J$.$P$.$ Morgan Asset Management publishes information about financial investments. Over the past $10$ years, the expected return for the S&P $500$ was $5\mathrm{.}04\%$ with a standard deviation of $19\mathrm{.}45\%$ and the expected return over that same period for a core bonds fund was $5\mathrm{.}78\%$ with a standard deviation of $2\mathrm{.}13\%.$ The publication also reported that the correlation between the S&P $500$ and core bonds is $0\mathrm{.}32.$

J$.$P$.$ Morgan Asset Management also reported that the expected return for real estate investment trusts $($REITs$)$ was $13\mathrm{.}07\%$ with a standard deviation of $23\mathrm{.}17\%.$ The correlation between the S&P $500$ and REITs is $0\mathrm{.}74$ and the correlation between core bonds and REITs is $0\mathrm{.}04.($Past performance is no guarantee of future results.$)$

You are considering portfolio investments that are composed of an S&P $500$ index fund and REITs as well as portfolio investments composed of a core bonds fund and REITs.

$($a$)$

Using the information provided, determine the covariance between the S&P $500$ and REITs and between core bonds and REITs. $($Round your answers to three decimal places.$)$

S&P $500$ and REITs

core bonds and REITs

$($b$)$

Construct a portfolio that is $50\%$ invested in an S&P $500$ fund and $50\%$ invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?

expected return

$\%($Round to $3$ decimal places$)$

standard deviation

$\%($Round to $2$ decimal places$)$

$($c$)$

Construct a portfolio that is $50\%$ invested in a core bonds fund and $50\%$ invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?

expected return

$\%($Round to $3$ decimal places$)$

standard deviation

$\%($Round to $2$ decimal places$)$

$($d$)$

Construct a portfolio that is $70\%$ invested in a core bonds fund and $30\%$ invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?

expected return

$\%($Round to $3$ decimal places$)$

standard deviation

$\%($Round to $2$ decimal places$)$

$($e$)$

Which of the portfolios in parts $($b$),($c$),$ and $($d$)$ would you recommend to an aggressive investor? Why?

The portfolio consisting of

$---$Select$---$

is recommended for the aggressive investor because of its

$---$Select$---$

return and moderate amount of risk.

Which would you recommend to a conservative investor? Why?

The portfolio consisting of

$---$Select$---$

is recommended to the conservative investor because of its moderate return and

$---$Select$---$

risk.