Portfolio return and standard deviation Jamie Wong is thinking of building an investment portfolio containing two exchange traded funds $($ETFs$).$ Jamie plans to invest $$4,000$ in Vanguard S&P $500$ ETF $($VOO$)$ and $$6,000$ 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.

CHAPTER $8$ Risk and Return $409$

Year

$2014$

$2015$

$2016$

$2017$

$2018$

$2019$

Historical return QQQ

VOO

$13\mathrm{.}63\%1\mathrm{.}35$

$11\mathrm{.}93$

$21\mathrm{.}78-4\mathrm{.}4231\mathrm{.}46$

$19\mathrm{.}12\%9\mathrm{.}547\mathrm{.}01$

$32\mathrm{.}70-0\mathrm{.}1439\mathrm{.}12$

LG $3$

P$818$

a$.$ Calculate the portfolio return, rp$,$ for each of the six years assuming that $40\%$ is invested in VOO and $60\%$ 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 portfo$-$ lio. How does the portfolio standard deviation compare to the standard devia$-$ tions of the individual ETFs?

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

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