Use the following security information to answer the questions below.

Security E$($R$)\backslash$sigma

American

Express

$8\mathrm{.}0\%16\mathrm{.}5\%$

Cisco Systems $19\mathrm{.}0\%33\mathrm{.}0\%$

Risk$-$free $4\mathrm{.}0\%$

a$)$ What would be the expected return AND standard deviation of a portfolio that

invests $70\%$ in American Express and $30\%$ in the risk$-$free security?

b$)$ You would like to create a portfolio combining American Express and the

risk$-$free security that earns an expected return of $10\%.$ What positions

would you need to take in American Express and the risk$-$free security in

order to achieve this objective?

c$)$ The correlation between American Express and Cisco Systems is $\backslash$rho $=0\mathrm{.}15.$

What would be the expected return AND standard deviation of a portfolio

that invests $40\%$ in American Express and $60\%$ in Cisco Systems?