in addition to the information in exercise $29$ on the S&P $500$ and core bonds, J$.$P$.$ Mor

gan Asset Management reported that the expected return for real estate investment trusts

$($REITs$)$ was $13\mathrm{.}07\%$ with a standard deviation of $23\mathrm{.}17\%($J$.$P$.$ Morgan asset Manage

ment, guide to the Markets, $1$st quarter, $2012).$ The correlation between the S&P $500$ and

REITs is $\mathrm{.}74$ and the correlation between core bonds and REITs is $\mathrm{.}04.$ You are consider

ing 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 here and in exercise $29,$ determine the covariance

between the S&P $500$ and REITs and between core bonds and REITs.

b$.$

c$.$

d$.$

e$.$

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?

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?

Construct a portfolio that is $80\%$ invested in a core bonds fund and $20\%$ invested in

REITs. In percentage terms, what are the expected return and standard deviation for

such a portfolio?

which of the portfolios in parts $($b$),($c$),$ and $($d$)$ would you recommend to an

aggressive investor? which would you recommend to a conservative investor?

why?