

The standard deviation c

d$.$ What does your analysis tell you about portfolio risk when combining risky assets in a portfolio? $($Select the best choice below.$)$

A$.$ You can maintain the same return in a portfolio but lower risk more if the stocks are positively correlated rather than negatively correlated. If correlation of the two stocks is the same, risk can also be lowered by investing a higher proportion of the portfolio in stock with lower standard deviation, this however will reduce return.