Portfolio return and standard deviation Jamie Wong is thinking of building an investment portfolio containing two exchange traded funds $($ETFs$).$ Jamie plans to invest $$4,500$ in Vanguard S&P $500$ ETF $($VOO$)$ and $$5,500$ in Invesco QQQ Trust $($QQQ$).$ Jamie has decided to analyze some historical returns to get a sense for her portfolio's possible future risk and return. Six years of historical annual returns for each ETF are shown in the following table:

a$.$ Calculate the portfolio return, $r_p,$ for each of the $6$ years assuming that $45\%$ is invested in VOO and $55\%$ is invested in QQQ

b$.$ Calculate the average annual return for each ETF and the portfolio over the six$-$year period.

c$.$ Calculate the standard deviation of annual returns for each ETF and the portfolio. How does the portfolio standard deviation compare to the standard deviations of the individual ETFs?

d$.$ Calculate the correlation coefficient for the two ETFs. How would you characterize the correlation of returns of the two ETFs?

e$.$ Discuss any likely benefits of diversification achieved by Jamie through creation of the portfolio.

a$.$ The portfolio return for year $2014$ is $\%.($Round to two decimal places.$)\%.($Round to two decimal places.$)$

Data table

$($Click on the icon here $5$ in order to copy the contents of the data table below into a spreadsheet.$)$

$\backslash$table$[[,$Historical return$],[$Year$,$VOO,QQQ$],[2014,14\mathrm{.}45\%,18\mathrm{.}01\%$