On list $,K,$ 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 $\frac{V}{O}O$ 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 th$$ portfolio.

Data table

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

$\backslash$table$[[,$Historical return$],[$Year$,$VOO,QQQ$],[2014,13\mathrm{.}79\%,19\mathrm{.}86\%$