investment$-$grade bond fund offered by Vanguard has an expected return of $5\mathrm{.}33\%$ with a standard deviation of $2\mathrm{.}65\%.$

of $25\mathrm{.}84\%.$ The correlation between the stock index fund and the real$-$estate fund is $0\mathrm{.}64,$ and the correlation between the investment$-$grade bond fund and the real$-$estate fund is $-0\mathrm{.}19.$

$($a$)$ Based on the information provided, what is the covariance between the stock index fund and the real$-$estate fund? $($Round your answer to four decimal places.$)$

What is the covariance between the investment$-$grade bond fund and the real$-$estate fund? $($Round your answer to four decimal places.$)$

$($b$)$ What is the expected return $($as a percent$)$ for a portfolio composed of $50\%$ invested in the stock index fund and $50\%$ invested in the real$-$estate fund?

$1\%$

What is the standard deviation $($as a percent$)$ for a portfolio composed of $50\%$ invested in the stock index fund and $50\%$ invested in the real$-$estate fund? $($Round your answer to four decimal places.$)$

$\%$

$($c$)$ What is the expected return $($as a percent$)$ for a portfolio composed of $50\%$ invested in the investment$-$grade bond fund and $50\%$ invested in the real$-$estate fund?

$\%$

$\%$

below.

Which portfolio would be most appropriate for a conservative investor?

portfolio that invests $50\%$ in the stock index fund and $50\%$ in the real$-$estate fund

portfolio that invests $60\%$ in the stock index fund and $40\%$ in the investment$-$grade bond fund

portfolio that invests $40\%$ in the stock index fund and $60\%$ in the investment$-$grade bond fund

portfolio that invests $50\%$ in the investment$-$grade bond fund and $50\%$ in the real$-$estate fund

Which portfolio would be most appropriate for an aggressive investor who wants the highest possible returns?

portfolio that invests $50\%$ in the stock index fund and $50\%$ in the real$-$estate fund

portfolio that invests $60\%$ in the stock index fund and $40\%$ in the investment$-$grade bond fund

portfolio that invests $40\%$ in the stock index fund and $60\%$ in the investment$-$grade bond fund

portfolio that invests $50\%$ in the investment$-$grade bond fund and $50\%$ in the real$-$estate fund