Use the efficient frontier tool on the website Portfolio Visualizer to construct the tangency portfolio consisting of different groups of securities using monthly data from $2012$ to $2022.$

Group $1$: the same list as above.

Group $2$: drop QQQ$,$ add GLD$.$

Group $3$: drop QQQ$,$ VOE, VOT, VBR$,$ VBK$,$ add XLU, XLE, SHY, and GLD$.$

Group $4$: SPY$,$ MSFT$,$ XLE, GLD$.$

Examine the $$efficient frontier$$ tab as well as the $$asset and correlations$$ tab. Describe and make sense of your findings. Are these results consistent or inconsistent with the theory you learned in class?