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 $2\mathrm{.}13\%($J$.$ P$.$ Morgan Asset Management, Guide to the Markets$).$ The publication also reported that the correlation between the S&P $500$ and Core Bonds is $-0\mathrm{.}32.$ You are considering portfolio investments that are composed of an S&P $500$ index fund and a Core Bonds fund.

a$.$ Using the information provided, determine the covariance between the S&P $500$ and Core Bonds. Round your answer to four decimal places. If required enter negative values as negative numbers.

$$

b$.$ Construct a portfolio that is $50\%$ invested in an S&P $500$ index fund and $50\%$ in a Core Bond fund. Let $x$ represent the S&P $500$ and $y$ represent the Core Bond fund. Round your answers to one decimal place.

$r=x+y$

In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places.

Expected return $\%$

Standard deviation $\%$

c$.$ Construct a portfolio that is $20\%$ invested in an S&P $500$ index fund and $80\%$ invested in a Core bond fund. Let $x$ represent the S&P $500$ and $y$ represent the Core Bond fund. Round your answers to one decimal place.

$r=x+y$

In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places.

Expected return $\%$

Standard deviation $\%$

d$.$ Construct a portfolio that is $80\%$ invested in an S&P $500$ index fund and $20\%$ invested in a Core bond fund. Let $x$ represent the S&P $500$ and $y$ represent the Core Bond fund. Round your answers to one decimal place.

$r=,x+,y$

In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places.

Expected return $\%$

Standard deviation $\%$

e$.$ Which of the portfolios in parts $($b$),($c$),$ and $($d$)$ above has the largest expected return?

Select your answer $-$