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.

$($answers $-13\mathrm{.}2571$ and $-13\mathrm{.}26$ are both incorrect.$)$

$$

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 yours ans ane decimal place.

$r={}_x$

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 $(\%$