Round all answers in this problem to $3$ decimal places.

J$.$P$.$ Morgan Asset Management publishes information about financial investments. Between $2002$ and $2011$ 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 $-.32.$ You are considering portfolio investments that are composed of an S&P $500$ index fund and a core bonds fund.

Using the information provided, determine the covariance between the S&P $500$ and core bonds.

For each of the following portfolios, find the expected return and standard deviation $($in percentages$)$:

$\backslash$table$[[$Portfolio$,$Expected Return,Standard Deviation$],[\backslash$table$[[($A$)50\%$ invested$],[$in an S&P $500],[$index fund and$],[50\%$ in a core$],[$bonds fund$]],,],[,],[,],[\%,\%],[,],[($B$)20\%$ invested$],[\backslash$table$[[$in an S&P $500],[$index fund and$],[80\%$ in a core$],[$bonds fund$]],,],[,],[\%,\%],[,],[\backslash$table$[[($C$)80\%$ invested$],[$in an S&P $500],[$index fund and$],[20\%$ in a core$],[$bonds fund$]],,],[,],[,],[\%,\%],[,]]$

Of the three portfolios above, which one would you recommend for a